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arXiv:2505.10196 · Physical review. B./Physical review. B

Unconventional superconductivity of an altermagnetic metal: Polarized BCS and inhomogeneous FFLO states

Hui Hu, Zhao Liu, Xia-Ji Liu

Published Oct 16, 2025• 10 citations
arXivHTMLPDF

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 a 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 tricritical 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 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 ${\mathrm{RuO}}_{2}$ 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.

DOI
10.1103/whm1-76jc

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We present an analytical study of the ground-state phase diagram for dilute two-dimensional spin-1/2 Fermi gases exhibiting ddd-wave altermagnetic spin splitting under sss-wave pairing. Within the Bogoliubov-de Gennes mean-field framework, four distinct phases are identified: a Bardeen-Schrieffer-Cooper-type superfluid, a normal metallic phase, a nodal superfluid with topological Bogoliubov Fermi surfaces (TBFSs), and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states with finite center-of-mass momentum. Among these, the FFLO states and TBFSs exemplify two unconventional forms of superconductivity. Considering the simplicity of this model, with only one band, zero net magnetization, and sss-wave paring, the emergence of both unconventional phases underscores the pivotal role of altermagnetic spin splitting in enabling exotic pairing phenomena. This analytical study not only offers a valuable benchmark for future numerical simulations, but also provides a concrete experimental roadmap for realizing FFLO states and TBFSs in altermagnets.
We discuss a detailed phase diagram and other microscopic characteristics on the applied magnetic field-temperature (H(a)-T) plane for a simple model of a correlated fluid represented by a two-dimensional (2D) gas of heavy quasiparticles with masses dependent on the spin direction and the effective field generated by the electron correlations. The consecutive transitions between the Bardeen-Cooper-Schrieffer (BCS) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases are either continuous or discontinuous, depending on the values of H(a) and T. In the latter case, weak metamagnetic transitions occur at the BCS-FFLO boundary. We single out two different FFLO phases, as well as a re-entrant behaviour of one of them at high fields. The results are compared with those for ordinary Landau quasiparticles in order to demonstrate the robustness of the FFLO states against the BCS state for the case with spin-dependent masses (SDM). We believe that the mechanism of FFLO stabilization by SDM is generic: other high-field low-temperature (HFLT) superconducting phases should benefit from SDM as well.
We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground-state phase diagrams including some unconventional superconducting phases such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, and the $\ensuremath{\eta}$ phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. It allows us to determine optimal regimes for the FFLO phase as well as $\ensuremath{\eta}$-pairing stability. We also investigate the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, at T=0T=0T=0. Finally, the obtained results show that in spite of the occurrence of the Lifshitz transition induced by an external magnetic field, the superconducting state can still exist in the system, at higher magnetic field values.
We study s-wave pairing of population imbalanced Fermi atoms in quasi two dimensions using a mean field theory. At zero temperature, we map out the phase diagram in the entire Bardeen, Cooper and Schrieffer-Bose Einstein condensation (BCS-BEC) crossover region by investigating the effect of weak atom tunneling between layers. We find that the superfluid phase stabilizes as one decreases the atom tunneling between layers. This allows one to control the superfluid-normal first order phase transition by tuning a single experimental parameter. Further, we find that a tunneling induced polarized superfluid phase appears in a narrow parameter region in the BEC regime. At Finite temperatures, we use a Landau-Ginzberg functional approach to investigate the possibility of spatially inhomogeneous Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase in the weakly interacting BCS limit near the tricritical point of spatially homogenous superfluid, FFLO, and normal phases. We find that the normal-FFLO phase transition is first order transition as opposed to the continues transition predicted in zero temperature theories.
We systematically investigate the emergence of finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductivity in a square lattice Hubbard model with finite filling, driven by either dxyd_{xy}dxy​ -wave or dx2−y2d_{x^{2}-y^{2}}dx2−y2​ -wave altermagnetic order in the presence of on-site sss -wave attractive interactions. Our study combines mean-field calculation in the superconducting phase with pairing instability analysis of the normal state, incorporating the next-nearest-neighbor hopping in the single-particle dispersion relation. We demonstrate that the two types of altermagnetism have markedly different impacts on the stabilization of FFLO states. Specifically, dxyd_{xy}dxy​ -wave altermagnetism supports FFLO superconductivity over a broad parameter regime at low fillings, whereas dx2−y2d_{x^{2}-y^{2}}dx2−y2​ -wave altermagnetism only induces FFLO pairing in a narrow range at high fillings. Furthermore, we find that the presence of a Van Hove singularity in the density of states tends to suppress FFLO superconductivity. These findings may provide guidance for experimental exploration of altermagnetism-induced FFLO states in real materials with more complex electronic structures.
We theoretically explore a promising route to achieve the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a spin-imbalanced ultracold Fermi gas. In the current stage of cold atom physics, search for this exotic Fermi superfluid is facing two serious difficulties: One is the desperate destruction of the FFLO long-range order by FFLO pairing fluctuations, which precludes entering the phase through a second-order transition, even in three dimension. The other is the fierce competition with the phase separation into the BCS (Bardeen-Cooper-Schrieffer) state and the spin-polarized normal state. By including strong FFLO pairing fluctuations within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that the anisotropy of Fermi surface introduced by an optical lattice makes the FFLO state stable against the paring fluctuations. This stabilized FFLO state is also found to be able to overcome the competition with the phase separation under a certain condition. Since the realization of unconventional Fermi superfluids is one of the most exciting challenges in cold atom physics, our results would contribute to the further development of this field.