Nonlocal Electron Coherence in MoS$_{2}$ Flakes Correlated through Spatial Self Phase Modulation*

Electron coherence among different flake domains of MoS$_{2}$ has been generated using ultrafast or continuous wave laser beams. Such electron coherence generates characteristic far-field diffraction patterns through a purely coherent nonlinear optical effect---spatial self-phase modulation (SSPM). A wind-chime model is developed to describe the establishment of the electron coherence through correlating the photo-excited electrons among different flakes using coherent light. Owing to its finite gap band structure, we find different mechanisms, including two-photon processes, might be responsible for the SSPM in MoS$_{2}$ [with a large nonlinear dielectric susceptibility $\chi^{(3)}=$ 1.6 $\times $ 10$^{-9}$ e.s.u. (SI: 2.23 $\times $ 10$^{-17}$ m$^{2}$/V$^{2})$ per layer]. Finally, we realized all optical switching based on SSPM, demonstrating that the electron coherence generation we report here is a ubiquitous property of layered quantum materials, by which novel optical applications are accessible.