Luttinger liquids with curvature: Density correlations and Coulomb drag effect

TL;DR

This paper studies how curvature in fermionic dispersion affects Luttinger liquids, especially in density correlations and Coulomb drag, revealing temperature-dependent behaviors and the impact of interwire interactions.

Contribution

It introduces a bosonization approach to analyze curvature effects in Luttinger liquids and provides exact calculations for Coulomb drag, including crossover behaviors and interaction effects.

Findings

Curvature modifies density correlation functions at finite temperatures.

Coulomb drag exhibits T^2 and T^5 regimes depending on temperature.

Interwire interactions lift degeneracy, affecting drag resistivity crossover.

Abstract

We consider the effect of the curvature in fermionic dispersion on the observable properties of Luttinger liquid (LL). We use the bosonization technique where the curvature is irrelevant perturbation, describing the decay of LL bosons (plasmon modes). When possible, we establish the correspondence between the bosonization and the fermionic approach. We analyze modifications in density correlation functions due to curvature at finite temperatures, T. The most important application of our approach is the analysis of the Coulomb drag by small momentum transfer between two LL, which is only possible due to curvature. Analyzing the a.c. transconductivity in the one-dimensional drag setup, we confirm the results by Pustilnik et al. for T-dependence of drag resistivity, R_{12} ~ T^2 at high and R_{12} ~ T^5 at low temperatures. The bosonization allows for treating both intra- and inter-wire electron-electron interactions in all orders, and we calculate exact prefactors in low-T drag regime. The crossover temperature between the two regimes is T_1 ~ E_F \Delta, with \Delta relative difference in plasmon velocities. We show that \Delta \neq 0 even for identical wires, due to lifting of degeneracy by interwire interaction, U_{12}, leading to crossover from R_{12} ~ U_{12}^2 T^2 to R_{12} \~ T^5/U_{12} at T ~ U_{12}.