Abstract
Wigner crystals are prime candidates for the realization of regular electron lattices under minimal requirements on external control and electronics. However, several technical challenges have prevented their detailed experimental investigation and applications to date. We propose an implementation of two-dimensional electron lattices for quantum simulation of Ising spin systems based on self-assembled Wigner crystals in transition-metal dichalcogenides. We show that these semiconductors allow for minimally invasive all-optical detection schemes of charge ordering and total spin. For incident light with optimally chosen beam parameters and polarization, we predict a strong dependence of the transmitted and reflected signals on the underlying lattice periodicity, thus revealing the charge order inherent in Wigner crystals. At the same time, the selection rules in transition-metal dichalcogenides provide direct access to the spin degree of freedom via Faraday rotation measurements.
Highlights
Ever since its theoretical inception 85 years ago [1], Wigner crystallization has stimulated both theoretical and experimental research to find unambiguous evidence for this elusive state of matter
We demonstrate the potential of scalable quantum simulators based on two-dimensional Wigner crystals (WCs) in transition-metal dichalcogenides (TMDs) and propose an all-optical detection scheme for charge ordering and partial spin information in these systems
We address the optical detection of charge ordering in TMD-based WCs and consider an incoming (z < 0) Gaussian laser beam Ein(r) with wavelength λ focused to a spot on the electron lattice (z = 0) at a tilt angle θ
Summary
Ever since its theoretical inception 85 years ago [1], Wigner crystallization has stimulated both theoretical and experimental research to find unambiguous evidence for this elusive state of matter. Monolayer transition-metal dichalcogenides (TMDs) [14] and TMD-based moiré superlattices [15,16,17] are unique platforms for realizing strongly correlated systems and the study of WCs, in particular, owing to the combination of reduced screening in two dimensions and a relatively high effective electron mass. Their optical band gap offers exciting possibilities to probe quasiparticle excitations, e.g., excitons or trions [18,19,20,21] optically [22,23,24]. The scheme possesses three key properties: (i) It provides clear evidence for Wigner crystallization in monolayer TMDs. (ii) Under conditions specified below, the detection scheme is noninvasive and leaves charge and spin order intact. (iii) Optical selection rules provide spin-selective addressability, which is a crucial requirement for quantum simulation
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