Melting of electronic/excitonic crystals in 2D semiconductor moiré patterns: A perspective from the Lindemann criterion

Abstract

Using the Lindemann criterion, we analyzed the quantum and thermal melting of electronic/excitonic crystals recently discovered in 2D semiconductor moiré patterns. We show that the finite 2D screening of the atomically thin material can suppress (enhance) the inter-site Coulomb (dipolar) interaction strength, thus inhibits (facilitates) the formation of the electronic (excitonic) crystal. Meanwhile, a strong enough moiré confinement is found to be essential for realizing the crystal phase with a wavelength near 10 nm or shorter. From the calculated Lindemann ratio which quantifies the fluctuation of the site displacement, we estimate that the crystal will melt into a liquid above a critical temperature ranging from several tens Kelvin to above 100 K (depending on system parameters).

Dipolar interactions enhanced by two-dimensional dielectric screening in few-layer van der Waals structures

“…D (r) is weakened by the 2D dielectric screening of TMDs layers just as expected. However, for r in the order of several nm or larger which is the typical separation between nearest-neighbor moiré potential minima, V (B) D (r) shows an anomalous enhancement by the 2D screening length r 0 , which has also been notices in several early works [42,43]. This can be seen more clearly from the calculated enhancement factor…”

“…In addition, the enhanced dipolar interaction is found to be sensitive to the free carrier screening of surrounding graphene layers, suggesting it can be efficiently tuned through dielectric engineering. Such enhanced inter-site dipolar interactions may significantly change the potential energy and the stability of the correlated insulator phase formed by dipolar and quadrupolar excitons in moiré patterns of fewlayer van der Waals structures, and can also increase the importance of phonon modes as low-energy collective excitations of these correlated insulators when under external perturbations [43,51]. Furthermore, the strong inter-site interaction can facilitate the study of novel quantum states in condensed matter physics, e.g.…”