Conductivity between Luttinger liquids: coupled chains and bilayer graphene

TL;DR

This paper demonstrates that in coupled Luttinger liquids, such as bilayer graphene, the transverse optical conductivity exhibits an anomalous power-law decay with frequency, revealing non-trivial interaction effects.

Contribution

The study provides a rigorous proof of the anomalous power-law behavior of transverse conductivity in coupled Luttinger liquids using exact Renormalization Group methods.

Findings

Transverse optical conductivity decreases as a power law with frequency.

Behavior observed in coupled chains and bilayer graphene models.

Results highlight non-Fermi liquid properties in these systems.

Abstract

The conductivity properties between Luttinger liquids are analyzed by exact Renormalization Group methods. We prove that in a two chain system or in a model of bilayer graphene, described by two coupled fermionic honeycomb lattices interacting with a gauge field, the transverse optical conductivity at finite temperature is anomalous and decreasing together with the frequency as a power law with Luttinger liquid exponent.