Xia-Ji Liu

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 $d_{xy}$-wave or $d_{x^{2}-y^{2}}$-wave altermagnetic order in the presence of on-site $s$-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, $d_{xy}$-wave altermagnetism supports FFLO superconductivity over a broad parameter regime at low fillings, whereas $d_{x^{2}-y^{2}}$-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 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.

By using both diagrammatic theory and Chevy ansatz approach, we derive an exact set of equations, which determines the spectral function of Fermi polarons with multiple particle-hole excitations at nonzero temperature. In the diagrammatic theory, we find out the complete series of Feynman diagrams for the multi-particle vertex functions, when the unregularized contact interaction strength becomes infinitesimal, a typical situation occurring in two- or three-dimensional free space. The latter Chevy ansatz approach is more widely applicable, allowing a nonzero interaction strength. We clarify the equivalence of the two approaches for an infinitesimal interaction strength and show that the variational coefficients in the Chevy ansatz are precisely the on-shell multi-particle vertex functions divided by an excitation energy. Truncated to a particular order of particle-hole excitations, the set of equations can be used to approximately calculate the finite-temperature polaron spectral function, once the numerical singularities in the equations are appropriately treated. As a concrete example, we calculate the finite-temperature spectral function of Fermi polarons in one-dimensional lattices, taking into account all the two-particle-hole excitations. We show that the inclusion of two-particle-hole excitations quantitatively improve the predictions on the polaron spectral function. Our results provide a useful way to solve the challenge problem of accurately predicting the finite-temperature spectral function of Fermi polarons in three-dimensional free space. In addition, our clarification of the complete set of Feynman diagrams for the multi-particle polaron vertex functions may inspire the development of more accurate diagrammatic theories of population-imbalanced strongly interacting Fermi gases, beyond the conventional many-body T-matrix approximation.

We consider the Fermi polaron problem of an impurity hopping around a two-dimensional square lattice and interacting with a sea of fermions at given filling factor. When the interaction is attractive, we find standard Fermi polaron quasiparticles, categorized as attractive polarons and repulsive polarons. When the interaction becomes repulsive, interestingly, we observe an unconventional highly-excited polaron quasiparticle, sharply peaked at the corner of the first Brillouin zone with momentum \mathbf{k}=(\pmπ,\pmπ). This super Fermi polaron branch arises from the dressing of the impurity's motion with holes, instead of particles of fermions. We show that super Fermi polarons become increasingly well-defined with increasing impurity-fermion repulsions and might be considered as a precursor of Nagaoka ferromagnetism, which would appear at sufficiently large repulsions and at large filling factors. We also investigate the temperature-dependence of super Fermi polarons and find that they are thermally robust against the significant increase in temperature.

We theoretically examine the finite-temperature spectral function of Fermi polarons in three dimensions, by using a self-consistent many-body $T$-matrix theory in real frequency. In comparison with the previous results from a non-self-consistent many-body $T$-matrix approach, we show that the treatment of self-consistency in the impurity Green function leads to notable changes in almost all the dynamical quantities, including the vertex function, impurity self-energy and spectral function. Eventually, it gives rise to quantitatively different predictions for the measurable radio-frequency spectrum and Raman spectrum at finite temperature. Using the recent spectroscopic measurements as a benchmark, we find that the self-consistent many-body $T$-matrix theory somehow provides a better explanation for the experimental data. The notable difference in the predictions from the non-self-consistent and self-consistent theories suggests that more accurate theoretical descriptions are needed, in order to fully account for the current spectroscopic observations on Fermi polarons.