Position- and momentum-dependent interlayer couplings in two-dimensional semiconductor moiré superlattices

In recent years, various novel phenomena have been observed in two-dimensional semiconductor moiré systems, including the excitons, strongly-correlated electronic states and vertical ferroelectricity. To gain an insight into underlying physical mechanisms of these intriguing phenomena, it is essential to understand interlayer coupling form electrons systems. this work, position- momentum-dependent effects superlattices are investigated. Starting from monolayer Bloch basis, between two treated as a perturbation, matrix elements commensurate incommensurate bilayer structures obtained, which found depend on momentum translation layers. Under effect external potential, localized wavepackets, their couplings wavepacket width well at center position. Meanwhile momentum-dependence results very different forms for ground-state <inline-formula><tex-math id="M8">\begin{document}$ \rm{S} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="2-20222046_M8.jpg"/><graphic xlink:href="2-20222046_M8.png"/></alternatives></inline-formula>-type excited-state id="M9">\begin{document}$ {\rm{P}}^{\pm } xlink:href="2-20222046_M9.jpg"/><graphic xlink:href="2-20222046_M9.png"/></alternatives></inline-formula>-type wavepackets. It shown that position where id="M10">\begin{document}$ xlink:href="2-20222046_M10.jpg"/><graphic xlink:href="2-20222046_M10.png"/></alternatives></inline-formula>-type wavepackets vanishes, id="M11">\begin{document}$ xlink:href="2-20222046_M11.jpg"/><graphic xlink:href="2-20222046_M11.png"/></alternatives></inline-formula>-type id="M12">\begin{document}$ {\rm{P}}^{+} xlink:href="2-20222046_M12.jpg"/><graphic xlink:href="2-20222046_M12.png"/></alternatives></inline-formula>-type (or id="M13">\begin{document}$ xlink:href="2-20222046_M13.jpg"/><graphic xlink:href="2-20222046_M13.png"/></alternatives></inline-formula>- type id="M14">\begin{document}$ {\rm{P}}^{-} xlink:href="2-20222046_M14.jpg"/><graphic xlink:href="2-20222046_M14.png"/></alternatives></inline-formula>-type wavepacket) reaches maximum strength. This can be used manipulate valley-selective transport through electric optical fields. Besides, ferroelectricity recently discovered systems attributed charge redistribution induced by conduction valence bands Using obtained combined with simplified tight-binding model monolayer, dipole density calculated whose order magnitude accord experimental observations.