Quantum Lifshitz points in an altermagnetic metal

TL;DR

This paper predicts two distinct quantum Lifshitz points in d-wave altermagnetic metals under magnetic fields, linking different phases and revealing unique transition behaviors influenced by the origin of the FFLO state.

Contribution

It introduces the concept of two types of quantum Lifshitz points in altermagnetic metals and characterizes their different transition behaviors and thermal sensitivities.

Findings

Two tri-critical quantum Lifshitz points identified in altermagnetic metals.

Distinct transition orders near field-driven and altermagnetism-driven Lifshitz points.

Altermagnetism-driven Lifshitz point is more sensitive to temperature effects.

Abstract

We predict the existence of two tri-critical quantum Lifshitz points in recently discovered $d$-wave altermagnetic metals subjected to an external magnetic field. These points connect a spatially modulated Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase, a uniform polarized Bardeen--Cooper--Schrieffer (BCS) superconducting phase, and the normal metallic phase in a nontrivial manner. Depending on whether the FFLO state is primarily induced by the magnetic field or by $d$-wave altermagnetism, we classify the corresponding Lifshitz points as field-driven or altermagnetism-driven, respectively. Notably, the two types exhibit distinct behaviors: the transition from the FFLO phase to the polarized BCS phase is first-order near the field-driven Lifshitz point, as might be expected, whereas it becomes continuous near the altermagnetism-driven Lifshitz point. We further explore the effects of finite temperature and find that the altermagnetism-driven Lifshitz point is significantly more sensitive to thermal fluctuations.