Effect of Time Reversal Symmetry Breaking on the Density of States in Small Superconducting Grains

TL;DR

This paper demonstrates that in ultra-small superconducting grains, magnetic impurities or fields eliminate the hard gap in the density of states, resulting in a soft gap with linear vanishing at low energies.

Contribution

It reveals how magnetic impurities and fields transform the density of states from a hard to a soft gap in small superconducting grains.

Findings

Hard gap is destroyed by magnetic impurities or fields.

Density of states exhibits linear soft gap behavior.

Soft gap persists even with infinitesimal magnetic effects.

Abstract

We show that in ultra-small superconducting grains any concentration of magnetic impurities or infinitely small orbital effect of magnetic field leads to destruction of the hard gap in the tunneling density of states. Instead, though exponentially suppressed at low energies, the tunneling density of states exhibits the ``soft gap'' behavior, vanishing linearly with excitation energy, as the energy approaches zero.