Superconducting orbital magnetoelectric effect and its evolution across the superconductor-normal metal phase transition

Wen-Yu He,K T Law

doi:10.1103/physrevresearch.3.l032012

Abstract

Superconducting magnetoelectric effect, which is the current-induced magnetization in a superconductor, mainly focused on the spin magnetization in previous studies, but ignore the effect of the orbital magnetic moments carried by the paired Bloch electrons. In this work, we show that orbital magnetic moments in superconductors can induce large orbital magnetization in the presence of a current. We constructed a unified description for the current-induced spin and orbital magnetization across the superconductivity normal metal phase transition. We find that in a superconductor with uniform pairing, the current-induced magnetization at a given current density is the same as that in its normal metal state, while with the nonuniform superconducting pairing, the current-induced magnetization exhibits an abrupt change in magnitude near the superconductivity normal metal phase transition. Importantly, our theory predicts the orbital magnetoelectric effect in superconducting twisted bilayer graphene which has paired Bloch electrons with large orbital magnetic moments and negligible spin-orbit coupling. We propose that the measurement of the current-induced orbital magnetoelectric effect can be used to detect the possible nonuniform pairings in twisted bilayer graphene and other newly discovered superconductors with non-trivial Berry curvatures.

Highlights

The superconducting magnetoelectric effect is the current-induced magnetization in the superconducting state of a material
The magnetization that involves orbital magnetic moments’ polarization in the normal state of materials has been observed through the optical Kerr effect [53], nuclear magnetic resonance measurements [54], and the superconducting quantum interference device (SQUID) [28], and these techniques can all be used to detect the magnetization in the superconducting state [55,56,57]
In the recent direct image of orbital magnetism in twisted bilayer graphene (TBG) [28], it can be deduced from the measurement that the surface magnetism at the order of 10−4 μB/nm2 corresponds to the generated static magnetic field around 1 nT, so a SQUID device with a resolution of 0.1 nT will be able to detect the orbital magnetization induced by the current density at 1 nA/nm in superconducting TBG

Summary

Introduction

The superconducting magnetoelectric effect is the current-induced magnetization in the superconducting state of a material. The orbital magnetic moments from the paired Bloch electrons are involved in Cooper pairs, but the effect of orbital magnetic moments has never been studied in the superconducting magnetoelectric effect. It raises the problem of how the current-induced orbital magnetization would evolve in the phase transition from the normal metal state to the superconducting state. We point out that the measurement of current-induced orbital magnetization across the superconductor-normal metal phase transition in TBG can test whether superconducting TBG has uniform or nonuniform pairing order parameters. Both the normal and superconducting states of a material can be

Published by the American Physical Society

This magnetization is associated with the current density

Discussion