Emergence of electron coherence and two-color all-optical switching in MoS2 based on spatial self-phase modulation

Generating electron coherence in quantum materials is essential in optimal control of many-body interactions and correlations. In a multidomain system this signifies nonlocal coherence and emergence of collective phenomena, particularly in layered 2D quantum materials possessing novel electronic structures and high carrier mobilities. Here we report nonlocal ac electron coherence induced in dispersed MoS₂ flake domains, using coherent spatial self-phase modulation (SSPM). The gap-dependent nonlinear dielectric susceptibility χ⁽³⁾ measured is surprisingly large, where direct interband transition and two-photon SSPM are responsible for excitations above and below the bandgap, respectively. A wind-chime model is proposed to account for the emergence of the ac electron coherence. Furthermore, all-optical switching is achieved based on SSPM, especially with two-color intraband coherence, demonstrating that electron coherence generation is a ubiquitous property of layered quantum materials.Recently 2D layered quantum materials have attracted tremendous interest since the discovery of graphene a decade ago (1). Various layered materials, ranging from boron nitride sheets to transition metal dichalcogenides and from topological insulators to high-temperature superconductors, have been intensively investigated (2–11). Strict 2D atomic crystals can now be produced at a macroscopic scale, using a variety of methods (11, 12). Among them molybdenum disulfide (MoS₂) and related layered quantum materials are particularly interesting due to their novel optical properties and potential valleytronics applications (4, 5, 8, 9) at a thickness of monolayer and few layers (2, 10, 13). Layered materials share common physical properties rooted in their ubiquitous 2D quantum nature, for which achieving pure coherence among electrons (lattices) is of particular interest (14–19). The presence of multiple domains is ubiquitous in many known 2D quantum materials, ranging from stripe-order cuprate superconductors to polycrystalline strongly correlated systems. For example, phase locking between different layers of stripe orders is crucial for enhancing the superconducting phase in layered high-temperature superconductors (20, 21).In this work we demonstrate unambiguously that nonlocal and intraband ac electron coherence, of which the electronic wave function oscillates at an optical frequency of 10¹⁴ Hz, can be generated in separate MoS₂ flakes, using spatial self-phase modulation (SSPM). The SSPM is a coherent third-order nonlinear optical process systematically investigated decades ago (22), where the nonlinear optical susceptibility χ⁽³⁾ is uniquely determined by the laser-intensity-dependent refractive index n = n₀ + n₂I, where n₀ and n₂ are linear and nonlinear refractive indexes, respectively. If this effect is strong enough in a material, the phenomenon of self-focusing can be directly observed. The SSPM is also frequently referred to as the optical Kerr effect or the ac Kerr effect (note the difference from the regular Kerr effect). It is parallel to the other third-order nonlinear optical processes, such as third harmonic generation (THG) and four-wave mixing (FWM).Our investigations show that gap-dependent SSPM is a general method for inducing electron coherence in 2D layered materials. Monolayer and few-layer MoS₂ (and other similar layered materials) have finite bandgaps, which lift the obstacle to versatile electronic and optical applications (2, 23, 24). Because SSPM using below-gap photons has not been reported, MoS₂ provides an ideal test platform for observing SSPM in finite-bandgap materials. A model has been developed to account for the coherence emergence process and theoretical calculations have been carried out to unravel the underlying mechanism. Moreover, we demonstrate all-optical switching based on SSPM, which employs intraband electron coherence. This optical switch has multiple advantages, including weak-control-strong performance, cascade-possible, and high-contrast two-color switching.