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arXiv:2609.14613

Altermagnetism across the BCS-BEC crossover

Iogann Tolbatov, Luca Salasnich

Published Sep 13, 2026• 0 citations
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Abstract

We study a two-dimensional paired Fermi system in which altermagnetism produces a spin splitting that depends on momentum. The interaction strength is described through the two-body binding energy, so that the chemical potential and pairing gap evolve self-consistently from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime to the strong-coupling Bose-Einstein-condensate (BEC) regime at fixed density. The stability of the uniform paired state is examined by giving the pairs a small center-of-mass momentum and following the resulting change in free energy. We show that at zero temperature, the phase stiffness follows a universal quadratic suppression, $J/J_0 = 1 - (α/α_0)^2$, across the entire fully gapped crossover regime. Deviations from this relation emerge only on the BCS side upon the opening of gapless Bogoliubov pockets, which rapidly reduce the stiffness and can trigger an instability toward finite-momentum pairing. In the BEC regime, this universal quadratic correction corresponds to the altered effective mass of the tightly bound composite bosons. The model therefore provides a simple setting in which to compare altermagnetic pair breaking on the BCS and BEC sides of the crossover.

DOI
10.48550/arxiv.2609.14613

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We study a two-dimensional paired Fermi system in which altermagnetism produces a spin splitting that depends on momentum. The interaction strength is described through the two-body binding energy, so that the chemical potential and pairing gap evolve self-consistently from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime to the strong-coupling Bose-Einstein-condensate (BEC) regime at fixed density. The stability of the uniform paired state is examined by giving the pairs a small center-of-mass momentum and following the resulting change in free energy. We show that at zero temperature, the phase stiffness follows a universal quadratic suppression, J/J0=1−(α/α0)2J/J_0 = 1 - (α/α_0)^2J/J0​=1−(α/α0​)2, across the entire fully gapped crossover regime. Deviations from this relation emerge only on the BCS side upon the opening of gapless Bogoliubov pockets, which rapidly reduce the stiffness and can trigger an instability toward finite-momentum pairing. In the BEC regime, this universal quadratic correction corresponds to the altered effective mass of the tightly bound composite bosons. The model therefore provides a simple setting in which to compare altermagnetic pair breaking on the BCS and BEC sides of the crossover.
We theoretically investigate the uniform spin susceptibility $\ensuremath{\chi}$ in the superfluid phase of an ultracold Fermi gas in the region of the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover. In our previous paper [H. Tajima et al., Phys. Rev. A 89, 033617 (2014)], including pairing fluctuations within an extended TTT-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\ensuremath{\chi}$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. In this paper, we extend this work to the superfluid phase below Tc{T}_{\mathrm{c}}Tc​, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\ensuremath{\chi}$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below Tc{T}_{\mathrm{c}}Tc​ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a 6Li^{6}\mathrm{Li}6Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.
Abstract Universality of the long-distance behavior across the Bardeen–Cooper–Schrieffer (BEC)-Bose–Einstein condensate (BCS) smooth transition for two-body density correlation functions and the Cooper-pair probability density is demonstrated in a balanced mixture of a two-component Fermi gas at T = 0. It is numerically shown at the mean-field level that these two-body quantities exhibit an exponential decay in terms of the chemical potential and the low-energy behavior of the gap. A general expression is found for the two-body distributions holding for different features of finite-range potentials, such as divergences at the origin, discontinuities at a finite radius, power-law decay, and exponential decay. The correlation length characterizing the long-distance behavior unravels the dependence on the energy needed to break pairs along the BEC-BCS crossover, a quantity meaningful to the stability of the many-body state.
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We investigate the uniform spin susceptibility ${\ensuremath{\chi}}_{\mathrm{s}}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended TTT-matrix approximation, we show that ${\ensuremath{\chi}}_{\mathrm{s}}$ exhibits nonmonotonic temperature dependence in the normal state. In particular, ${\ensuremath{\chi}}_{\mathrm{s}}$ is suppressed near the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature Ts{T}_{\mathrm{s}}Ts​ as the temperature at which ${\ensuremath{\chi}}_{\mathrm{s}}$ takes a maximum value. Determining Ts{T}_{\mathrm{s}}Ts​ in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner.
The ability to control the interaction strength between atoms within strongly interacting Fermi gases by sweeping a magnetic field across a Feshbach resonance provides a powerful experimental system in which to study many-body physics. One example is the crossover from a Bose-Einstein condensate (BEC) regime, in which the atoms are strongly coupled into pairs, to the weak-coupling regime that mimics Bardeen-Cooper-Schrieffer (BCS) coupling of electrons in superconducting metals. Although behavior on either side of the resonance is fairly well understood, of immediate interest is to find out what happens in the BEC-BCS crossover regime. However, determining the relative contributions of atom pairing mechanisms is an experimental and theoretical challenge.
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