Topological $p_x+i{p}_y$ 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 MoTe${}_2$/WSe${}_2$ heterobilayers at half-filling. More recent layer-resolved magnetic circular dichroism (MCD) measurements revealed that spin-polarized moiré bands from both the MoTe${}_2$ and the WSe${}_2$ 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 $p_x+i{p}_y$ inter-valley coherent state (TIVC). We point out that the massive Dirac spectrum of the MoTe${}_2$ 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 $p_x+i{p}_y$-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.

13 pages, 6 figures

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• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe${}_2$
• Topological Kondo semimetals emulated in hetero-bilayer transition metal dichalcogenides