Moiré quantum chemistry: Charge transfer in transition metal dichalcogenide superlattices

Transition metal dichalcogenide (TMD) bilayers have recently emerged as a robust and tunable moiré system for studying and designing correlated electron physics. In this Rapid Communication, by combining a large-scale first-principles calculation and continuum model approach, we provide an electronic structure theory that maps long-period TMD heterobilayer superlattices onto diatomic crystals with cations and anions. We find that the interplay between the moiré potential and Coulomb interaction leads to filling-dependent charge transfer between different moiré superlattice regions. We show that the insulating state at half filling found in recent experiments on $\mathrm{W}{\mathrm{Se}}_2/\mathrm{W}{\mathrm{S}}_2$ is a charge-transfer insulator rather than a Mott-Hubbard insulator. Our work reveals the richness of simplicity in moiré quantum chemistry.

Figure 1

(a) Lattice structure of $MM, MX, XM$ spots for $AA$ stacking heterobilayer ($M$ stands for metal atom and $X$ stands for chalcogen atom). (b) Real-space moiré pattern of a TMD heterobilayer with $\delta =4.0\%$, where $MM, MX, XM$ spots within one supercell are labeled, and a schematic diagram for the moiré potential landscape for $\varphi =0$ and $\varphi =\pi /4$, along the path from $MM$ to $XM$ and $MX$ spots as indicated by the array in the left figure.

Figure 2

(a) Brillouin zone (BZ) folding in a $\mathrm{W}{\mathrm{Se}}_2/\mathrm{W}{\mathrm{S}}_2$ moiré superlattice, where $a_{{\text{WSe}}_2}/a_{{\text{WS}}_2}$ is taken as 6/5 for the illustrative purpose. (b) Schematic low-energy band structure from two layers where $\pm {\mathit{K}}_{t\left(b\right)}$ are two valleys of the top (bottom) layer. (c) DFT band structure (open circle) and continuum model band structure (blue lines) at $\theta =5.{68}^{\circ }$. (d) Continuum model band structures of $\mathrm{W}{\mathrm{Se}}_2/\mathrm{W}{\mathrm{S}}_2$ at $\theta =0^{\circ }$.

Figure 3

(a) Filling factor $n/n_s$ as a function of chemical potential $\mu$ in a $\mathrm{W}{\mathrm{Se}}_2/\mathrm{W}{\mathrm{S}}_2$ system at $\theta =3^{\circ }$ with $\epsilon =12,20,50$. (b) and (c) are the charge distributions at half filling when $\epsilon =50$ and 12.

Figure 4

(a) TMD heterobilayers can be described by different limits and tight-binding models for the first and second moiré bands. Each colored line denotes a TMD bilayer. The nearly free limit and tight-binding limit are separated by the dashed line where $W=\mathrm{\Delta }$. (b) Schematic phase diagram at half filling $n=1$. The solid curve illustrates the landscape of the moiré potential, and the solid and open circles denote occupied holes at $n=1$ and additional holes above $n=1$, respectively. In phases (II) and (III), LHB, UHB, and $MX$ denote the lower Hubbard band, upper Hubbard band, and $MX$ anion band, respectively. The densities of states are shown for all phases.