Tunneling Anomaly in Superconductor above Paramagnetic Limit

TL;DR

This paper investigates the tunneling density of states in superconductors under strong magnetic fields, revealing a universal singularity caused by fluctuations even after the BCS gap vanishes, aligning with recent experimental findings.

Contribution

It analytically describes the DoS singularity near the paramagnetic limit across different system dimensions, extending understanding of superconducting fluctuations beyond the BCS gap.

Findings

Identifies a universal energy E^* where the DoS singularity occurs.

Shows the singularity's shape varies from a hard gap in small grains to a finite dip in higher dimensions.

Results are consistent with recent experimental observations in superconducting films.

Abstract

We study the tunneling density of states (DoS) in the superconducting systems driven by Zeeman splitting E_Z into the paramagnetic phase. We show that, even though the BCS gap disappears, superconducting fluctuations cause a strong DoS singularity in the vicinity of energies -E^* for electrons polarized along the magnetic field and E^* for the opposite polarization. The position of the singularity E^*=(1/2) (E_Z + \sqrt{E_Z^2- \Delta^2}) (where \Delta is BCS gap at E_Z=0) is universal. We found analytically the shape of the DoS for different dimensionality of the system. For ultrasmall grains the singularity has the form of the hard gap, while in higher dimensions it appears as a significant though finite dip. Our results are consistent with recent experiments in superconducting films.