Crystal-field effects in the formation of Wigner-molecule supercrystals in moir\'e TMD superlattices

Abstract

For moir\'e bilayer TMD superlattices, full-configuration-interaction (FCI) calculations are presented that take into account both the intra-moir\'e-quantum-dot (MQD) charge-carrier Coulombic interactions, as well as the crystal-field effect from the surrounding moir\'e pockets (inter-moir\'e-QD interactions). The effective computational embedding strategy introduced here allows for an FCI methodogy that enables the complete interpretation of the counterintuitive experimental observations reported recently in the context of moir\'e TMD superlattices at integer fillings $\nu=2$ and 4. Two novel states of matter are reported: (i) a genuinely quantum-mechanical supercrystal of $sliding$ Wigner molecules (WMs) for unstrained moir\'e TMD materials (when the crystal field is commensurate with the trilobal symmetry of the confining potential in each embedded MQD) and (ii) a supercrystal of $pinned$ Wigner molecules when the crystal field is incommensurate with the trilobal symmetry or straining of the whole material is involved. The case of $\nu=3$ is an exception, in that even the unstrained case is associated with a supercrystal of pinned WMs, which is due to the congruence of intrinsic (that of the WM) and external (that of the confining potential of the MQD) $C_3$ point-group symmetries. Furthermore, it is shown that the unrestricted Hartree-Fock approach fails to describe the supercrystal of sliding WMs in the unstrained case, providing a qualitative agreement only in the case of a supercrystal of pinned WMs