Magnetic-Field-Induced Odd-Frequency Superconductivity in MgB$_2$

TL;DR

This paper provides ab initio evidence that applying a magnetic field induces odd-frequency superconductivity in MgB₂, revealing a new state with distinct experimental signatures.

Contribution

The study demonstrates, through solving anisotropic Eliashberg equations, the emergence of odd-frequency pairing in MgB₂ under magnetic fields, a phenomenon previously unobserved in bulk materials.

Findings

Odd-frequency pairing appears under magnetic field in MgB₂.

Full momentum, frequency, and spin dependence of pair amplitudes is characterized.

Predicted experimental signatures in tunnelling experiments.

Abstract

In all known superconductors the pairing of fermions is not sensitive to the sign of their time-argument difference, leading to a Cooper pair wavefunction that is even in time/frequency. Four decades ago it was suggested that odd-frequency superconductivity should in principle be realizable. However, observation of odd-frequency superconductivity in bulk materials has remained elusive. Solving the field-dependent anisotropic Eliashberg equations, we present \textit{ab initio} evidence for the emergence of odd-frequency pairing under an applied magnetic field in the archetypal superconductor MgB$_2$. We provide the full momentum, frequency and spin resolved dependence and magnetic field-temperature phase diagrams of the even and odd-frequency superconducting pair amplitudes and predict fingerprints of the odd-frequency state in tunnelling experiments.