Odd-frequency Cooper pairs and zero-energy surface bound states in superfluid 3He

TL;DR

This paper investigates the formation of odd-frequency Cooper pairs near the surface of superfluid 3He, deriving a formula linking pair amplitude and local density of states, and relates these to observed surface states.

Contribution

The study provides a general formula connecting odd-frequency pair amplitude with local density of states, applicable to arbitrary boundary conditions, and offers numerical analysis for superfluid 3He-B.

Findings

Odd-frequency pairs are closely related to surface density of states.

Derived a universal formula linking pair amplitude and local density of states.

Numerical results interpret midgap surface states as odd-frequency states.

Abstract

We study the odd-frequency Cooper pairs formed near the surface of superfluid 3He. The odd-frequency pair amplitude is closely related to the local density of states in the low energy limit. We derive a formula relating explicitly the two quantities. This formula holds for arbitrary boundary condition at the surface. We also present some numerical results on the surface odd-frequency pair amplitude in superfluid 3He-B. Those analytical and numerical results allow one to interpret the midgap surface density of states, observed recently by transverse acoustic impedance measurements on superfluid 3He-B, as the manifestation of the surface odd-frequency state.