Anomalous density of states of a Luttinger liquid in contact with a superconductor

TL;DR

This paper investigates how connecting a Luttinger liquid to a superconductor alters its local density of states, revealing a strong enhancement near the Fermi level due to electron interactions and interface effects.

Contribution

It demonstrates the significant modification of the Luttinger liquid's density of states caused by superconductor coupling, highlighting the interplay of interactions and back-scattering.

Findings

Enhanced density of states near Fermi level

Power-law vanishing in isolated LL is replaced by enhancement

Anomalous behavior persists over large distances from the interface

Abstract

We study the frequency and space dependence of the local tunneling density of states of a Luttinger liquid (LL) which is connected to a superconductor. This coupling {\em strongly} modifies the single-particle properties of the LL. It significantly enhances the density of states near the Fermi level, whereas this quantity vanishes as a power law for an isolated LL. The enhancement is due to the interplay between electron-electron interactions and multiple back-scattering processes of low-energy electrons at the interface between the LL and the superconductor. This anomalous behavior extends over large distances from the interface and may be detected by coupling normal probes to the system.