Large scale theoretical investigation of the phase diagram of twisted bilayer MoTe$_2$ at fractional fillings: agreements and contradictions with current experiments

Abstract

We present a comprehensive exact-diagonalization study of interaction-driven phases in twisted bilayer MoTe$_2$ across experimentally relevant twist angles ($2.13^\circ$--$4^\circ$) and hole fillings. Using continuum-model moiré bands, we compare the one-band-per-valley (1BPV) projection with a two-band-per-valley (2BPV) calculation that includes interaction-driven band mixing, and we benchmark both the widely used first-harmonic continuum model and a parameter-free DFT ``fitting-free'' model. At odd-denominator fillings, the 2BPV calculation reproduces the experimentally observed hierarchy of fractional Chern insulators (FCIs) around $θ\approx 3.7^\circ$, including robust incompressible states at $ν=-2/3$, $-3/5$, and $-4/7$ while correctly finding the absence of an FCI at $ν=-3/7$, and it favors a charge density wave ground state at $ν=-1/3$ over the FCI. At half filling $ν=-1/2$, the 1BPV calculation exhibits clear composite Fermi liquid (CFL) signatures, whereas the band mixing in 2BPV calculations destabilizes the CFL ground state. Finally, motivated by the Landau-level analogy at $θ\approx 2.13^\circ$, we test the proposed non-abelian Pfaffian state at $ν=-3/2$ in the fully-polarized spin sector but find no evidence for this state within the models and parameters studied. Our results establish a unified numerical benchmark for correlated and topological phases in twisted bilayer MoTe$_2$ and clarify where multi-band physics is essential for a quantitative comparison with experiments.