Unconventional superconductivity of an altermagnetic metal: Polarized BCS and inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states

TL;DR

This paper explores the complex phase diagram of two-dimensional altermagnetic superconductors under magnetic fields, revealing novel phase transitions and states like polarized BCS and FFLO, with implications for unconventional magnets and ultracold atom systems.

Contribution

It introduces the effects of altermagnetism on superconductivity, revealing new phase transitions, Lifshitz points, and the coexistence of polarized BCS and FFLO states in 2D systems.

Findings

Altermagnetism induces a second-order transition from BCS to FFLO state.

Magnetic field creates a polarized BCS superconductor with spin imbalance.

Presence of altermagnetism narrows FFLO phase window and introduces Lifshitz points.

Abstract

We investigate the superconductivity of two-dimensional spin-1/2 Fermi systems with $d$-wave altermagnetism under external magnetic field near zero temperature. At large altermagnetic coupling without magnetic field, we show that altermagnetism drives a second-order phase transition from the standard Bardeen-Cooper-Schrieffer (BCS) state to an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The inclusion of magnetic field turns the BCS state into a long-sought polarized BCS superconductor with spin-population imbalance. It also shrinks the parameter window of the FFLO state and eventually leads to a nontrivial quantum tri-critical Lifshitz point, where two second-order phase transition lines between the polarized BCS, FFLO and normal states intersect. At small altermagnetic coupling, we find the usual route to the FFLO state driven by magnetic field. The presence of the altermagnetic coupling narrows the phase window of the FFLO state and creates another quantum Lifshitz point, where a first-order transition curve meets a second-order transition line. Between the two Lifshitz points, the transition from the polarized BCS state to the normal state is smooth. Our predicted rich phase diagram is relevant to some recently discovered unconventional magnets, including RuO$_{2}$ that exhibits a relatively high superconducting temperature in the thin film limit under applied strain. Our results of unconventional superfluidity are also testable in ultracold atom laboratories, where a spin-1/2 altermagnetic Fermi gas might be realizable upon loading into two-dimensional Hubbard lattices.