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arXiv:2610.01011

Highly anisotropic collective modes of altermagnetic superconductors with Bogoliubov Fermi surfaces

Huaisong Zhao, Peng Zou, Xia-Ji Liu, Hui Hu

Published Oct 1, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate collective modes in charge-neutral altermagnetic superconductors with $d$-wave spin-split bands, focusing on the impact of emergent Bogoliubov Fermi surfaces. In the absence of a magnetic field, the BCS state supports collective modes that inherit the underlying $d$-wave symmetry, resulting in pronounced momentum-space anisotropy. The broken time-reversal symmetry further couples these modes to spin-density fluctuations, allowing their signatures to emerge in the spin dynamical structure factor. Upon applying a magnetic field, Bogoliubov Fermi surfaces emerge and qualitatively reshape the collective-mode dynamics through gapless particle-hole excitations and strongly anisotropic Landau damping. The damping is strongest along the momentum-space diagonal, where it can suppress the low-energy phonon mode at small momenta. Remarkably, the suppressed phonon is accompanied by the emergence of an in-gap structure in the Higgs mode and an associated pronounced enhancement of the spin response. These results establish Bogoliubov Fermi surfaces as a mechanism for generating highly anisotropic collective-mode dynamics and identify spin response as a sensitive probe of in-gap Higgs excitations in altermagnetic superconductors.

DOI
10.48550/arxiv.2610.01011

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We investigate collective modes in charge-neutral altermagnetic superconductors with ddd-wave spin-split bands, focusing on the impact of emergent Bogoliubov Fermi surfaces. In the absence of a magnetic field, the BCS state supports collective modes that inherit the underlying ddd-wave symmetry, resulting in pronounced momentum-space anisotropy. The broken time-reversal symmetry further couples these modes to spin-density fluctuations, allowing their signatures to emerge in the spin dynamical structure factor. Upon applying a magnetic field, Bogoliubov Fermi surfaces emerge and qualitatively reshape the collective-mode dynamics through gapless particle-hole excitations and strongly anisotropic Landau damping. The damping is strongest along the momentum-space diagonal, where it can suppress the low-energy phonon mode at small momenta. Remarkably, the suppressed phonon is accompanied by the emergence of an in-gap structure in the Higgs mode and an associated pronounced enhancement of the spin response. These results establish Bogoliubov Fermi surfaces as a mechanism for generating highly anisotropic collective-mode dynamics and identify spin response as a sensitive probe of in-gap Higgs excitations in altermagnetic superconductors.
Altermagnetism, featuring momentum-dependent spin splitting without net magnetization, has attracted a growing interest for spintronics. We study a Fermi Hubbard model with altermagnetic order arising from the spin-anisotropic hopping near half-filling using constrained-path quantum Monte Carlo. Spin-dependent hopping breaks SU(2) symmetry and disrupts Fermi surface nesting, giving rise to an altermagnetic state with momentum-space spin splitting but no net magnetization. We find that increasing anisotropy suppresses long-range antiferromagnetic order and significantly enhances effective ddd-wave pairing correlations. Our results demonstrate a doping-free route to unconventional superconductivity mediated by short-range spin fluctuations in an altermagnetic background.
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 investigate the emergence of nonreciprocal dissipationless supercurrents in one-dimension manifested through the superconducting diode effect (SDE) and the Josephson diode effect (JDE) in the absence of any external magnetic field, where inversion symmetry (IS) and time-reversal symmetry (TRS) can be intrinsically broken by spin-orbit coupling (SOC), and altermagnetism (AM), respectively. We investigate Ising and Rashba SOC separately in two models where two-component AM, assembled with crystallographic angle, can lead to qualitatively similar indirect band-gap closing and non-reciprocal supercurrent in a Fulde-Ferrell (FF) superconductor. Interestingly, in the absence of the above SOCs, SDE persists and the sign of efficiency can be altered by tuning the angle only. Parallel spin components with complementary momentum functions, ensuring the breaking of IS and TRS, can induce SDE in the presence of FF pairing. Continuing the analysis in the context of JDE, we explore the interplay between SOCs and AM with the p-wave and Fulde-Ferrell superconductivity in three different setups. The bulk bands contributes to the non-reciprocity in the case of p-wave superconductivity while JDE is dominated by Andreev bound states for FF superconductivity. Importantly, JDE continues to exist due to finite momentum Cooper pair even without AM and SOC unlike the p-wave superconductivity. The sign of JD efficiency can be tuned with angle for p-wave superconductivity while absence of such sign reversal is a hallmark signature of FF superconductivity. Similar to SDE, parallel spin components in conjunction with p-wave superconductivity can lead to JDE that can also be mediated by only FF pairing in the absence of SOC and AM.
Altermagnets - collinear, zero-net-moment magnets with momentum-odd spin splitting protected by crystalline symmetries - offer a tunable route to suppress long-range antiferromagnetism while preserving strong short-range spin fluctuations. We show that this environment robustly stabilizes unconventional superconductivity and naturally produces mixed-symmetry pairing. Through a strong-coupling analysis of a spin-anisotropic Hubbard model, we derive an anisotropic t-J model where exchange interactions cooperatively enhance singlet d-wave pairing and promote triplet p-wave pairing. Our mean-field analysis reveals a pairing evolution driven by altermagnetic anisotropy: for small spin anisotropy, the d-wave channel is enhanced, closely resembling the dominant pairing symmetry in cuprate superconductors, which suggests that weak spin anisotropy may be an essential ingredient in realistic models of these materials. Constrained-path quantum Monte Carlo simulations confirm this picture, showing a regime where dominant d-wave correlations coexist with an emergent p-wave component near optimal doping. As spin anisotropy increases, strong C2 anisotropy and spin splitting activate the triplet channel, leading to a stable d+p mixed-pairing state. This synergistic state exhibits significantly enhanced overall pairing strength, suggesting the possibility of a higher superconducting transition temperature.
We numerically study the collective excitations present in isotropic superconductors including a screened Coulomb interaction. By varying the screening strength, we analyze its impact on the system. We use a formulation of the effective phonon-mediated interaction between electrons that depends on the energy transfer between particles, rather than being a constant in a small energy shell around the Fermi edge. This justifies considering also rather large attractive interactions. We compute the system’s Green’s functions using the iterated equations of motion (iEoM) approach, which ultimately enables a quantitative analysis of collective excitations. For weak couplings, we identify the well-known amplitude (Higgs) mode at the two-particle continuum’s lower edge and the phase (Anderson-Bogoliubov) mode at \omega = 0 ω = 0 for a neutral system, which shifts to higher energies as the Coulomb interaction is switched on. As the phononic coupling is increased, the Higgs mode separates from the continuum, and additional phase and amplitude modes appear, persisting even in the presence Coulomb interactions.
We consider multiband BCS superconductors that exhibit time-reversal symmetry and uniform pairing, and analyze their dynamic density and spin structure factors using linear-response theory within the mean-field BCS-BEC crossover framework at zero temperature. Our results for the multi-orbital Hubbard model satisfy the associated f-sum rules in several limits. In particular, in the strong-coupling limit, they coincide with those of a weakly-interacting Bose gas of Cooper pairs, where the low-energy collective Goldstone modes serve as Bogoliubov phonons. We further reveal that the quantum-geometric origin of the low-energy structure factors, along with related observables such as the superfluid-weight tensor and the effective-mass tensor of Cooper pairs, can be traced all the way back to the effective-mass theorem for Bloch bands in this limit. As an illustration, we investigate the pyrochlore-Hubbard model numerically and demonstrate that the Goldstone modes are the only relevant collective degrees of freedom in the flat-band regime.