Melting of electronic and excitonic crystals in 2D semiconductor moir\'e patterns: a perspective from the Lindemann criterion

Abstract

Using the Lindemann criterion, we analyzed the quantum and thermal melting of electronic and excitonic crystals recently discovered in 2D semiconductor moir\'e 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 moir\'e confinement is found to be essential for realizing the crystal phase with a lattice constant 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 temperature in the order of several tens Kelvin