Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators

Topological insulators and graphene present two unique classes of materials, which are characterized by spin-polarized (helical) and nonpolarized Dirac cone band structures, respectively. The importance of many-body interactions that renormalize the linear bands near Dirac point in graphene has been well recognized and attracted much recent attention. However, renormalization of the helical Dirac point has not been observed in topological insulators. Here, we report the experimental observation of the renormalized quasiparticle spectrum with a skewed Dirac cone in a single Bi bilayer grown on Bi₂Te₃ substrate from angle-resolved photoemission spectroscopy. First-principles band calculations indicate that the quasiparticle spectra are likely associated with the hybridization between the extrinsic substrate-induced Dirac states of Bi bilayer and the intrinsic surface Dirac states of Bi₂Te₃ film at close energy proximity. Without such hybridization, only single-particle Dirac spectra are observed in a single Bi bilayer grown on Bi₂Se₃, where the extrinsic Dirac states Bi bilayer and the intrinsic Dirac states of Bi₂Se₃ are well separated in energy. The possible origins of many-body interactions are discussed. Our findings provide a means to manipulate topological surface states.     

From antiferromagnetic insulator to correlated metal in pressurized and doped LaMnPO

Widespread adoption of superconducting technologies awaits the discovery of new materials with enhanced properties, especially higher superconducting transition temperatures T(c). The unexpected discovery of high T(c) superconductivity in cuprates suggests that the highest T(c)s occur when pressure or doping transform the localized and moment-bearing electrons in antiferromagnetic insulators into itinerant carriers in a metal, where magnetism is preserved in the form of strong correlations. The absence of this transition in Fe-based superconductors may limit their T(c)s, but even larger T(c)s may be possible in their isostructural Mn analogs, which are antiferromagnetic insulators like the cuprates. It is generally believed that prohibitively large pressures would be required to suppress the effects of the strong Hund's rule coupling in these Mn-based compounds, collapsing the insulating gap and enabling superconductivity. Indeed, no Mn-based compounds are known to be superconductors. The electronic structure calculations and X-ray diffraction measurements presented here challenge these long held beliefs, finding that only modest pressures are required to transform LaMnPO, isostructural to superconducting host LaFeAsO, from an antiferromagnetic insulator to a metallic antiferromagnet, where the Mn moment vanishes in a second pressure-driven transition. Proximity to these charge and moment delocalization transitions in LaMnPO results in a highly correlated metallic state, the familiar breeding ground of superconductivity.     

Nonlocal topological insulators: Deterministic aperiodic arrays supporting localized topological states protected by nonlocal symmetries

The properties of topological systems are inherently tied to their dimensionality. Indeed, higher-dimensional periodic systems exhibit topological phases not shared by their lower-dimensional counterparts. On the other hand, aperiodic arrays in lower-dimensional systems (e.g., the Harper model) have been successfully employed to emulate higher-dimensional physics. This raises a general question on the possibility of extended topological classification in lower dimensions, and whether the topological invariants of higher-dimensional periodic systems may assume a different meaning in their lower-dimensional aperiodic counterparts. Here, we demonstrate that, indeed, for a topological system in higher dimensions one can construct a one-dimensional (1D) deterministic aperiodic counterpart which retains its spectrum and topological characteristics. We consider a four-dimensional (4D) quantized hexadecapole higher-order topological insulator (HOTI) which supports topological corner modes. We apply the Lanczos transformation and map it onto an equivalent deterministic aperiodic 1D array (DAA) emulating 4D HOTI in 1D. We observe topological zero-energy zero-dimensional (0D) states of the DAA—the direct counterparts of corner states in 4D HOTI and the hallmark of the multipole topological phase, which is meaningless in lower dimensions. To explain this paradox, we show that higher-dimension invariant, the multipole polarization, retains its quantization in the DAA, yet changes its meaning by becoming a nonlocal correlator in the 1D system. By introducing nonlocal topological phases of DAAs, our discovery opens a direction in topological physics. It also unveils opportunities to engineer topological states in aperiodic systems and paves the path to application of resonances associates with such states protected by nonlocal symmetries.

The dimensionality of a topological system plays a determining role in defining its symmetry classification and, therefore, the topological invariants that identify the topological phase specific to such a system (1–3). For instance, four-dimensional (4D) quantum Hall systems can exhibit a nonvanishing second-class Chern number that is not shared by systems with three or fewer dimensions, and hence it cannot be implemented in three physical dimensions without mapping to a lower-dimensional analog (4). However, already 3D topological materials imply challenging fabrication demands due to the complex structures of the lattices (5–9). This quest has been approached in two ways: 1) introducing synthetic dimensions or 2) mapping a higher-dimensional system onto its lower-dimensional counterpart. The first approach implements lattices with dimensions higher than the spatial dimensions by exploiting internal degrees of freedom, which could be spectral (10–18), temporal, or spatial in nature (19–23). The second approach, based on dimensional reduction and mapping onto a lower-dimensional system, has been proven quite fruitful too; as an example, the celebrated Harper–Hofstadter Hamiltonian has been recently emulated in reconfigurable quasi-periodic 1D resonant acoustic lattices (24, 25). The topological properties of quasiperiodic models via dimensional reduction have also been studied (26–28). In addition, the existence of boundary modes stemming from the second Chern class topological phase has been reported in photonics (4) and in an angled optical superlattice of ultracold bosonic atoms (29).As we show here, the second approach, in addition to the possibility to emulate higher-dimensional physics in lower dimensions, establishes an approach to engineer novel nonlocal topological phases supporting localized topological states. We focus here on the recently introduced class of higher-order topological insulators (30, 31) and show that their lower-dimensional analogs are characterized by nonlocal symmetries which ensure the presence and protect the localized topological states. In recent years higher-order topological insulators (HOTIs) were successfully realized in 2D (32–39), and more recently 3D octupole topological states were implemented in 3D acoustic metamaterials (40, 41). The choice of HOTIs as an exemplary system is justified by the fact that their dimensionality defines the multiplicity of hosted topological boundary modes protected by higher-dimensional reflection and chiral symmetries.In this work we apply dimensionality reduction and experimentally realize a 1D counterpart of 4D hexadecapolar HOTI (h-HOTI) in the form of a deterministic aperiodic array (DAA). To this aim, we apply Lanczos tridiagonalization introduced recently by Maczewsky et al. (42) which allows mapping of any multidimensional system onto aperiodic 1D tight-binding system with nearest-neighbor coupling. In their original work Maczewsky et al. introduced the mapping of a periodic higher-dimensional system onto a 1D tight-binding model (TBM) based on Lanczos transformation, and they demonstrated how introduction of a point defect leads to the localization in systems of different dimensionalities. Here, we apply Lanczos transformation to investigate topological systems, where, due to the bulk-boundary correspondence, the localization of topological boundary modes is caused by the nontrivial bulk topology of a higher-dimensional system. By this approach we map a prototypical 4D h-HOTI tight-binding system onto a 1D DAA with strictly local aperiodic coupling distribution. We note that the obtained aperiodic system is not and should not be confused with quasiperiodic systems which can exhibit rich topological physics on their own (26–28). The transformation of topological invariant of the original 4D system—the quadrupole polarization—yields a new 1D invariant, a topological correlator, with the same value as its 4D analogs, which ensures the presence of 16 zero-energy topological states localized in the bulk of DAA. By the special choice of the Lanczos transformation (42–45) we obtain one topological state localized the edge of our sample. Other corner states are distributed in the bulk of the array. All the states preserve their topological characteristics, being protected by nonlocal symmetries of 1D DAA originating in higher-dimensional symmetries of 4D h-HOTI.The designed 1D DAA with nonlocal topological phase is then realized in an array of coupled acoustic resonators. The presence of localized topological states is directly observed by measuring local acoustic pressure field distribution in the array.     

Structure and control of charge density waves in two-dimensional 1T-TaS2

The layered transition metal dichalcogenides host a rich collection of charge density wave phases in which both the conduction electrons and the atomic structure display translational symmetry breaking. Manipulating these complex states by purely electronic methods has been a long-sought scientific and technological goal. Here, we show how this can be achieved in 1T-TaS₂ in the 2D limit. We first demonstrate that the intrinsic properties of atomically thin flakes are preserved by encapsulation with hexagonal boron nitride in inert atmosphere. We use this facile assembly method together with transmission electron microscopy and transport measurements to probe the nature of the 2D state and show that its conductance is dominated by discommensurations. The discommensuration structure can be precisely tuned in few-layer samples by an in-plane electric current, allowing continuous electrical control over the discommensuration-melting transition in 2D.Layered 1T-TaS₂ exhibits a number of unique structural and electronic phases. At low temperature and ambient pressure, the ground state is a commensurate (C) charge density wave (CDW). On heating, it undergoes a sequence of first-order phase transitions to a nearly commensurate (NC) CDW at 225 K, to an incommensurate (IC) CDW at 355 K, and finally to a metallic phase at 545 K. Each transition involves both conduction electron and lattice degrees of freedom—large changes in electronic transport properties occur, concomitant with structural changes to the crystal. By either chemical doping or applying high pressures, it is possible to suppress the CDWs and induce superconductivity (1–3). For device applications, it is desirable to control these phases by electrical means, but this capability is difficult to achieve in bulk crystals due to the high conduction electron density. Recent efforts to produce thin samples by mechanical exfoliation provide a new avenue for manipulating the CDWs in 1T-TaS₂ (4–8). These studies have demonstrated the suppression of CDW phase transitions using polar electrolytes, as well as resistive switching between the different phases. As the material approaches the 2D limit, however, significant changes have been observed in the transport properties (4, 5, 8). However, the microscopic nature of the 2D state remains unclear. In this work, we use transmission electron microscopy (TEM) together with transport measurements to develop a systematic understanding of the CDW phases and phase transitions in ultrathin 1T-TaS₂. We find that charge ordering disappears in flakes with few atomic layers due to surface oxidation. When samples are instead environmentally protected, the CDWs persist and their transitions can be carefully tuned by electric currents.Both the atomic and CDW structure of 1T-TaS₂ can be visualized in reciprocal space by TEM electron diffraction (9, 10). In Fig. 1A, we show diffraction images taken from a bulk-like, 50-nm-thick crystal at low and room temperature (C phase, blue panel; NC phase, red panel). The bright peaks (connected by dashed lines) correspond to Bragg scattering from a triangular lattice of Ta atoms with lattice constant a = 3.36 Å. Additional weaker diffraction peaks appear from the periodic atomic displacements of the CDW. In the low-temperature C phase, Ta atoms displace to make Star-of-David clusters (blue inset, Fig. 1B). The outer 12 atoms within each star displace slightly inward toward the atom at the center, giving rise to a commensurate superstructure with wavelength λ_C = 13a that is rotated ϕ_C = 13.9° with respect to the atomic lattice. The NC phase at room temperature also consists of such 13-atom distortions. Scanning tunneling microscope (STM) measurements have revealed, however, that such ordering is only preserved in quasi-hexagonal domains consisting of tens of stars (11, 12), with domain periodicity 60–90 Å depending on temperature (13, 14). The domains are separated by a discommensuration network forming a Kagome lattice, inside of which the Ta displacements are substantially reduced (15). A schematic of this structure is shown in the red inset of Fig. 1B.Open in a separate windowFig. 1.NC-C CDW phase transition in bulk 1T-TaS₂ and CDW suppression by oxidation in thin flakes. (A) TEM diffraction images of 50-nm-thick 1T-TaS₂ at 295 K (red, NC phase) and 100 K (blue, C phase). Weaker peaks are due to CDW distortion. (B) Resistivity vs. temperature of bulk 1T-TaS₂ crystal around the first-order, NC-C transition. (Insets) Real space schematics of CDW structure. (C) (Left) TEM diffraction of few-layer 1T-TaS₂ flake shows absence of CDW order. (Right) High-resolution, cross section electron microscopy image reveals presence of amorphous oxide. (D) Free energy schematic of CDW evolution with temperature. Vertical and horizontal axis represent free energy (E) and reaction coordinate (q), respectively. NC domains grow slowly upon cooling until abrupt transition into the C phase. Energy barrier increases in 2D samples protected from oxidation.When ultrathin 1T-TaS₂ crystals (approximately <5 nm thickness) are exfoliated in an ambient air environment, the CDW structure is not observed by the TEM electron diffraction. In the left panel of Fig. 1C, we show a room temperature electron diffraction pattern taken on a few-layer flake. The presence of Bragg peaks without CDW scattering suggests that the 1T-TaS₂ layers are in a phase that is not observed in bulk crystals at this temperature. High-resolution electron microscopy and energy dispersive spectroscopy on fully suspended samples reveal a strong presence of oxidation as well as an amorphous layer on the surface (Figs. S1 and ​andS2).S2). The amorphous oxide (∼2 nm thickness) can be clearly seen atop both surfaces of the 1T-TaS₂ layers in cross section (Fig. 1C, Right). It is possible that oxidation leads to strong surface pinning, which destroys charge ordering in ultrathin samples. Recent resistivity measurements on exfoliated 1T-TaS₂ crystals have also reported the disappearance of CDWs in sufficiently thin flakes (5). It is not clear, however, whether these are intrinsic effects related to dimensionality or extrinsic consequences of oxidation.Open in a separate windowFig. S1.High-resolution STEM image of ultrathin 1T-TaS₂ prepared in air. (A) Amorphous layers appear on the top and bottom surfaces. (B) Overview of a curled sheet providing in-plane (A) and planar (C) and viewing. (C) High-resolution STEM image of the 1T-TaS₂ sheet shows the high-frequency atomic structure and a lower frequency intensity variation corresponding to the amorphous surface layers. The amorphous surfaces are more clearly visualized in D, which uses Lab Color space to create blue/yellow contrast of the amorphous (low-frequency) intensity variation.Open in a separate windowFig. S2.Chemical analysis with STEM-spectroscopy of ultrathin 1T-TaS₂ exfoliated in air. In addition to the expected presence of Ta and S, oxygen and trace amounts of carbon are present in both the (A) dispersive X-ray and (B) electron energy loss spectroscopy. The sample was suspended such that all detected elements represent chemical species present in the specimen.To prevent surface oxidation, we exfoliated 1T-TaS₂ crystals within a nitrogen-filled glove box with under 2-ppm oxygen concentration. The flakes were protected by a capping layer of thin hexagonal boron nitride (hBN) before transfer out into the ambient environment (Methods). TEM diffraction performed on these protected samples reveals that CDW formation persists down to the lowest thicknesses measured (2 nm), as we discuss in detail in Fig. 4. This finding indicates that the absence of charge order in ultrathin, uncovered flakes is most likely caused by the effects of oxidation. The study and utilization of CDWs in 2D 1T-TaS₂ thus requires careful sample preparation in inert atmosphere.Open in a separate windowFig. 4.Dimensional dependence of phase transition—electron diffraction. (A) Overlaid TEM diffraction images of ultrathin 1T-TaS₂ covered with hBN taken at 295 K (red peaks) and 100 K (blue peaks) for two flake thicknesses. hBN preserves CDW order (circled peaks) but introduces additional diffraction spots. (B) (Upper Right) Zoom-in schematic of CDW diffraction peaks showing temperature evolution. Position of NC spot can be used to estimate commensurate domain periodicity D_NC (Upper Left). (Lower) D_NC vs. temperature with cooling measured for the two covered samples compared with data reproduced from ref. 14. Reduced thickness pushes NC to C phase transition to lower temperature.The different structural phases of 1T-TaS₂ exhibit distinct electronic transport properties that may be exploited for device applications. In the main panel of Fig. 1B, we show temperature-dependent resistivity of a bulk crystal measured across the NC-C phase transition. Resistivity abruptly increases (decreases) by over an order of magnitude on entering the C (NC) phase. The hysteresis loop between cooling and warming defines the temperature region of metastability between the two phases and can be understood by a free energy picture (Fig. 1D). In a first-order transition, an activation barrier separates the stable energy minima corresponding to the NC and C states. With cooling from the NC phase, both the C state energy and the height of the barrier decrease with respect to the NC energy. When the C state has lower energy, the NC phase becomes metastable, but the system only transitions into the C phase when the activation barrier becomes comparable to the thermal energy. The situation is reversed when warming from the C phase. In oxidation-free 2D samples, this electronic transition is qualitatively unchanged.Fig. 2A shows an example of hBN-encapsulated 1T-TaS₂ flakes before (Upper) and after device fabrication (Lower). To make electrical contact to the covered samples, we used a technique of edge metallization developed for graphene/hBN heterostructures (Methods) (16). A side-view device schematic is shown in the Inset of the lower panel. In the main panel of Fig. 2B (I = 0, black curve), we plot resistance as a function of temperature for a 4-nm-thick sample measured across the NC-C phase transition. The behavior is similar to that of the bulk crystal (Fig. 1B); however, the hysteretic region between cooling and warming is substantially widened, indicating that one or both of the CDW phases become more metastable.Open in a separate windowFig. 2.Electrical control of NC-C transition in oxidation-free, 2D devices. (A) Optical images of 1T-TaS₂ flakes on a SiO₂/Si wafer covered by hBN in inert atmosphere before (Upper) and after (Lower) side electrical contact. (Inset) Side-view device schematic. (B) ac resistance vs. temperature for 4-nm-thick device as a function of dc current. Continuous current flow stabilizes NC phase at low temperature. Normalized resistance difference between cooling and warming is plotted as a function of dc current in Inset. (C) (Upper) Current vs. voltage sweep at 150 K starting in NC phase shows abrupt decreases in current and transition to the C phase. (Lower) Same at 200 K starting in C phase shows abrupt increase in current and transition to NC phase. Sweep rate is 3–6 V/min. Free energy schematics of electrically induced transitions are plotted in Insets.Metastable phases of a CDW system are generally more susceptible to electronic perturbations, because CDWs directly couple to electric field (6–8, 17). In our device, we observe that continuous current flow stabilizes the NC phase at low temperatures. In Fig. 2B (main panel), we show ac resistance with temperature while also applying a continuous, in-plane dc current, starting at room temperature (300 K). As the dc current I is increased, the final resistance at low temperature is monotonically lowered. Concomitant with this trend, the resistance jump resulting from the NC-C phase transition also decreases with increasing I. In the Inset, we plotted the ratio of the resistance difference between cooling and warming, ∆R, to resistance R in the more conducting state at T = 180 K, the temperature in the middle of the hysteresis region, as a function of the dc current level. For I = 35 μA (blue curve in main panel), the NC-C phase transition is completely absent. This measurement indicates that C phase formation in the current driven sample is very different compared with the zero-current, equilibrium condition. Current flow hinders the formation of the C phase and maintains the sample in the more conductive NC state at low temperature. We exclude Joule heating of the sample as a possible explanation by slowly turning off the current at low temperature and verifying that the resistance does not change. We also note that cooling and warming the sample again without dc current flow reproduces the original phase transitions (Fig. S3), indicating that the currents have not damaged the flake irreversibly.Open in a separate windowFig. S3.Resistance vs. temperature before and after dc current measurements. Trace for I = 0 (after) reproduces original phase transitions suppressed by large dc current.Our observation suggests that it is possible to maintain the NC phase in a temperature region where it is not thermodynamically stable. We now show that the opposite phenomenon is also possible, i.e., we can drive a transition toward the thermodynamically stable state, if we apply an in-plane current after cooling or warming the sample in equilibrium. Fig. 2C shows the current induced phase transitions in the same device (4 nm thickness). Here, we start in the NC phase at room temperature and cool the sample down to 150 K without current flow. At this temperature, although the sample remains in the NC state, the NC phase is now metastable, and the C phase is the thermodynamically stable state. As we increase the voltage across the device (upper panel, dark green curve), the measured current through the device decreases in abrupt steps (marked by red arrows) when it reaches a critical current I_c ∼ 30 μA (marked by red dashed line). On sweeping the bias current back to zero (light green curve), the device remains in a more insulating state. Warming up the sample after this point produces a temperature curve similar to the C phase, and a transition to the NC phase is observed. We have demonstrated that a bias current applied to the sample can be used to drive the metastable NC phase toward the thermodynamically preferred C state. The dashed green arrow in Fig. 2B marks the direction of this current-induced NC to C phase transition and a free energy schematic of this process is shown in the Inset of the upper panel of Fig. 2C.Similarly, the metastable C state can also be driven toward the NC phase with current. Here, we start in the C phase at 50 K and warm up to 200 K. The sample remains in the C phase, but now the NC phase is the thermodynamic ground state. As shown in the lower panel of Fig. 2C, sweeping the voltage in this case results in a sharp increase in current and drives the sample toward the more conducting NC state. We have used the dashed orange arrow in Fig. 2B and the free energy picture in the inset of the lower panel of Fig. 2C to represent this opposite C to NC transition. Interestingly, both induced transitions occur when the current reaches about I_c ∼ 30 μA, indicating that indeed current flow rather than electric field is the underlying mechanism that drives the transition. We repeated this measurement at various temperatures and initial conditions. In all cases, whenever the initial system is metastable, reaching a current threshold of 30 to 40 μA drives the system toward the thermodynamically stable state, regardless of device resistance. In contrast, we observe no induced transition up to 45 μA at 260 K, where a metastable phase ceases to exist.Taken together, the results of Fig. 2 demonstrate that it is possible to electrically control the NC-C transition in 2D 1T-TaS₂, where the temperature region of metastability is significantly enhanced. A more detailed study of this phase transition in 2D samples, however, can provide a better understanding of our experimental observations. The key structural difference between the two CDW phases is the presence of the discommensuration network in the NC phase (Fig. 1B, red inset). The NC-C transition can then be interpreted as a discommensuration-melting transition, which can be significantly affected by dimensionality (18, 19). The discommensurations have a striking effect on the electronic transport properties in 1T-TaS₂. The NC phase is an order of magnitude more conductive than the C phase. If we assume that the interior of each commensurate domain has similar transport properties as the C phase, this then implies the discommensuration regions in the NC phase are at least 10 times more conductive than the domain interior (3). Such a view is supported by the fact that the atomic structure within the discommensurations is close to the high-temperature metallic phase (15). With this interpretation, we can use transport measurements to better understand the role of dimensionality on the discommensuration-melting transition.As the number of 1T-TaS₂ layers decreases, the resistivity change corresponding to the NC-C phase transition evolves in a continuous manner down to 2 nm thickness in environmentally protected samples. Fig. 3A shows resistivity as a function of temperature for four hBN-covered 1T-TaS₂ flakes, all measured using a 1 K/min sweep rate. Their thicknesses are 2, 4, 6, and 8 nm as determined using an atomic force microscope. For comparison, we show data from an unprotected, 20-nm-thick flake, which exhibits characteristics similar to the bulk crystal, indicating that the effects of oxidation are less pronounced in thicker samples. The temperature hysteresis associated with the phase transition between cooling and warming is substantially increased in thinner samples, consistent with our earlier observations of the device in Fig. 2A. The progressive widening of the hysteresis loop continues down to the 4-nm-thick device, below which there is no longer a detectable transition. A guide to the eye for the expansion of this metastable region is shown by the colors in Fig. 3A. In the upper panel of Fig. 3B, we plot ∆T = T_c,warm – T_c,cool as a function of flake thickness, where T_c,warm and T_c,cool are the experimentally observed NC to C or C to NC transition temperature during the warming or cooling process, respectively. Here, T_c is determined by the temperature at which the first derivative peaks in the temperature sweep. ∆T is 60 K for the 20-nm flake, slightly larger than that for the bulk crystal (40 K), and grows to 120 K for the 4-nm device. In the same panel, we also plot the average temperature T_c,avg = (T_c,warm + T_c,cool)/2 of the transition. T_c,avg does not change substantially with thickness and remains between 180 and 190 K, which then implies that lower dimensionality does not stabilize either the NC or C phase. Instead, the NC (C) phase becomes increasingly metastable during cooling (warming) for thinner samples, indicating that the size of the energy barrier separating the NC and C phases increases (Fig. 1D).Open in a separate windowFig. 3.Dimensional dependence of phase transition—electron transport. (A) Thickness evolution of temperature-dependent resistivity around NC-C phase transition measured on hBN-covered ultrathin samples and 20-nm-thick flake. (B) Average transition temperature and temperature hysteresis (Upper) and normalized resistivity difference (Lower) between cooling and warming as a function of sample thickness. Open squares are corrections from contact resistance (Fig. S4). Hysteresis widens and resistivity difference decreases in thinner samples, whereas average transition temperature remains constant. Resistivity change can be used to estimate the discommensuration density 1/d at low temperature. (C) Circuit model of discommensuration network.Although ∆T increases when sample thickness is reduced, the resistivity jump associated with the phase transition decreases with decreasing thickness. In the bottom panel of Fig. 3B, we plot the resistivity difference ∆ρ between cooling and warming at T = 180 K, normalized to ρ in the more conducting state as a function of flake thickness. The closed circles are extracted directly from the data in Fig. 3A, whereas the open squares are corrections due to the effects of contact resistance (Fig. S4). For the 20-nm device, resistivity changes by an order of magnitude. The change is smaller for thinner devices and disappears completely for the 2-nm device, which indicates that more conducting NC discommensurations persist at low temperatures for thinner samples, consistent with the larger energy barriers required to remove them. Also, the resistivity jump becomes less abrupt, which is a reflection that the phase transition has slowed, as larger energy barriers generally act also to impede the kinetics of a phase transition. A simple circuit model presented in Fig. 3C allows us to connect the measured resistance jump in the NC-C transition, ∆R, with the estimated density of discommensurations 1/d left in the low temperature phase. We assume that the device resistance at low temperature is dominated by conduction through a random network of discommensuration channels (shown as white lines), which is generally sensitive to the particular microstructure formed. However, for device sizes much larger than d, we find the resistance with discommensuration channels would be R ∼ ρ_DC d, where ρ_DC is the resistivity per unit length of each discommensuration channel. Similarly, in the high temperature NC phase with a well-defined discommensuration network, we have R_NC ∼ ρ_DC D_NC, where we assume D_NC ∼ 80 Å (13, 14). From this, we can use the resistivity change in Fig. 3B to determine d: (ΔR/R_NC) ～ (d/D_NC) ? 1. On the right axis, we plotted d extracted for the different sample thicknesses. For the 2-nm sample, d ∼ D_NC, whereas it grows to 70–160 nm for the 20-nm sample.Open in a separate windowFig. S4.Extracting contact resistivity. Two- and four-terminal resistivity vs. temperature for 4-nm-thick flakes. The difference is proportional to resistivity of edge contacts.We can further substantiate the microscopic picture presented above by providing atomic structural analysis based on TEM. As before, the CDW structure is preserved by environmentally controlled hBN encapsulation. In Fig. 4A, we show diffraction images taken from two 1T-TaS₂ flakes of different thicknesses (12 and 2 nm). To highlight their temperature dependence, we have overlaid the diffraction patterns for each flake at 295 K (red peaks) and 100 K (blue peaks), our lowest achievable temperature. Ta Bragg peaks are again connected by a dashed triangle. Multiple scattering from hBN creates additional discernable peaks. The CDW peaks have been circled for easy identification. Although the peaks circled in gray appear qualitatively similar for both flakes, only the thicker flake displays additional peaks (circled in blue) at 100 K, indicating that it makes the transition to the C phase (compare with blue panel in Fig. 1A), whereas the thinner flake remains in the NC phase. This observation is consistent with our transport data as larger energy barriers in thinner samples require lower temperatures to realize the C phase.The movement of the gray-circled peaks with cooling (denoted by arrows, Fig. 4A) can be understood more quantitatively with reference to the zoom-in schematic shown in Fig. 4B (Upper Right). The position of this CDW peak is related to the periodicity D_NC of the NC domains (Upper Left) by a simple geometric expression (14): DNC=a/(2πΔϕ/360°)2+(Δλ/λC)2, where ∆ϕ is the difference in degrees between ϕ and ϕ_C = 13.9°, and ∆λ is the difference between the apparent wavelength averaged over many domains and λ_C = 13a. Thus, as the domain size grows, the NC peaks move closer to the C phase positions. We explicitly measured the position and angle of the CDW wave vectors for these two samples at several different temperatures during cooling to determine the domain period D_NC using the expression above. The results are plotted in the lower panel of Fig. 4B. For comparison, we also reproduce STM results obtained by Thomson et al. on the surface of a bulk crystal (14). For bulk samples, D_NC grows steadily from 60 to 90 Å on cooling from 340 to 215 K and then jumps to an arbitrarily large value on transition into the C phase at ∼180 K. At the same time, the width of the discommensuration regions remains relatively constant (∼22 Å) in all of the NC phase (13). As with our transport results, we find that reducing sample thickness suppresses the NC to C phase transition to lower temperatures during cooling and slows the CDW domain growth rate during the transition. For both of the thin flakes, the initial domain size at room temperature is similar to that that of the bulk crystal (D_NC = 60–70 Å). D_NC increases slightly upon cooling in the NC phase. For the 12-nm flake, the C phase is formed between 100 and 150 K, whereas the 2-nm flake remains in the NC phase even at 100 K. Its domain size here is much larger (D_NC ∼ 500 Å), however, indicating that the phase transition has begun to take place. This result is in clear contrast to bulk samples where the transition is abrupt.Our transport and TEM measurements both indicate that reduced dimensionality increases the energy barrier separating the NC and C CDW phases and thus widens the metastable region of the phase transition. The transition into the C phase involves melting or removal of the NC discommensuration network. Microscopically, energy barriers to discommensuration motion have been attributed to the presence of defects or impurities in the material, which act to pin them locally (20). Even in nominally pure CDW samples, clusters of localized defects have been observed by STM (21, 22), where the distance between defects is on the order of ∼10 nm. In bulk 1T-TaS₂, the interlayer stacking of NC domains make the discommensuration walls extended planar objects (15, 23), which are generally more difficult to pin. In two dimensions, however, the discommensurations become lines, which may be more easily immobilized. We have constructed a model of discommensuration pinning for a 2D system of thickness t (Fig. S5). We find that in the ultrathin limit where t is smaller than the mean distance between impurities, the pinning energy for a discommensuration plane scales as E_pin ∼ t^−2/3, corresponding to a cross-over from collective weak pinning to strong individual pinning. These strong pinning centers stabilize the NC discommensuration network at low temperatures during cooling and will also hinder the nucleation and growth of discommensurations when warming from the C phase, thus increasing the temperature region of metastability for both CDW phases in accordance with our experimental observation.Open in a separate windowFig. S5.Schematic picture of a DC plane and important length scales. A shows 3D view and B shows 2D projection. Red dots denote the location of impurities inside a dc plane. The effective mean impurity distance is l for t > l, whereas it is l_1D for t < l.By using this microscopic understanding of the NC-C phase transition in 2D samples, we may further elucidate the role of dc current in the measurements of Fig. 2 B and C. When the sample is cooled in equilibrium starting in the NC phase, the activation barrier between the NC and C states is continuously lowered, and therefore discommensurations are driven away and domain size grows steadily. Near the transition temperature, the small barrier can then be overcome with sufficient current flow, which depins the discommensurations to form the C phase ground state (Fig. 2C). On the other hand, when the sample is cooled out of equilibrium in the presence of a large dc current, it is likely that the domain size does not grow—the activation barrier remains large and the small-domain NC state persists on cooling to the lowest temperatures (Fig. 2B). The dc current is thus effectively a way to control the activation barrier between the NC and C phases.Although a spatially resolved study is still needed to fully understand these effects, our results have both clarified the nature of the 2D state in 1T-TaS₂ and demonstrated clear electrical control over the NC-C phase transition in ultrathin samples, further establishing the material’s relevance for device applications. We also expect our environmentally controlled techniques to be applicable for the study of other 2D transition-metal dichalcogenides that may be unstable under ambient conditions (24).     

INAUGURAL ARTICLE by a Recently Elected Academy Member:Theory of point contact spectroscopy in correlated materials

We developed a microscopic theory for the point-contact conductance between a metallic electrode and a strongly correlated material using the nonequilibrium Schwinger-Kadanoff-Baym-Keldysh formalism. We explicitly show that, in the classical limit, contact size shorter than the scattering length of the system, the microscopic model can be reduced to an effective model with transfer matrix elements that conserve in-plane momentum. We found that the conductance dI/dV is proportional to the effective density of states, that is, the integrated single-particle spectral function A(ω = eV) over the whole Brillouin zone. From this conclusion, we are able to establish the conditions under which a non-Fermi liquid metal exhibits a zero-bias peak in the conductance. This finding is discussed in the context of recent point-contact spectroscopy on the iron pnictides and chalcogenides, which has exhibited a zero-bias conductance peak.Heavy fermion systems (1, 2), high-T_c cuprates (3, 4), and very recently the iron-based superconductors (5, 6) all exhibit symptoms of quantum criticality. The most striking feature of quantum criticality is that the quantum fluctuations associated with the quantum critial point (QCP) couple strongly to itinerant electrons, giving rise to drastic changes in the electronic properties. Typically, such emergent properties are non-Fermi liquid like and hence fall outside the standard theory of metals. Although measurements of several physical properties, for example, the heat capacity, magnetic susceptibility, and DC electrical resistivity, have been identified with non-Fermi liquid (NFL) behavior, a direct probe of the hallmark feature of a NFL, namely the imaginary part of the single-particle self energy Σ(ω) ～ ω^ν with ν < 1, is still lacking. In principle, the temperature dependence of the DC electrical resistivity is expected to be related to ν, but it is also sensitive to many other factors, rendering such measurements inconclusive. In this context angle-resolved photoemission (ARPES) is an ideal probe of this hallmark feature. However, the resolution of the ARPES data are typically not high enough to pin-down ν conclusively. As a result, a reliable experimental setup to judge whether ν is larger or smaller than 1 is one of the most important topics in this field.We demonstrate here how point contact spectroscopy (PCS) can be used to resolve this problem. Our work here is motivated by recent PCS experiments on iron-pnictide superconductors in which an excess zero-bias conductance was measured well above the temperature associated with the structural rearrangement. Based on an analogy with earlier theoretical work on nematic quantum phase transitions (7), Lee et al. argued that the excess zero-bias conductance measured experimentally is likely due to an excess density of states associated with fluctuations near the orbital-ordering quantum phase transition. However, a direct link between the two remains missing as there is no rigorous argument relating the PCS signal in strongly correlated systems to the single-particle density of states. The theoretical foundations for the tunneling density of states have been well established (8, 9), but we stress here that PCS is not tunneling, and this work establishes a clear connection between PCS conductance and an effective density of states arising from NFL behavior.In this paper, we build on earlier work (10) to fill in this missing link and as a result are able to establish the circumstances under which the PCS signal is a direct measure of the single-particle density of states in strongly correlated electron systems and hence offers a window into a key probe of non-Fermi liquid behavior, namely the imaginary part of the single-particle self-energy. Of course, PCS is an old field dating back to the pioneering work of Yanson’s (11) in 1974 when he was attempting to measure the tunneling conductance across a superconducting/insulator/normal-metal (SIN) planar junction. According to Harrison’s theorem (12), when the superconductor is driven normal, the resulting planar tunneling conductance must be ohmic: assuming a one-dimensional model, which holds for good planar tunnel junctions, in the standard tunneling conductance formula that assumes weakly correlated electron (conventional) materials, the Fermi velocity v_f = (1/?)(dk_x/dE) exactly divides out the density of states D(E) = (L/π)(dE/dk_x). Yanson discovered weak conductance nonlinearities in an SIN junction above the critical field (S = Pb) and that the second harmonic of the conductance (d²I/dV²) revealed the Eliashberg function, α²F(ω), the strength of about 1% of the background conductance. This behavior resulted from the junctions being leaky with nanoscale metallic shorts between S and N, allowing electrons to be directly injected through the junction without any tunneling processes; hence, Harrison’s theorem did not apply. He went on to show that when the junction is large such that the mean free path is smaller than the junction (thermal regime), no spectroscopic information can be obtained, but if the junction is smaller than the elastic (Sharvin or ballistic limit) or inelastic (diffusive regime) mean free path, spectroscopic information is revealed. Quasiparticles backscattered through the junction reveal the phonon spectrum; therefore, this technique is also called quasiparticle scattering spectroscopy (QPS). Researchers in the field proceeded to map out bosonic spectra (phonons and magnons) in a variety of materials (13, 14), quasiparticle scattering from Kondo impurities (13), spin and charge density waves (15, 16), and recently a Kondo insulator (17). With the advent of the Blonder-Tinkham-Klapwijk (BTK) theory (18), in a clean S/N junction, Andreev scattering was shown to reveal details of the superconducting gap structure, including magnitude and symmetry (19). This technique has been shown to be particularly useful in superconductors that are difficult to grow in thin film form, e.g., heavy-fermion superconductors (10, 20, 21) and the iron-based high-temperature superconductors (22). In the heavy-fermions, the Fano background could be accounted for via multichannel tunneling models (10, 23–25). Our focus here is on establishing a clear link between the suggestive relationship that excess zero-bias signal measured in PCS is a direct measure of the effective density of states arising from electron correlations (6, 19, 21, 26, 27).To this end, we use the Schwinger-Kadanoff-Baym-Keldysh (SKBK) formalism (28–30), coupled with certain reasonable assumptions, to show that the conductance measured from PCS is proportional to the effective density of states (31–37). Because the effective density of states is defined as the integrated single-particle spectral function A(ω = eV) over the whole Brillouin zone, it contains the information about the single particle self energy Σ(ω). We show that a fingerprint of non-Fermi liqud behavior with ν < 1 is an enhancement of the PCS conductance at zero bias. As a comparison, we also discuss the case of a junction in the thermal regime, in which only DC resistivity is detected. We highlight here that the DC resistivity is fundamentally different from the PCS conductance. The former is corresponding to the current-current correlation function evaluated by Kubo formula, whereas the latter is related to the single particle Green function as described by the SKBK formalism. Consequently, we conclude that the zero-bias peak in the PCS could be identified as a unique signature of non-Fermi liquid metal.     

Filming the formation and fluctuation of skyrmion domains by cryo-Lorentz transmission electron microscopy

Magnetic skyrmions are promising candidates as information carriers in logic or storage devices thanks to their robustness, guaranteed by the topological protection, and their nanometric size. Currently, little is known about the influence of parameters such as disorder, defects, or external stimuli on the long-range spatial distribution and temporal evolution of the skyrmion lattice. Here, using a large (7.3 × 7.3?μm²) single-crystal nanoslice (150 nm thick) of Cu₂OSeO₃, we image up to 70,000 skyrmions by means of cryo-Lorentz transmission electron microscopy as a function of the applied magnetic field. The emergence of the skyrmion lattice from the helimagnetic phase is monitored, revealing the existence of a glassy skyrmion phase at the phase transition field, where patches of an octagonally distorted skyrmion lattice are also discovered. In the skyrmion phase, dislocations are shown to cause the emergence and switching between domains with different lattice orientations, and the temporal fluctuation of these domains is filmed. These results demonstrate the importance of direct-space and real-time imaging of skyrmion domains for addressing both their long-range topology and stability.In a noncentrosymmetric chiral lattice, the competition between the symmetric ferromagnetic exchange, the antisymmetric Dzyaloshinskii–Moriya interaction, and an applied magnetic field can stabilize a highly ordered spin texture, presenting as a hexagonal lattice of spin vortices called skyrmions (1–4).Magnetic skyrmions have been experimentally detected in materials having the B20 crystal structure such as MnSi (5), Fe_1?xCo_xSi (6, 7), FeGe (8), and Cu₂OSeO₃ (9) and, recently, also on systems like GaV₄S₈ (10) and beta-Mn-type alloys (11). Small-angle neutron scattering studies of bulk solids evidenced the formation of a hexagonal skyrmion lattice confined in a very narrow region of temperature and magnetic field (T-B) in the phase diagram (5, 6). In thin films and thinly cut slices of the same compounds, instead, skyrmions can be stabilized over a wider T-B range as revealed by experiments using cryo-Lorentz transmission electron microscopy (LTEM) (12, 13). Furthermore, it was proposed and recently observed that skyrmions can also exist as isolated objects before the formation of the ordered skyrmion lattice (14, 15). A recent resonant X-ray diffraction experiment also suggested the formation of two skyrmion sublattices giving rise to regular superstructures (16).In a 2D landscape, long-range ordering can be significantly altered by the presence of defects and disorder. Indeed, the competition between order and disorder within the context of lattice formation continues to be an issue of fundamental importance. Condensed matter systems are well known to provide important test beds for exploring theories of structural order in solids and glasses. An archetypal and conceptually relevant example is the superconducting vortex lattice, where real-space imaging studies allow direct access to the positional correlations and local coordination numbers (17–19). Up until now, however, analogous studies of skyrmion lattices have not been reported even though (as for superconducting vortices) it is well known that defects and dislocations present in a sample can pin the motion of skyrmions induced by external perturbations such as an electric field (20) or a magnetic field (16). This competition between disorder and elasticity will clearly give rise to a complex energy landscape promoting diverse metastable states (21) and superstructures (22, 23). Furthermore, previous imaging studies of skyrmion lattices could probe only the short-range order due to limitations in the size of the imaged area and its homogeneity.In this paper, by systematic observations using cryo-LTEM, we reveal the magnetic field-dependent evolution of the skyrmion-related spin textures in a Cu₂OSeO₃ thin plate and study their long-range ordering properties imaging up to ∼1,000 lattice constants. The different phases of the spin textures are analyzed with state-of-the-art methods to unravel their spatial properties. At low magnetic fields, the coexistence of two helical domains is observed, in contrast to previous studies (9); the angle between the two helices’ axis is retrieved via a reciprocal space analysis. At the magnetic field close to the helical–skyrmion phase transition, evidence for a glassy skyrmion phase is found via cross-correlation analysis, a method that has recently been applied to the analysis of both X-rays and electron diffraction patterns to retrieve information on the local order and symmetry of colloidal systems (24–26). In this phase, we reveal also patches of octagonally distorted skyrmion lattice crystallites. In the skyrmion phase, by locating the position of each skyrmion and generating an angle map of the hexagonal unit cell they formed, we obtain a direct-space distortion map of the skyrmion lattice. This distortion map evidences the presence of orientation-disordered skyrmion lattice domains present within the single-crystalline sample. Each domain boundary coincides with a dislocation formed by a seven–five or a five–eight–five Frenkel-type defect. The number of such dislocations decreases with increasing magnetic field, and large single-domain regions are formed. The formation of these mesoscopic domains was also filmed with camera-rate (millisecond) time resolution. The presence of differently oriented skyrmion lattice domains was observed in spatially separated regions, or in the same area of the sample but at a different moment in time. Based on our observation, we propose an alternative scenario for the appearance of split magnetic Bragg peaks reported in ref. 16. Instead of the formation of regular superstructures of coexisting misoriented skyrmion lattices in real space, we suggest that the splitting is caused by a spatial or temporal integration of an orientation-fluctuating skyrmion lattice. This result highlights the importance of a direct-space, real-time probe for assessing the dynamical topological properties of a large number of skyrmions.     

Magnetism and superconductivity driven by identical 4f states in a heavy-fermion metal

The apparently inimical relationship between magnetism and superconductivity has come under increasing scrutiny in a wide range of material classes, where the free energy landscape conspires to bring them in close proximity to each other. Particularly enigmatic is the case when these phases microscopically interpenetrate, though the manner in which this can be accomplished remains to be fully comprehended. Here, we present combined measurements of elastic neutron scattering, magnetotransport, and heat capacity on a prototypical heavy fermion system, in which antiferromagnetism and superconductivity are observed. Monitoring the response of these states to the presence of the other, as well as to external thermal and magnetic perturbations, points to the possibility that they emerge from different parts of the Fermi surface. Therefore, a single 4f state could be both localized and itinerant, thus accounting for the coexistence of magnetism and superconductivity.     

Density-independent plasmons for terahertz-stable topological metamaterials

To efficiently integrate cutting-edge terahertz technology into compact devices, the highly confined terahertz plasmons are attracting intensive attention. Compared to plasmons at visible frequencies in metals, terahertz plasmons, typically in lightly doped semiconductors or graphene, are sensitive to carrier density (n) and thus have an easy tunability, which leads to unstable or imprecise terahertz spectra. By deriving a simplified but universal form of plasmon frequencies, here, we reveal a unified mechanism for generating unusual n-independent plasmons (DIPs) in all topological states with different dimensions. Remarkably, we predict that terahertz DIPs can be excited in a two-dimensional nodal line and one-dimensional nodal point systems, confirmed by the first-principle calculations on almost all existing topological semimetals with diverse lattice symmetries. Besides n-independence, the feature of Fermi velocity and degeneracy factor dependencies in DIPs can be applied to design topological superlattice and multiwalled carbon nanotube metamaterials for broadband terahertz spectroscopy and quantized terahertz plasmons, respectively. Surprisingly, high spatial confinement and quality factor, also insensitive to n, can be simultaneously achieved in these terahertz DIPs. Our findings pave the way for developing topological plasmonic devices for stable terahertz applications.

Bridging the gap between microwave and infrared regimes, terahertz radiation promises many cutting-edge applications in radar, imaging, biosensing, nondestructive evaluation, and ultrahigh-speed communications (1, 2). While realizing compact terahertz integrated circuits is a big challenge, terahertz plasmons, collective oscillations of electrons at terahertz frequency, provide a revolutionary way to effectively reduce the sizes of terahertz devices down to subwavelength scales (3–8). To achieve highly confined terahertz plasmons, the extensive research has been devoted to various metamaterials, including spoof plasmon polaritons in structured metal surfaces (7–10), terahertz plasmons in lightly doped semiconductors (2, 11–13), and recently developed graphene plasmons (14–16). Compared to the plasmons at visible or ultraviolet (UV) frequency in metals with ultra-high intrinsic charge density (n), the terahertz plasmons (e.g., in doped semiconductors and graphene with ultra-low n) are quite sensitive to the oscillation of n (13–18), as a low n can be greatly changed by the defects (17), thermal fluctuation (2, 16, 19), charge inhomogeneity (20), electrical gating (14, 16, 18), optical excitations (21–23), or charge transfer at interface (Fig. 1A). Consequently, their fundamental properties, such as resonance frequency, confinement, and loss of terahertz plasmons (2, 16–18), will be largely affected by the surrounding environments. Therefore, the n-dependence feature leads to unfavorable terahertz applications, such as low temperature limit, high-quality sample requirements, unstable or imprecise terahertz sources, and detection.Open in a separate windowFig. 1.DIPs and their realizations. (A) Schematic comparison between DDP and DIP. Concentric red, blue, or orange circles illustrate plasmon waves excited by electron systems (represented by the cyan plane). For an excited DDP, its resonance frequency (ωp) or wavelength (λp) is sensitive to the oscillation of n. When increasing (red arrow) or decreasing (blue arrow) n, the ωp or λp of a DDP will increase (red circles) or decrease (blue circles) correspondingly. The properties (ωp or λp) of a DIP (orange circles) are stable against the changes of n. (B) Linear band structures of 2D nodal line and 1D nodal point and their constant DOS versus E_F. Collective DIPs are labeled schematically by red arrows.It is known that the classical plasmon frequency in conventional electron gas (EG) has an n1/2 dependence, while graphene plasmon shows a weaker n1/4 power-law scaling (14, 15). Recently, the linear band structures have been extended to a large number of topological semimetals (TSMs) (24, 25), following the fast development of topological matter. Surprisingly, the plasmons with diverse n dependencies have been found in these TSMs even though they have a similar linear band crossing as graphene. For example, the plasmon frequency of three-dimensional (3D) Dirac systems shows n1/3 scaling (26), while unconventional n0-dependent plasmons solely in midinfrared have been found in one-dimensional (1D) metallic carbon nanotubes (CNTs) (27) or 3D nodal-surface electrides (28). Since most previous theories are system dependent, a unified theory to intuitively understand all these plasmonic behaviors in different electronic systems is still lacking, which significantly prevents the design of superior metamaterials for revolutionary terahertz technology and overcoming the intrinsic terahertz-unstable bottlenecks in conventional plasmonic devices.In this article, we derive a simplified but universal form of plasmon frequencies at a long-wavelength limit that can be applied to understand the collective excitations of all electronic systems with different dimensions. Significantly, a unified mechanism is revealed for generating n-independent plasmons (DIPs), which can be excited in some specific topological states. As demonstrated in Fig. 1A, the properties of a DIP, such as its resonance frequency or wavelength, are not affected by the changes of n, which can fundamentally overcome intrinsic terahertz-unstable bottlenecks raised by n-dependent plasmons (DDPs) in conventional systems. Importantly, we predict that the terahertz DIPs can be realized in two reduced systems: two-dimensional (2D) nodal line and 1D nodal point. Extensive first-principle calculations are employed to confirm the DIP excitations among 22 known 2D nodal line semimetals (NLSMs) and 1D CNTs. Besides the n independence, the frequencies of DIPs can be tuned by Fermi velocity, substrate screening, and degeneracy factor, revealing that a novel, ultrastable terahertz spectrum from narrowband to broadband and a tunable quantization can be achieved in 2D superlattice and 1D multiwalled CNT metamaterials, respectively. Remarkably, stable performance with high spatial confinement and quality factor, critical for device applications, can be simultaneously obtained for terahertz DIPs.     

From the Cover: Rare-earth vs. heavy metal pigments and their colors from first principles

Many inorganic pigments contain heavy metals hazardous to health and environment. Much attention has been devoted to the quest for nontoxic alternatives based on rare-earth elements. However, the computation of colors from first principles is a challenge to electronic structure methods, especially for materials with localized f-orbitals. Here, starting from atomic positions only, we compute the colors of the red pigment cerium fluorosulfide as well as mercury sulfide (classic vermilion). Our methodology uses many-body theories to compute the optical absorption combined with an intermediate length-scale modelization to assess how coloration depends on film thickness, pigment concentration, and granularity. We introduce a quantitative criterion for the performance of a pigment. While for mercury sulfide, this criterion is satisfied because of large transition matrix elements between wide bands, cerium fluorosulfide presents an alternative paradigm: the bright red color is shown to stem from the combined effect of the quasi-2D and the localized nature of states. Our work shows the power of modern computational methods, with implications for the theoretical design of materials with specific optical properties.     

Edge-controlled growth and kinetics of single-crystal graphene domains by chemical vapor deposition

The controlled growth of large-area, high-quality, single-crystal graphene is highly desired for applications in electronics and optoelectronics; however, the production of this material remains challenging because the atomistic mechanism that governs graphene growth is not well understood. The edges of graphene, which are the sites at which carbon accumulates in the two-dimensional honeycomb lattice, influence many properties, including the electronic properties and chemical reactivity of graphene, and they are expected to significantly influence its growth. We demonstrate the growth of single-crystal graphene domains with controlled edges that range from zigzag to armchair orientations via growth–etching–regrowth in a chemical vapor deposition process. We have observed that both the growth and the etching rates of a single-crystal graphene domain increase linearly with the slanted angle of its edges from 0° to ∼19° and that the rates for an armchair edge are faster than those for a zigzag edge. Such edge-structure–dependent growth/etching kinetics of graphene can be well explained at the atomic level based on the concentrations of the kinks on various edges and allow the evolution and control of the edge and morphology in single-crystal graphene following the classical kinetic Wulff construction theory. Using these findings, we propose several strategies for the fabrication of wafer-sized, high-quality, single-crystal graphene.Graphene, a one-atom-thick, two-dimensional (2D) crystal, has attracted increasing interest because of its interesting properties, which include a large carrier mobility, high transparency, extremely high thermal conductivity, and high tensile strength (1–3). Wafer-sized single-crystal graphene is highly desired and required for numerous applications, especially in electronics and optoelectronics, because grain boundaries between the graphene domains markedly degrade its quality and properties (4–8). Chemical vapor deposition (CVD) has shown great potential for growing large-sized single-crystal graphene domains (8–12); however, the growth rate with CVD is low, typically less than 20 μm/min, which is obviously not conducive to the fabrication of wafer-sized single crystals. In addition, the graphene produced by CVD suffers from poor controllability and low quality. For example, only zigzag (ZZ) or randomly oriented edges have been fabricated via CVD, and the electron mobility in CVD-produced graphene is substantially lower than that in mechanically exfoliated graphene (13). Understanding the atomistic mechanism that governs graphene growth is necessary for the controlled growth of wafer-sized, high-quality, single-crystal graphene. The edge structure of graphene has been shown to significantly influence its various fundamental properties, such as its electronic and magnetic properties, its edge stability, and its chemical reactivity (14–18). Similarly, the graphene edges, as the sites at which carbon accretion to the two-dimensional honeycomb lattice occurs, likely influence the graphene growth (19–21).We report the growth of single-crystal graphene domains with controlled edges with orientations that range from ZZ to armchair (AC) via a CVD growth–etching–regrowth (G–E–RG) process. We observed that both the graphene growth and etching via CVD are strongly dependent on the edge structure. Such growth/etching behavior is well explained at the atomic level given the concentrations of kinks on the various edges and allows the evolution and control of the graphene edges and the morphology according to the classical kinetic Wulff construction (KWC) theory. Thus, we explain the commonly observed ZZ edges and low graphene growth rate under CVD and propose several strategies for the fabrication of wafer-sized, high-quality, single-crystal graphene.     

Phase Analysis and Thermoelectric Properties of Cu-Rich Tetrahedrite Prepared by Solvothermal Synthesis

Because of the large Seebeck coefficient, low thermal conductivity, and earth-abundant nature of components, tetrahedrites are promising thermoelectric materials. DFT calculations reveal that the additional copper atoms in Cu-rich Cu₁₄Sb₄S₁₃ tetrahedrite can effectively engineer the chemical potential towards high thermoelectric performance. Here, the Cu-rich tetrahedrite phase was prepared using a novel approach, which is based on the solvothermal method and piperazine serving both as solvent and reagent. As only pure elements were used for the synthesis, the offered method allows us to avoid the typically observed inorganic salt contaminations in products. Prepared in such a way, Cu₁₄Sb₄S₁₃ tetrahedrite materials possess a very high Seebeck coefficient (above 400 μVK⁻¹) and low thermal conductivity (below 0.3 Wm⁻¹K⁻¹), yielding to an excellent dimensionless thermoelectric figure of merit ZT ≈ 0.65 at 723 K. The further enhancement of the thermoelectric performance is expected after attuning the carrier concentration to the optimal value for achieving the highest possible power factor in this system.     

Development of Composite,Reinforced, Highly Drug-Loaded Pharmaceutical Printlets Manufactured by Selective Laser Sintering—In Search of Relevant Excipients for Pharmaceutical 3D Printing

3D printing by selective laser sintering (SLS) of high-dose drug delivery systems using pure brittle crystalline active pharmaceutical ingredients (API) is possible but impractical. Currently used pharmaceutical grade excipients, including polymers, are primarily designed for powder compression, ensuring good mechanical properties. Using these excipients for SLS usually leads to poor mechanical properties of printed tablets (printlets). Composite printlets consisting of sintered carbon-stained polyamide (PA12) and metronidazole (Met) were manufactured by SLS to overcome the issue. The printlets were characterized using DSC and IR spectroscopy together with an assessment of mechanical properties. Functional properties of the printlets, i.e., drug release in USP3 and USP4 apparatus together with flotation assessment, were evaluated. The printlets contained 80 to 90% of Met (therapeutic dose ca. 600 mg), had hardness above 40 N (comparable with compressed tablets) and were of good quality with internal porous structure, which assured flotation. The thermal stability of the composite material and the identity of its constituents were confirmed. Elastic PA12 mesh maintained the shape and structure of the printlets during drug dissolution and flotation. Laser speed and the addition of an osmotic agent in low content influenced drug release virtually not changing composition of the printlet; time to release 80% of Met varied from 0.5 to 5 h. Composite printlets consisting of elastic insoluble PA12 mesh filled with high content of crystalline Met were manufactured by 3D SLS printing. Dissolution modification by the addition of an osmotic agent was demonstrated. The study shows the need to define the requirements for excipients dedicated to 3D printing and to search for appropriate materials for this purpose.