# Quantum phase fluctuations and density of states in superconducting nanowires

## TL;DR

This paper investigates how quantum phase fluctuations in ultrathin superconducting nanowires alter the electron density of states, leading to smearing of the gap singularity and subgap quasiparticle states, with implications for tunneling experiments.

## Contribution

It provides a non-perturbative theoretical framework for understanding quantum phase fluctuation effects on the DOS in superconducting nanowires, accounting for dissipative plasma modes.

## Key findings

- Quantum fluctuations smear the DOS singularity near the gap at non-zero temperature.
- Large wire impedance suppresses the singularity even at zero temperature.
- DOS exhibits power-law behavior above the superconducting gap.

## Abstract

We argue that quantum fluctuations of the phase of the order parameter may strongly affect the electron density of states (DOS) in ultrathin superconducting wires. We demonstrate that the effect of such fluctuations is equivalent to that of a quantum dissipative environment formed by sound-like plasma modes propagating along the wire. We derive a non-perturbative expression for the local electron DOS in superconducting nanowires which fully accounts for quantum phase fluctuations. At any non-zero temperature these fluctuations smear out the square-root singularity in DOS near the superconducting gap and generate quasiparticle states at subgap energies. Furthermore, at sufficiently large values of the wire impedance this singularity is suppressed down to $T=0$ in which case DOS tends to zero at subgap energies and exhibits the power-law behavior above the gap. Our predictions can be directly tested in tunneling experiments with superconducting nanowires.