Enhancement in tunneling density of states in Luttinger liquid -- role of non-local interaction

TL;DR

This paper introduces a theoretical model showing that non-local interactions in a Luttinger liquid can lead to an unexpected enhancement of the local tunneling density of states, contrary to the typical suppression.

Contribution

The study demonstrates that non-local, repulsive interactions can cause TDOS enhancement in a stable Luttinger liquid, highlighting the role of broken parity symmetry.

Findings

TDOS enhancement occurs in a stable RG regime.

Non-local interactions can reverse the usual TDOS suppression.

Parity symmetry breaking is crucial for TDOS enhancement.

Abstract

Power law suppression of local electronic tunneling density of states (TDOS) in the zero-energy limit is a hallmark of Luttinger liquid (LL) phase of the interacting 1-D electron system. We present a theoretical model which hosts LL state with the surprising feature of enhancement rather than suppression in local TDOS originating from non-local and repulsive density-density interactions. Importantly, we find enhancement of TDOS in the manifold of parameter space where the system is stable in the renormalization group (RG) sense. We argue that enhancement of TDOS along with RG stability is possible only when the system has broken parity symmetry about the position of local TDOS enhancement. Such a model could be realized on the edge states of a bi-layer quantum Hall system where both intra-layer and inter-layer density-density interactions are present mimicking the role of local and non-local interactions respectively.