arXiv subjects

Xia-Ji Liu

Publications and source records attributed to Xia-Ji Liu.

At least 19 recordsLinked to original sources

arXiv2026

Altermagnetism and Superconductivity: A Short Historical Review

This review is organized into three parts. In the first part, we explore the deep interconnections among three seemingly unrelated concepts in condensed matter physics: electronic liquid crystal phases, multipole expansions, and altermagnetism. At the heart of these phenomena lies a shared foundation: spin-momentum locking in the nonrelativistic regime. Originally proposed in the context of electronic liquid crystal phases, nonrelativistic spin-momentum locking was later elegantly incorporated into the formalism of multipole expansions. This framework can be further extended across multiple atomic sites, making it particularly effective for describing altermagnets, which host localized magnetic moments with anisotropic magnetization densities distributed over sublattices. In the second part, we examine superconducting phenomena associated with altermagnetism from three complementary perspectives. First, we investigate superconductivity associated with nonrelativistic spin-momentum locked Fermi surfaces, the unifying theme of the first part, highlighting a rich variety of unconventional superconducting states. These include finite-momentum pairing, $d$-wave and spin-triplet superconductivity, and topological Bogoliubov Fermi surfaces, among others. We then review superconductivity emerging from either static altermagnetic order or altermagnetic fluctuations. Finally, we discuss the possible competition and intertwining between altermagnetic order and superconductivity, illustrated using the repulsive Hubbard model. Additional related topics are addressed in the concluding part. Overall, this work offers both an accessible introduction to the newly identified magnetic order known as altermagnetism and a conceptual guide for researchers aiming to harness the ensuing unconventional superconductivity in the development of future quantum technologies.

cond-mat.supr-con↗

arXiv2026

Finite-momentum superconductivity with singlet-triplet mixing in an altermagnetic metal: A pairing instability analysis

We analyze the pairing instability of an altermagnetic metal on a square lattice driven by an attractive nearest-neighbor interaction. This interaction enables multiple pairing channels, including even-parity extended $s$-wave and $d$-wave states, as well as two odd-parity $p$-wave channels. We verify that altermagnetic spin-splitting in the single-particle dispersion gives rise to finite-momentum pairing between electrons with unlike spins, in agreement with earlier predictions. Quite unexpectedly, this pairing typically emerges across multiple channels with mixed parity. Consequently, the resulting finite-momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting phase is expected to exhibit a multi-component order parameter featuring singlet-triplet mixing. We examine several forms of altermagnetism, specifically $d_{xy}$-wave and $d_{x^{2}-y^{2}}$-wave altermagnetic couplings, and present the corresponding phase diagrams. Additionally, we study triplet pairing between electrons with identical spins and find that it always occurs at zero center-of-mass momentum. Although it is unfavorable in the regime of weak altermagnetic coupling and low electron filling, it can dominate the phase diagram when the altermagnetic coupling is sufficiently strong. The influence of on-site attractive interactions on mixed-parity pairing is also explored.

cond-mat.supr-con↗

arXiv2026

Finite-momentum bound pairs of two electrons in an altermagnetic metal

We solve the two-electron problem on a square lattice with d-wave altermagnetism, considering both on-site and nearest-neighbor attractive interactions. The altermagnetic spin-splitting in the single-particle dispersion naturally gives rise to a ground state of two-electron bound pairs with nonzero center-of-mass momentum. The emergence of finite-momentum bound states suggests that altermagnetic spin splitting may favor pairing at nonzero center-of-mass momentum, which could be relevant for proposed Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductivity in altermagnetic systems. Additionally, when the nearest-neighbor attraction is strong, the resulting finite-momentum bound pairs exhibit a mixture of both spin-singlet and spin-triplet characteristics, suggesting the possibility of unconventional superconductors, where spin-singlet and spin-triplet pairings coexist.

cond-mat.supr-con↗

arXiv2026

Properties of Bose-Einstein condensates with altermagnetism

We investigate a weakly interacting two-component Bose--Einstein condensate in the miscible regime in the presence of \emph{altermagnetism}, i.e., a collinear and globally compensated magnetic order that breaks spin-rotation symmetry while maintaining zero net magnetization. Within Bogoliubov theory, we derive the quasiparticle spectrum and coherence factors and show that altermagnetic order generically induces an angular dependence of the low-energy excitations. As a result, the sound velocity, momentum-resolved magnetization in the quantum depletion, and density--spin response functions acquire anisotropic components. We show that these anisotropic contributions vanish after angular averaging, consistent with the defining feature of altermagnetism: nontrivial local spin polarization without a global magnetization. Finally, we evaluate the Lee--Huang--Yang correction to the ground-state energy in the altermagnetic phase. Our results should be testable with ultracold-atom experiments in the foreseeable future.

cond-mat.quant-gas↗

arXiv2026

Altermagnetism-driven FFLO superconductivity in finite-filling 2D lattices

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.

cond-mat.supr-con↗

arXiv2025

Hyperspherical Analysis of Dimer-Dimer Scattering in One-Dimensional Systems

We present a comprehensive analysis of four-body scattering in one-dimensional (1D) quantum systems using the adiabatic hyperspherical representation (AHR). Focusing on dimer-dimer collisions between two species of fermions interacting via the sinh-cosh potential, we implement the slow variable discretization (SVD) method to overcome numerical challenges posed by sharp avoided crossings in the potential curves. Our numerical approach is benchmarked against exact analytical results available in integrable regimes, demonstrating excellent agreement. We further explore non-integrable regimes where no analytical solutions exist, revealing novel features such as resonant enhancement of the scattering length associated with tetramer formation. These results highlight the power and flexibility of the AHR+SVD framework for accurate few-body scattering calculations in low-dimensional quantum systems, and establish a foundation for future investigations of universal few-body physics in ultracold gases.

cond-mat.quant-gas↗

arXiv2025

Quantum Lifshitz points in an altermagnetic metal

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.

cond-mat.supr-con↗

arXiv2025

Unconventional superconductivity of an altermagnetic metal: Polarized BCS and inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov states

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 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 tri-critical 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 the 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 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.

cond-mat.supr-con↗

arXiv2025

Exact spectral properties of Fermi polarons in one-dimensional lattices: Anomalous Fermi singularities and polaron quasiparticles

We calculate the exact spectral function of a single impurity repulsively interacting with a bath of fermions in one-dimensional lattices, by deriving the explicit expression of the form factor for both regular Bethe states and the irregular spin-flip state and $η$-pairing state, based on the exactly solvable Lieb-Wu model. While at low impurity momentum $Q\sim0$ the spectral function is dominated by two power-law Fermi singularities, at large momentum we observe that the two singularities develop into two-sided distributions and eventually become anomalous Fermi singularities at the boundary of the Brillouin zone (i.e., $Q=\pmπ$), with the power-law tails extending towards low energy. Near the quarter filling of the Fermi bath, we also find two broad polaron peaks at large impurity momentum, collectively contributed by many excited many-body states with non-negligible form factors. Our exact results of those distinct features in one-dimensional Fermi polarons, which have no correspondences in two and three dimensions, could be readily probed in cold-atom laboratories by trapping highly imbalanced two-component fermionic atoms into one-dimensional optical lattices.

cond-mat.quant-gas↗

arXiv2025

Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices

By using the exact Bethe wavefunctions of the one-dimensional Hubbard model with $N$ spin-up fermions and one spin-down impurity, we derive an analytic expression of the impurity form factor, in the form of a determinant of a $(N+1)$ by $(N+1)$ matrix. This analytic expression enables us to exactly calculate spectral properties of one-dimensional Fermi polarons in lattices, when the masses of the impurity particle and the Fermi bath are equal. We present the impurity spectral function as functions of the on-site interaction strength and the filling factor of the Fermi bath, and discuss the origin of Fermi singularities in the spectral function at small momentum and the emergence of polaron quasiparticles at large momentum near the boundary of Brillouin zone. Our analytic expression of the impurity form factors pave the way to exploring the intriguing dynamics of a particle interacting with a Fermi bath. Our exact predictions on the impurity spectral function could be directly examined in cold-atom laboratories by using the radio-frequency spectroscopy and Ramsey spectroscopy.

cond-mat.quant-gas↗

arXiv2024

Breakdown of the single-mode description of ultradilute quantum droplets in binary Bose mixtures: A perspective from a microscopic bosonic pairing theory

In his seminal proposal of quantum droplets in binary Bose mixtures {[}Phys. Rev. Lett. \textbf{115}, 155302 (2015){]}, Dmitry Petrov suggested that the density ratio $n_{2}/n_{1}$ of the two bosonic components are locked to an optimal value, which is given by the square root of the ratio of the two intra-species scattering lengths, i.e., $\sqrt{a_{11}/a_{22}}$. Due to such a density locking, quantum droplets can be efficiently described by using an extended Gross--Pitaevskii equation within the single-mode approximation. Here, we find that this single-mode description necessarily breaks down in the deep quantum droplet regime, when the attractive inter-species scattering length $a_{12}$ significantly deviates away from the threshold of mean-field collapse (i.e., $-\sqrt{a_{11}a_{22}}$). By applying a bosonic pairing theory, we show that the density ratio is allowed to fluctuate in a sizable interval. Most importantly, the optimal density ratio would be very different from $\sqrt{a_{11}/a_{22}}$, in the case of unequal intra-species scattering lengths ($a_{11}\neq a_{22}$). Our finding might provide a plausible microscopic explanation of the puzzling low critical particle number of quantum droplets, as experimentally observed. Our predicted interval of the density ratio, as a function of the inter-species scattering length, could also be experimentally examined in cold-atom laboratories in the near future.

cond-mat.quant-gas↗

arXiv2024

Exact Polaron-Polaron interactions in a Quantum Hall Fluid

We present an exact solution for effective polaron-polaron interactions between heavy impurities, mediated by a sea of non-interacting light fermions in the quantum Hall regime with highly degenerate Landau levels. For weak attraction between impurities and fermions, where only the manifold of lowest Landau levels is relevant, we obtain an analytical expression of mediated polaron-polaorn interactions. Remarkably, polaron interactions are exactly zero when fermions in lowest Landau levels outnumber heavy impurities. For strong attraction, different manifolds of higher Landau levels come into play and we derive a set of equations that can be used to numerically solve the mediated polaron interaction potential. We find that the potential vanishes when the distance R between impurities is larger than the magnetic length, but strongly diverges at short range following a Coulomb form -1/R. Our exact results of polaron-polaron interactions might be examined in cold-atom setups, where a system of Fermi polarons in the quantum Hall regime is realized with synthetic gauge field or under fast rotation. Our predictions could also be useful to understand the effective interaction between exciton-polarons in electron-doped semiconductors under strong magnetic field.

cond-mat.mes-hall↗

arXiv2024

Theory of the spectral function of Fermi polarons at finite temperature

We develop a general theory of Fermi polarons at nonzero temperature, including particle-hole excitations of the Fermi sea shake-up to arbitrarily high orders. The exact set of equations of the spectral function is derived by using both Chevy ansatz and diagrammatic approach, and their equivalence is clarified to hold in free space only, with an unregularized infinitesimal interaction strength. The correction to the polaron spectral function arising from two-particle-hole excitations is explicitly examined, for an exemplary case of Fermi polarons in one-dimensional optical lattices. We find quantitative improvements at low temperatures with the inclusion of two-particle-hole excitations, in both polaron energies and decay rates. Our exact theory of Fermi polarons with arbitrary orders of particle-hole excitations might be used to better understand the intriguing polaron dynamical responses in two or three dimensions, whether in free space or within lattices.

cond-mat.quant-gas↗

arXiv2024

Exact theory of the finite-temperature spectral function of Fermi polarons with multiple particle-hole excitations: Diagrammatic theory versus Chevy ansatz

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, our exact set of equations can be used to numerically 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.

cond-mat.quant-gas↗

arXiv2024

Microscopic many-body theory of two-dimensional coherent spectroscopy of exciton-polarons in one-dimensional materials

We have developed a microscopic many-body theory of two-dimensional coherent spectroscopy (2DCS) for a model of polarons in one-dimensional (1D) materials. Our theory accounts for contributions from all three processes: excited-state emission (ESE), ground-state bleaching (GSB), and excited-state absorption (ESA). While the ESE and GSB contributions can be accurately described using a Chevy's ansatz with one particle-hole excitation, the ESA process requires information about the many-body eigenstates involving two impurities. To calculate these double polaron states, we have extended the Chevy's ansatz with one particle-hole excitation. The validity of this ansatz was verified by comparing our results with an exact calculation using Bethe's ansatz. Our numerical results reveal that in the weak interaction limit, the ESA contribution cancels out the total ESE and GSB contributions, resulting in less significant spectral features. However, for strong interactions, the features of the ESA contribution and the combined ESE and GSB contributions remain observable in the 2DCS spectra. These features provide valuable information about the interactions between polarons. Additionally, we have investigated the mixing time dynamics, which characterize the quantum coherences of the polaron resonances. Overall, our theory provides a comprehensive framework for understanding and interpreting the 2DCS spectra of polarons in 1D materials, shedding light on their interactions and coherent dynamics.

cond-mat.mes-hall↗

arXiv2023

Fermi spin polaron and dissipative Fermi-polaron Rabi dynamics

We consider a spin impurity with multiple energy levels moving in a non-interacting Fermi sea, and theoretically solve this Fermi spin polaron problem at nonzero temperature by using a non-self-consistent many-body $T$-matrix theory. We focus on the simplest case with spin half, where the two energy states of the impurity are coupled by a Rabi flip term. At small Rabi coupling, the impurity exhibits damped Rabi oscillations, where the decoherence is caused by the interaction with the Fermi sea, as recently reported in Fermi polaron experiments with ultracold atoms. We investigate the dependence of Rabi oscillations on the Rabi coupling strength and examine the additional nonlinear damping due to large Rabi coupling. At finite temperature and at nonzero impurity concentration, the impurity can acquire a pronounced momentum distribution. We show that the momentum/thermal average can sizably reduce the visibility of Rabi oscillations. We compare our theoretical predictions to the recent experimental data and find a good agreement without any adjustable parameter.

cond-mat.quant-gas↗

arXiv2023

Super Fermi polaron and Nagaoka ferromagnetism in a two-dimesnional square lattice

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.

cond-mat.quant-gas↗

arXiv2023

Spectral function of Fermi polarons at finite temperature from a self-consistent many-body $T$-matrix approach in real frequency

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.

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