Stabilization of the surface CDW order parameter by long-range Coulomb interaction

TL;DR

This paper theoretically demonstrates that long-range Coulomb interactions can stabilize surface charge density wave order in 2D systems, even at finite temperatures, by suppressing phase fluctuations.

Contribution

It introduces a model showing how unscreened Coulomb interactions stabilize 2D CDW order at the surface, a novel insight into surface phase stability.

Findings

Long-range Coulomb interactions stabilize finite CDW order at finite temperatures.

Screened Coulomb interactions lead to slow decay of the order parameter.

Phase fluctuations decay as a power-law with a small exponent.

Abstract

We study theoretically formation of two-dimensional (2D) charge density wave (CDW) in a system of conducting chains at the surface of an insulator due to interaction of quasi 1D surface electrons with phonons. We show that the unscreened long-range Coloumb interaction between the charges induced by fluctuations of the CDW phase stabilizes the finite order parameter value at finite temperatures, and thus the long-range order (LRO) exists. In the case of screened Coloumb interaction the phase fluctuations suppress the phase transition, but decay of the order parameter is rather slow, it obeys a power-law $<\Delta^*(r) \Delta(0)> \propto r^{-\gamma}$ with small exponent $\gamma$