Topological $p_x+ip_y$ inter-valley coherent state in Moiré MoTe$_2$/WSe$_2$ heterobilayers

Abstract

Recently, a quantum anomalous Hall (QAH) state was observed in AB stacked moiré MoTe2/WSe2 heterobilayers at half-filling. More recent layer-resolved magnetic circular dichroism (MCD) measurements revealed that spin-polarized moiré bands from both the MoTe2 and the WSe2 layers are involved at the formation of the QAH state. This scenario is not expected by existing theories. In this work, we suggest that the observed QAH state is a new state of matter, namely, a topological px + ipy inter-valley coherent state (TIVC). We point out that the massive Dirac spectrum of the MoTe2 moiré bands, together with the Hund's interaction and the Coulomb interactions give rise to this novel QAH state. Through a self-consistent Hartree-Fock analysis, we find a wide range of interaction strengths and displacement fields that the px + ipy-pairing phase is energetically favourable. Besides explaining several key features of the experiments, our theory predicts that the order parameter would involve the pairing of electrons and holes with a definite momentum mismatch such that the pairing would generate a new unit cell which is three times the size of the original moiré unit cell, due to the order parameter modulations.

Valley-coherent quantum anomalous Hall state in AB-stacked MoTe2/WSe2 bilayers

“…Such a state could occur, for instance, via an exciton condensation mechanism near band inversion 34,35 . The excitonic mechanism could be important here given the weak interlayer coupling in AB-stacked TMD bilayers 20,34,35 . Future experiments with an ultrathin spacer between the TMD bilayers that quenches the interlayer tunneling while maintaining the strong Coulomb interaction and reasonable moiré potential could test the validity of the mechanism.…”

“…hybridization of states from different layers but from the same valley near the Fermi level [15][16][17][18][19][20] . The spin-polarized QAH state requires mixing states from different layers and different valleys; a correlated charge gap is opened at the Fermi level; the state is thus spontaneous layer-and valley-coherent 34,35 . Such a state could occur, for instance, via an exciton condensation mechanism near band inversion 34,35 .…”

“…The spin-polarized QAH state requires mixing states from different layers and different valleys; a correlated charge gap is opened at the Fermi level; the state is thus spontaneous layer-and valley-coherent 34,35 . Such a state could occur, for instance, via an exciton condensation mechanism near band inversion 34,35 . The excitonic mechanism could be important here given the weak interlayer coupling in AB-stacked TMD bilayers 20,34,35 .…”

“…hybridization of states from different layers and different valleys near the Fermi level, thus opening a correlated charge gap. Theoretical studies beyond the current frame of non-interacting valley states may be required to understand the experimental results 34,35 .…”

Intrinsically-multilayer moiré heterostructures

“…The observation of superconductivity and correlated insulators in twisted bilayer graphene [1,2] launched the study of "moiré materials," where two-dimensional materials with the same or similar [36][37][38][39][40][41][42][43][44][45] lattice constants are stacked at a small relative twist angle. This paradigm is naturally extended to trilayer stacking and beyond, both with some layers aligned [46][47][48][49][50][51][52] and with multiple twist angles [53][54][55][56][57][58].…”