From fractional Chern insulators to topological electronic crystals in moiré MoTe2: quantum geometry tuning via remote layer

The quantum geometry of Bloch wavefunctions,encoded in the Berry curvature and quantum metric, is believed to be a decisive ingredient in stabilizing fractional quantum anomalous Hall (FQAH) effect(i.e., fractional Chern insulator, FCI, at zero magnetic field), against competing symmetry-breaking phases.A direct experimental demonstration of quantum geometry-driven switching between distinct correlated topological phases, however, has been lacking. Here, we report experimental evidence of such a switch in a high-quality 3.7 twisted MoTe2 (tMoTe2) device consisting of both A-A bilayer and A-AB trilayer regions. While composite Fermi liquid CFL/FQAH phases are established in A-A tMoTe2,the A-AB region-effectively an A-A moire bilayer proximitized by a remote B layer-develops a series of topological electronic crystal (TEC, also referred to as generalized QAH crystal, QAHC) states with integer quantized Hall conductance at commensurate fractional fillings v=1/2, 2/3, and an incommensurate filling factor v=0.53.The electrostatic phase diagram is mapped out by combined transport and optical measurements, showing that these TEC states emerge within the first moir'e valence band prior to any charge transfer to the B layer. Exact diagonalization (ED) incorporating the remote-layer-induced intralayer potential demonstrates a transition from a CFL-like manifold in the A-A limit to a Chern number C=1 ground-state consistent with a TEC at v=1/2 , accompanied by the further breakdown of ideal band geometry. Our results provide experimental evidence of quantum geometry-tuned competition between FQAH/CFL and TEC phases in a moiré Chern band and pave the way for further exploring correlation-driven topological phenomena by tuning quantum geometry.