Fulde-Ferrell-Larkin-Ovchinnikov States and Topological Bogoliubov Fermi Surfaces in Altermagnets: an Analytical Study

We present an analytical study of the ground-state phase diagram for dilute two-dimensional spin-1/2 Fermi gases exhibiting $d$-wave altermagnetic spin splitting under $s$-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 $s$-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.

💡 Research Summary

This paper presents a comprehensive analytical investigation of the zero‑temperature phase diagram of a dilute two‑dimensional spin‑½ Fermi gas that experiences a d‑wave altermagnetic (AM) spin splitting while undergoing conventional s‑wave pairing. Using the Bogoliubov‑de‑Gennes (BdG) mean‑field framework, the authors identify four distinct ground‑state phases: (i) a conventional Bardeen‑Cooper‑Schrieffer (BCS) superfluid with zero center‑of‑mass momentum, (ii) a normal metallic phase, (iii) a nodal superfluid that hosts topological Bogoliubov Fermi surfaces (TBFS), and (iv) Fulde‑Ferrell‑Larkin‑Ovchinnikov (FFLO) states characterized by a finite pairing momentum q.

The model Hamiltonian incorporates a kinetic term, a d‑wave AM spin‑splitting term 𝑡_AM kₓk_y (with 𝑡_AM>0 controlling the eccentricity of the spin‑resolved Fermi ellipses), and a short‑range attractive interaction regularized by a two‑body binding energy ε_B. The pairing order parameter is taken as Δ(𝑟)=Δ e^{i q·r}, allowing the study of plane‑wave FF states; the LO amplitude‑modulated case is left for future work.

By diagonalizing the BdG Hamiltonian, the quasiparticle spectrum is obtained as
E_k^{±}=A_k ± B_k, where A_k=√