Symmetric Wannier states and tight-binding model for quantum spin Hall bands in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:mi>B</mml:mi></mml:mrow></mml:math>-stacked <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mtext>MoTe</mml:mtext><mml:mn>2</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mtext>WSe</mml:mtext><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
Xun-Jiang Luo, Minxuan Wang, Fengcheng Wu
Abstract
Motivated by the observation of topological states in $AB$-stacked ${\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}$, we construct the symmetry-adapted Wannier states and tight-binding model for the quantum spin Hall bands in this system. Our construction is based on the symmetry analysis of Bloch states obtained from the continuum moir\'e Hamiltonian. For model parameters extracted from first-principles calculations, we find that the quantum spin Hall bands can be described by a tight-binding model defined on a triangular lattice with two Wannier states per site per valley. The two Wannier states in a given valley have the same Wannier center but different angular momenta under threefold rotation. The tight-binding model reproduces the energy spectrum and accurately describes the topological phase transition induced by the out-of-plane displacement field. Our study sheds light on the topological states in moir\'e transition metal dichalcogenides bilayers and provides a route to addressing the many-body physics in $AB$-stacked ${\mathrm{MoTe}}_{2}/{\mathrm{WSe}}_{2}$.