Motivated by recent experiments on atomic Dirac fermions in a tunable honeycomb optical lattice, we study the attractive Hubbard model of superfluidity in the anisotropic honeycomb lattice. At weak-coupling, we find that the maximum mean field pairing transition temperature, as a function of density and interaction strength, occurs for the case with isotropic hopping amplitudes. In this isotropic case, we go beyond mean field theory and study collective fluctuations, treating both pairing and density fluctuations for interaction strengths ranging from weak to strong coupling. We find evidence for a sharp sound mode, together with a well-defined Leggett mode over a wide region of the phase diagram. We also calculate the superfluid order parameter and collective modes in the presence of nonzero superfluid flow. The flow-induced softening of these collective modes leads to dynamical instabilities involving stripe-like density modulations as well as a Leggett-mode instability associated with the natural sublattice symmetry breaking charge-ordered state on the honeycomb lattice. The latter provides a non-trivial test for the experimental realization of the one-band Hubbard model. We delineate regimes of the phase diagram where the critical current is limited by depairing or by such collective instabilities, and discuss experimental implications of our results.
We study superconducting properties of population-imbalanced ultracold Fermi mixtures in the honeycomb lattice that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain ground state phase diagrams including some unconventional superconducting phases such as the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase. We show that this phase is characterized by atypical behaviour of the Cooper pairs total momentum in the external magnetic field. We show that the momentum changes its valu…
Mean-field Bloch bands of a Bose-Einstein condensate in a honeycomb optical lattice are computed. We find that the topological structure of the Bloch bands at the Dirac point is changed completely by the atomic interaction of arbitrary small strength: the Dirac point is extended into a closed curve and an intersecting tube structure arises around the original Dirac point. These tubed Bloch bands are caused by the superfluidity of the system. Furthermore, they imply the inadequacy of the tight-binding model to describe an interacting Boson system around the Dirac point and the breakdown of adia…
Despite the multi-band spectrum of the widely-known Hofstadter butterfly, it turns out that the pairing correlations of the time-reversal-symmetric Hofstadter-Hubbard model are well-described by a single order parameter that is uniform in real space. By exploiting a BCS mean-field theory for the nearly-flat butterfly-bands regime of low magnetic-flux limit, here we reveal a number of unusual superfluid properties both in the ground state and at finite temperatures. Our thorough analysis includes but is not limited to the order parameter, condensate and superfluid fractions, and the critical BC…
We theoretically investigate the inhomogeneous Fulde-Ferrell (FF) superfluidity in a three dimensional atomic Fermi gas with Rashba spin-orbit coupling near a broad Feshbach resonance. We show that within mean-field theory the FF superfluid state is always more favorable than the standard Bardeen-Cooper-Schrieffer (BCS) superfluid state when an in-plane Zeeman field is applied. We present a qualitative finite-temperature phase diagram near resonance and argue that the predicted FF superfluid is observable with experimentally attainable temperatures (i.e., $T\sim0.2T_{F}$, where $T_{F}$ is the …
The Mielke checkerboard is known to be one of the simplest two-band lattice models exhibiting an energetically flat band that is in touch with a quadratically dispersive band in the reciprocal space, i.e., its flat band is not isolated. Motivated by the growing interest in understanding the origins of flat-band superfluidity in various contexts, here we provide an in-depth analysis showing how the mean-field BCS correlations prevail in this particular model. Our work reveals the quantum-geometric origin of flat-band superfluidity through uncovering the leading role by a band-structure invarian…
The transition from the weakly interacting BCS regime to the strongly interacting unitary regime is explored for ultracold trapped Fermi gases assuming a normal mode description of the gas instead of the conventional Cooper pairing. The Pauli principle is applied ``on paper'' by using specific normal mode assignments. Energies, entropies, critical temperatures, and an excitation frequency are studied and compared to existing results in the literature. These normal modes have been derived analytically for N identical, confined particles from a first-order L=0 group theoretic solution of a three…
We examine two dimensional mixture of single-component fermions and dipolar bosons. We calculate the self-enregies of the fermions in the normal state and the Cooper pair channel by including first order vertex correction to derive a modified Eliashberg equation. We predict appearance of superfluids with various non-standard pairing symmetries at experimentally feasible transition temperatures within the strong-coupling limit of the Eliashberg equation. Excitations in these superfluids are anyonic and follow non-Abelian statistics.
Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of states and large interaction strength. This limits the critical temperature to an experimentally challenging regime where, for example, even ultracold atoms and molecules in optical lattices would struggle to realize the topological superfluid. We propose that the introduction of a weaker longer-range repulsion, in addition to the short-range attraction bet…
In this paper, we put forward to another route realizing topological superfluid (TS). In contrast to conventional method, spin-orbit coupling and external magnetic field are not requisite. Introducing an experimentally feasible technique called on-site rotation (OSR) into p-band honeycomb optical lattices for spinless Fermi gases and considering CDW and pairing on the same footing, we investigate the effects of OSR on superfluidity. The results suggest that when OSR is beyond a critical value, where CDW vanishes, the system transits from a normal superfluid (NS) with zero TKNN number to TS lab…
Non-equilibrium stimulation of superfluidity in trapped Fermi gases is discussed by analogy to the work of Eliashberg [G. M. Eliashberg, in "Nonequilibrium Superconductivity," edited by D. N. Langenberg and A. I. Larkin (North-Holland, New York, 1986)] on the microwave enhancement of superconductivity. Optical excitation of the fermions balanced by heat loss due to thermal contact with a boson bath and/or evaporative cooling enables stationary non-equilibrium states to exist. Such a state manifests as a shift of the quasiparticle spectrum to higher energies and this effect effectively raises t…
We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the…
In addition to the conventional contribution that is directly controlled by the single-particle energy spectrum, the superfluid phase stiffness of a two-component Fermi gas has a geometric contribution that is governed by the quantum metric of the honeycomb's band structure. Here, we take both contributions into account, and construct phase diagrams for the critical superfluid transition temperature as a function of the chemical potential, particle filling, onsite interaction and next-nearest-neighbor hopping. Our theoretical approach is based on a self-consistent solution of the BCS mean-fiel…
We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion a…
We investigate the properties of the nearest-neighbor singlet pairing and the emergence of d-wave superconductivity in the doped honeycomb lattice considering the limit of large interactions and the $t-J_1-J_2$ model. First, by applying a renormalized mean-field procedure as well as slave-boson theories which account for the proximity to the Mott insulating state, we confirm the emergence of d-wave superconductivity in agreement with earlier works. We show that a small but finite $J_2$ spin coupling between next-nearest neighbors stabilizes d-wave symmetry compared to the extended s-wave scena…
We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to $(i)$ Fulde-Ferrell-like superfluidity and $(ii)$ skyrmion-like polarization textures near the edges of the system. We also discussed the effects of interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the superfluid ground state and polarization textures.
We investigate color superfluidity and trimer formation in resonantly interacting SU(3) Fermi gases with a finite interaction range. The finite range is crucial to avoid the Thomas collapse and treat the Efimov effect occurring in this system. Using the Skorniakov-Ter-Martirosian (STM) equation with medium effects, we show the effects of the atomic Fermi distribution on the Efimov trimer energy at finite temperature. We show the critical temperature of color superfluidity within the non-selfconsistent $T$-matrix approximation (TMA). In this way, we can provide a first insight into the phase di…
We theoretically investigate two-particle and many-particle Anderson localizations of a spin-orbit coupled ultracold atomic Fermi gas trapped in a quasi-periodic potential and subjected to an out-of-plane Zeeman field. We solve exactly the two-particle problem in a finite length system by exact diagonalization and solve approximately the many-particle problem within the mean-field Bogoliubov-de Gennes approach. At a small Zeeman field, the localization properties of the system are similar to that of a Fermi gas with conventional $s$-wave interactions. As the disorder strength increases, the tw…
It is well-known that when the magnetic field is stronger than a critical value, the spin imbalance can break the Cooper pairs of electrons and hence hinder the superconductivity in a spin-singlet channel. In a bilayer system of ultra-cold Fermi gases, however, we demonstrate that the critical value of the magnetic field at zero temperature can be significantly increased by including a spin-flip tunnelling, which opens a gap in the spin-triplet channel near the Fermi surface and hence reduces the influence of the effective magnetic field on the superfluidity. The phase transition also changes …
We describe the effects of disorder on the critical temperature of s-wave superfluids from the BCS to the BEC regime, with direct application to ultracold Fermi atoms. In the BCS regime the pair breaking and phase coherence temperature scales are essentially the same allowing strong correlations between the amplitude and phase of the order parameter. As non-pair breaking disorder is introduced the largely overlapping Cooper pairs conspire to maintain phase coherence such that the critical temperature remains essentially unchanged. However, in the BEC regime the pair breaking and phase coherenc…
Topological superfluids are recently discovered quantum matters that host topologically protected gapless edge states known as Majorana fermions - exotic quantum particles that act as their own anti-particles and obey non-Abelian statistics. Their realizations are believed to lie at the heart of future technologies such as fault-tolerant quantum computation. To date, the most efficient scheme to create topological superfluids and Majorana fermions is based on the Sau-Lutchyn-Tewari-Das Sarma model with a Rashba-type spin-orbit coupling on the }\textbf{\textit{x-y}}\textbf{ plane and a large ou…
We describe the effects of disorder on the critical temperature of $s$-wave superfluids from the BCS to the BEC regime, with direct application to ultracold fermions. We use the functional integral method and the replica technique to study Gaussian correlated disorder due to impurities, and we discuss how this system can be generated experimentally. In the absence of disorder, the BCS regime is characterized by pair breaking and phase coherence temperature scales which are essentially the same allowing strong correlations between the amplitude and phase of the order parameter for superfluidity…
The tremendous development of cold atom physics has opened up a whole new opportunity to study novel states of matter which are not easily accessible in solid state systems. Here we propose to realize the $f$-wave pairing superfluidity of spinless fermions in the $p_{x,y}$-orbital bands of the two dimensional honeycomb optical lattices. The non-trivial orbital band structure rather than strong correlation effects gives rise to the unconventional pairing with the nodal lines of the $f$-wave symmetry. With a confining harmonic trap, zero energy Andreev bound states appear around the circular bou…
We investigate the formation of Cooper pairs, bound dimers and the dimer-dimer elastic scattering of ultra- cold dipolar Fermi molecules confined in a 2D optical lattice bilayer configuration. While the energy and their associated bound states are determined in a variational way, the correlated two-molecule pair is addressed as in the original Cooper formulation. We demonstrate that the 2D lattice confinement favors the formation of zero center mass momentum bound states. Regarding the Cooper pairs binding energy, this depends on the molecule populations in each layer. Maximum binding energies…
Nuclear matter and finite nuclei exhibit the property of superfluidity by forming Cooper pairs. We review the microscopic theories and methods that are being employed to understand the basic properties of superfluid nuclear systems, with emphasis on the spatially extended matter encountered in neutron stars, supernova envelopes, and nuclear collisions. Our survey of quantum many-body methods includes techniques that employ Green functions, correlated basis functions, and Monte Carlo sampling of quantum states. With respect to empirical realizations of nucleonic and hadronic superfluids, this r…
We study the Higgs amplitude mode in the s-wave superfluid state on the honeycomb lattice inspired by recent cold atom experiments. We consider the attractive Hubbard model and focus on the vicinity of a quantum phase transition between semi-metal and superfluid phases. On either side of the transition, we find collective mode excitations that are stable against decay into quasiparticle-pairs. In the semi-metal phase, the collective modes have "Cooperon" and exciton character. These modes smoothly evolve across the quantum phase transition, and become the Anderson-Bogoliubov mode and the Higgs…
Similar to what has recently been achieved with Bose-Bose mixtures [Lamporesi et al., Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($σ\equiv \{\uparrow, \downarrow \}$), such a way that only one of the species feel the lattice potential and is confined to a quasi-two-dimensional geometry, while having negligible effect on the other, that is leaving it three dimensional. We investigate the ground state phase diagram of superfluidity for such mixtures in the B…
We consider a cold two-species atomic Fermi gas confined in a trap. We combine the Hermitian coupling between the states (we assume them to be the states with different spins) with the Cooper pairing of atoms with these different spins. This opens up a new prospect for investigation of interplay between various phenomena involving Raman coupling (e.g., atom lasers, dark-state polaritons) and effects caused by Cooper pairing of particles (e.g., superfluidity). We have obtained a threshold of transition from oscillatory to amplifying behavior of matter waves.
We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity,…
We build a holographic model for the pairing fluctuation pseudogap phase in fermionic high temperature superconductivity/superfluidity based on the BCS-BEC crossover scenario. The pseudogap originates from incoherent Cooper pairing and has been observed in recent cold atom experiments. The strength of Cooper pairing and hence the BCS-BEC crossover is controlled by an effective 4-Fermi interaction and we argue that the double-trace deformation for charged scalar operator is a close analog in large N field theories. We employ the double-trace deformed Abelian Higgs model of holographic supercond…
We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS) state of ultra-cold atoms in a deep hexagonal optical lattice. The dynamical evolution is triggered by a quench of the lattice potential, such that the interaction strength $U_f$ is much larger than the hopping amplitude $J_f$. The quench initiates collective oscillations with frequency $|U_f|/(2π)$ in the momentum occupation numbers and imprints an oscillating phase with the same frequency on the BCS order parameter $Δ$. The oscillation frequency of $Δ$ is not reproduced by treating the time evolution in mean-field …
Cooper pairing caused by an induced interaction represents a paradigm in our description of fermionic superfluidity. Here, we present a strong coupling theory for the critical temperature of $p$-wave pairing between spin polarised fermions immersed in a Bose-Einstein condensate. The fermions interact via the exchange of phonons in the condensate, and our self-consistent theory takes into account the full frequency/momentum dependence of the resulting induced interaction. We demonstrate that both retardation and self-energy effects are important for obtaining a reliable value of the critical te…
We theoretically analyze the pairing instability of a three-dimensional ultracold atomic Fermi gas towards a Fulde-Ferrell superfluid, in the presence of Rashba spin-orbit coupling and in-plane Zeeman field. We use the standard Thouless criterion for the onset of superfluidity, with which the effect of pair fluctuations is partially taken into account by approximately using a mean-field chemical potential at zero temperature. This gives rise to an improved prediction of the superfluid transition temperature beyond mean-field, particularly in the strong-coupling unitary limit. We also investiga…
We map out the critical velocity in the crossover from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer superfluidity with ultracold $^{6}$Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity $v_c$. In the same samples, we measure the speed of sound $v_s$ by exciting density waves and compare the results to the measured values of $v_c$. We perform numerical simulations in the BEC regime and find very good agreement, validating the approach. In the strongly correlated re…
We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterize…
