Abstract
Geometrical moir\'e patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moir\'e superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band edges. Such hybridization determines the optical activity of interlayer excitons in transition-metal dichalcogenide (TMD) heterostructures, as well as energy shifts in the exciton spectrum. We show that the resonantly hybridized exciton (hX) energy should display a sharp modulation as a function of the interlayer twist angle, accompanied by additional spectral features caused by umklapp electron-photon interactions with the mSL. We analyze the appearance of resonantly enhanced mSL features in absorption and emission of light by the interlayer exciton hybridization with both intralayer A and B excitons in $\mathrm{MoSe}_2/\mathrm{WS}_2$, $\mathrm{MoTe}_2/\mathrm{MoSe}_2$, $\mathrm{MoSe}_2/\mathrm{MoS}_2$, $\mathrm{WS}_2/\mathrm{MoS}_2$, and $\mathrm{WSe}_2/\mathrm{MoSe}_2$.
Highlights
Van der Waals heterostructures consist of layers of atomically thin two-dimensional (2D) crystals, vertically stacked and held together by vdW forces [1,2]
We have studied the interplay between band alignment and the presence of emergent moiré superlattices in twisted heterobilayers of transition-metal dichalcogenides (TMDs)
Our results show that the influence of higher moiré superlattice minibands for the low-energy electron band structure in these heterobilayers becomes increasingly important as the interlayer band edges offset is reduced; in other words, that resonant interlayer hybridization amplifies the moiré superlattice effects on the electronic structure
Summary
Van der Waals (vdW) heterostructures consist of layers of atomically thin two-dimensional (2D) crystals, vertically stacked and held together by vdW forces [1,2]. It was shown that matrix elements tcv and tvc exist, representing electron hopping between the conduction and valence bands of different layers, which are significantly smaller than tc As the latter couple states separated by energies comparable to the heterostructure’s band gap, we neglect them in the following. When these ratios are small, one can treat Ht perturbatively, in terms of the kdependent energy corrections produced by the tunneling processes, which in real space form a periodic potential [44,45] This approach to describing the effects of a moiré superlattice on the electronic states has been used in Ref. √ with eigenvalues ε + 2 Re V and ε − Re V ± 3|Im V |, which allow a gap opening at κ
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