Low-energy properties of fractional helical Luttinger liquids

TL;DR

This paper explores the low-energy behaviors of fractional helical Luttinger liquids, revealing unique transport properties, tunneling density of states, and conductance characteristics that differ from conventional systems.

Contribution

It provides a detailed analysis of the optical conductivity, density of states, and conductance in fractional helical Luttinger liquids, highlighting their distinct low-energy properties and independence from Luttinger parameters.

Findings

Low-energy tunneling density of states vanishes in fractional wires.

Conductance of fractional helical Luttinger liquids is non-integer.

Conductance depends only on the relative locking of charge and spin, not on Luttinger parameters.

Abstract

We investigate the low-energy properties of (quasi) helical and fractional helical Luttinger liquids. In particular, we calculate the Drude peak of the optical conductivity, the density of states, as well as charge transport properties of the interacting system with and without attached Fermi liquid leads at small and large (compared to the gap) frequencies. For fractional wires, we find that the low energy tunneling density of states vanishes. The conductance of a fractional helical Luttinger liquid is non-integer. It is independent of the Luttinger parameters in the wire, despite the intricate mixing of charge and spin degrees of freedom, and only depends on the relative locking of charge and spin degrees of freedom.