Electrons in zero-flux periodic gauge fields: Supersymmetry, contrasted topology, and realization in strained 2D semiconductors*

Supersymmetric systems exhibit non-negative energy spectrum, in which each positive energy level is doubly degenerate forming superpartners (SPs), while the zero modes might remain unpaired. An important supersymmetric system corresponds to spin-1/2 electrons in a magnetic field, where electrons with opposite spin correspond to SPs. Here we consider zero-flux periodic gauge fields, which exhibit intriguing distinctions compared to a uniform field. We reveal that such SPs share identical energy dispersions composed of isolated quasi-flat bands. Importantly, the first energy bands of the SPs that contain the zero modes exhibit contrasted topology, i.e., zero vs nonzero Chern numbers. The difference of the Chern numbers is directly connected to the dispersion around zero energy, making it possible to manipulate the Chern numbers by tuning the band structure. The profiles of such supersymmetric band structures, thus the band topology, are robust against variations in typical tuning parameters. We show that such SPs can be realized with strain and twist engineering in multilayer 2D semiconductors. Our results will guide the search for candidate materials with topological flat bands that will host topological and correlation-driven phenomena.