Is disorder a friend or a foe to melting of Wigner-Mott insulators?

Abstract

Wigner crystals are extremely fragile, which is shown to result from very strong geometric frustration germane to long-range Coulomb interactions. Physically, this is manifested by a very small characteristic energy scale for shear density fluctuations, which are gapless excitations in a translationally invariant system. The presence of disorder, however, breaks translational invariance, thus suppressing gapless excitations and pushing them to higher density. We illustrate this general principle by explicit microscopic model calculations, showing that this mechanism very effectively stabilizes disordered Wigner lattices to much higher temperatures and densities than in the clean limit. On the other hand, we argue that in two dimensions disorder significantly ``smears" the melting transition, producing spatial coexistence of solid-like and liquid-like regions -- just as recently observed in STM experiments. Our results paint a new physical picture for melting of Wigner-Mott solids in two dimensions, corresponding to a Mott-Hubbard model with spatially varying local electronic bandwidth.

Figures (3)

• Figure 1: This schematic figure illustrates how the fraction of melted sites increases as the electron density is tuned from low to high from left to right. The individual Gaussian wave packets are constructed using an Einstein-phonon approximation. Contour lines are drawn around regions that have locally melted; bright yellow denotes unmelted sites, whereas faded blue indicates melted sites. Here, the disorder strength used is $x_d=2\,\xi_0$, where $\xi_0$ is the bare bandwidth of the transverse phonon at the given density (see Ref. SM).
• Figure 2: The phase diagram of a two-dimensional electron system as a function of electron density and temperature for different disorder strengths. The solid red line denotes the melting line estimated from the global (bond) Lindemann ratio. The color gradient indicates the fraction of melted sites, calculated from the local (bond) Lindemann ratio. The color gradient goes from blue (dark shade) at zero to yellow (light shade) at one. The disorder strength is given in units of $\xi_0$, which is the bare bandwidth of the transverse phonon at the given density. (a) The clean limit is presented where there is "nominally" a phase transition expected. (b) The disorder strength is given by $x_d=0.5\,\xi_0$ (c) The disorder strength is given by $x_d=2\,\xi_0$. As discussed in the main text, in the presence of disorder—which breaks translational symmetry—the melting/freezing transition that usually distinguishes a solid from a liquid is no longer well defined. Therefore, we do not label the phases in that way in the figures. (b) and (c).
• Figure 3: (a) The local (bond) Lindemann ratio is plotted against the local disorder strength for three different densities at $x_d=2\,\xi_0$. The horizontal black dashed line marks the critical Lindemann ratio at which local melting occurs, implying that, depending on the local disorder strength, different lattice sites can undergo melting independently. (b) The probability distributions of the local bond Lindemann ratio for these same disorder strengths are numerically calculated and shown here.