Probing fractional quantum Hall effect by photoluminescence

Photoluminescence (PL) spectroscopy has recently revealed fractional quantum anomalous Hall (FQAH) states in twisted transition-metal dichalcogenide (TMD) bilayers. In absence of a microscopic theory for FQAH systems, we study the analogous PL problem in Landau Levels (LLs) using composite fermions (CFs). Mapping the conduction and valence bands to pseudospin (up and down) bands reveals an SU(2) symmetry that is present for a perfectly 2 dimensional system with identical electron and hole masses. This symmetry blocks certain electron-hole states from recombining allowing one to classify these states as "dark" and the remaining states as "bright". We show that the lowest energy electron-hole states at all fillings except ν = 1/3 are dark. Thus, at T=0, the PL intensity is zero except at ν = 1/3. At non-zero temperatures, we show the that there are peaks in PL intensity at incompressible fillings while the PL is suppressed at compressible fractions, with the intensities at incompressible Jain fillings (n/2n+1) decreasing with n. The "darkness" of lowest energy states arises from either binding of CF-holes to the CF-electron CF-hole pair or through CF kinetic energy lowering relaxation processes. The filling factor dependence of PL intensity is shown to be robust to SU(2) breaking perturbations. The filling ν in our case is to be compared to the filling factor ν−1 in twisted TMDs.