Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals

TL;DR

This paper predicts that in two-dimensional clean metals, density-of-states fluctuations are anomalously strong and diverge as 1/T^2 at low temperatures due to Goldstone modes, contrasting with standard expectations.

Contribution

It introduces a novel prediction of divergence in density-of-states fluctuations in 2D metals caused by Goldstone modes, highlighting a significant deviation from traditional statistical behavior.

Findings

Density-of-states fluctuations diverge as 1/T^2 at low temperatures.

Goldstone modes cause anomalously strong fluctuations.

Standard statistics predict fluctuations of order T, not 1/T^2.

Abstract

It is shown that density-of-states fluctuations, which can be interpreted as the order-parameter susceptibility \chi_OP in a Fermi liquid, are anomalously strong as a result of the existence of Goldstone modes and associated strong fluctuations. In a 2-d system with a long-range Coulomb interaction, a suitably defined \chi_OP diverges as 1/T^2 as a function of temperature in the limit of small wavenumber and frequency. In contrast, standard statistics suggest \chi_OP = O(T), a discrepancy of three powers of T. The reasons behind this surprising prediction, as well as ways to observe it, are discussed.