Moving Dirac nodes by chemical substitution

Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, BaNiS2, through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of BaCo1−xNixS2 across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the Γ−M symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making BaCo1−xNixS2 a model system to functionalize Dirac materials by varying the strength of electron correlations.

In the vast domain of topological Dirac and Weyl materials (1–9), the study of various underlying mechanisms (10–15) leading to the formation of nontrivial band structures is key to discovering new topological electronic states (16–23). A highly desirable feature of these materials is the tunability of the topological properties by an external parameter, which will make them suitable in view of technological applications, such as topological field-effect transistors (24). While a thorough control of band topology can be achieved, in principle, in optical lattices (25) and photonic crystals (26) through the wandering, merging, and reshaping of nodal points and lines in k-space (27, 28), in solid-state systems, such a control is much harder to achieve. Proposals have been made by using optical cavities (29), twisted van der Waals heterostructures (30), intercalation (31), chemical deposition (32, 33), impurities (34), and magnetic and electric applied fields (35), both static (36) and time-periodic (17, 37). Here, we prove that it is possible to move and reshape Dirac nodal lines in reciprocal space by chemical substitution. Namely, by means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, we observe a sizable shift of robust massive Dirac nodes toward Γ in BaCo1−xNixS2 as a function of doping x, obtained by replacing Ni with Co. At variance with previous attempts of controlling Dirac states by doping (19, 38), in our work, we report both a reshape and a significant k-displacement of the Dirac nodes.BaCo1−xNixS2 is a prototypical transition metal system with a simple square lattice (39). In BaCo1−xNixS2 , the same doping parameter x that tunes the position of the Dirac nodes also controls the electronic phase diagram, which features a first-order metal-insulator transition (MIT) at a critical substitution level, xcr∼ 0.22 (40, 41), as shown in Fig. 1A. The Co rich side (x=0) is an insulator with columnar antiferromagnetic (AF) order and with local moments in a high-spin (S = 3/2) configuration (42). This phase can be seen as a spin density wave (SDW) made of antiferromagnetically coupled collinear spin chains. Both electron-correlation strength and charge-transfer gap ΔCT increase with decreasing x, as typically found in the late-transition metal series. The MIT at x=0.22 is of interest because it is driven by electron correlations (43) and is associated with a competition between an insulating antiferromagnetic phase and an unconventional paramagnetic semimetal (44), where the Dirac nodes are found at the Fermi level. We show that a distinctive feature of these Dirac states is their dominant d-orbital character and that the underlying band-inversion mechanism is driven by a large d−p hybridization combined with the nonsymmorphic symmetry (NSS) of the crystal (Fig. 1B). It follows that an essential role in controlling the properties of Dirac states is played by electron correlations and by the charge-transfer gap (Fig. 1C), as they have a direct impact on the hybridization strength. This results into an effective tunability of shape, energy, and wave vector of the Dirac lines in the proximity of the Fermi level. Specifically, the present ARPES study unveils Dirac bands moving from M to Γ with decreasing x. The bands are well explained quantitatively by ab initio calculations, in a hybrid density functional approximation suitable for including nonlocal correlations of screened-exchange type, which affect the hybridization between the d and p states. The same functional is able to describe the insulating SDW phase at x=0, driven by local correlations, upon increase of the optimal screened-exchange fraction. These calculations confirm that the Dirac nodes mobility in k-space stems directly from the evolution of the charge-transfer gap, i.e., the relative position between d and p on-site energies. These results clearly suggest that BaCo1−xNixS2 is a model system to tailor Dirac states and, more generally, that two archetypal features of correlated systems, such as the hybrid d−p bands and the charge-transfer gap, constitute a promising playground to engineer Dirac and topological materials using chemical substitution and other macroscopic control parameters.Open in a separate windowFig. 1.Experimental observation of Dirac states in the phase diagram of BaCo1−xNixS2. (A) Phase diagram of BaCo1−xNixS2. The transition lines between the PM, the paramagnetic insulator (PI), and the antiferromagnetic insulator (AFI) are reported. Colored circles indicate the different doping levels x studied in this work. This doping alters the d−p charge-transfer gap (ΔCT). (B) Crystal structure of BaNiS2. Blue, red, and yellow spheres represent the Ni, S, and Ba atoms, respectively. The tetragonal unit cell is indicated by black solid lines. Lattice parameters are a = 4.44 Å and c = 8.93 Å (45). (B, Upper) Projection of the unit cell in the xy plane, containing two Ni atoms. (C) Schematics of the energy levels. The hybridization of d− and p− orbitals creates the Dirac states, and the d−p charge-transfer gap fixes the position of these states in the E−k space. (D) A three-dimensional ARPES map of BaNiS2 (x=1) taken at 70-eV photon energy. The top surface shows the Fermi surface, and the sides of the cube present the band dispersion along high-symmetry directions. The linearly dispersing bands along Γ−M cross each other at the Fermi level, EF, thus creating four Dirac nodes. (E) We observe the oval-shaped section of the linearly dispersing bands on the kx−ky plane for E−EF=−100 meV. The linearly dispersing bands along the major and minor axis of the oval are also shown.