Abrikosov vortices in altermagnetic superconductors

TL;DR

This paper investigates how altermagnetic order affects magnetic vortex structures in superconductors, revealing elliptical vortices and nonreciprocal magnetization behaviors due to anisotropic effective mass and vortex interactions.

Contribution

It introduces the concept of elliptical vortices in altermagnetic superconductors and explains their orientation dependence on magnetic field reversal, highlighting new anisotropic vortex phenomena.

Findings

Vortices become elliptical with a major axis aligned along the crystallographic axis of maximal spin splitting.

Reversing the magnetic field component along the Nél vector reorients the vortices.

Nonreciprocal magnetization curves arise from vortex interaction energy differences.

Abstract

We study the penetration of an external magnetic field into a superconductor with collinear $d$-wave altermagnetic order. We demonstrate that instead of circular Abrikosov vortices, the magnetic field generates elliptical vortices with their major axis oriented along one of the crystallographic axis, along which the altermagnetic spin splitting is maximal. Upon reversing the component of the magnetic field parallel to the altermagnetic N\'eel vector, the vortices reorient towards the other crystallographic axis with maximal spin splitting. We demonstrate that this effect originates from an altermagnetism-induced anisotropy of the effective mass, which is controlled by the coupling between the external magnetic field and the N\'eel vector. As a consequence, a superconducting film hosting such altermagnetic order and containing pinning defects exhibits nonreciprocal magnetization curves under reversal of the magnetic field parallel to its N\'eel vector, due to the different vortex--vortex interaction energies for the two field orientations. Our results broaden the understanding of the coexistence of altermagnetism and superconductivity, both in materials hosting these orders intrinsically or in superconductor/altermagnet hybrid structures, and open new experimental avenues for exploring supercurrent vortices in these systems.