BCS-BEC Crossover Research Articles

Exotic superfluidity and pairing phenomena in atomic Fermi gases in mixed dimensions

Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction, while one component is confined on a one-dimensional (1D) optical lattice whereas the other is in a homogeneous 3D continuum. We study the phase diagram and the pseudogap phenomena throughout the entire BCS-BEC crossover, using a pairing fluctuation theory. We find that the effective dimensionality of the non-interacting lattice component can evolve from quasi-3D to quasi-1D, leading to strong Fermi surface mismatch. Upon pairing, the system becomes effectively quasi-two dimensional in the BEC regime. The behavior of Tc bears similarity to that of a regular 3D population imbalanced Fermi gas, but with a more drastic departure from the regular 3D balanced case, featuring both intermediate temperature superfluidity and possible pair density wave ground state. Unlike a simple 1D optical lattice case, Tc in the mixed dimensions has a constant BEC asymptote.

The possible role of van Hove singularities in the high Tc of superconducting H3S

We observe that H3S has a BCC structure and, with nearest neighbor hopping only, a strong singularity occurs at zero energy. This singularity is accompanied with a highly nested Fermi surface, which is not conducive to a stable superconducting instability. Introduction of next-nearest-neighbor hopping removes the singularity, but a “robust” peak remains in the electron density of states. Solution of the BCS equations shows an enhanced superconducting [Formula: see text] due to this peak. Furthermore, nesting is no longer present, so other instabilities will not compete effectively with superconductivity. We find high critical temperatures are possible, even with very modest coupling strengths. We also examine a limit of the [Formula: see text] equations (in an Appendix) where an analytical solution is possible over the entire range of coupling strengths, and therefore the BCS-BEC crossover is fully covered.

A holographic model for pseudogap in BCS–BEC crossover (I): Pairing fluctuations, double-trace deformation and dynamics of bulk bosonic fluid

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 superconductors and propose that the incoherent fluctuations of the charged scalar in the bulk is the holographic dual of the fluctuating Cooper pairs. Using a Madelung transformation and the velocity-potential formalism, we develop a quantum fluid dynamics as an effective theory for these bulk fluctuations. The new fluid dynamics takes care of the boundary conditions required by AdS/CFT and encodes the vacuum polarization effect in curved spacetime. The pseudogap in conductivity can be related to the plasma oscillation of this bulk fluid.

Dynamical instability of a driven-dissipative electron-hole condensate in the BCS-BEC crossover region

We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla \theta({\bf r})$ (where $\theta({\bf r})$ is the phase of the condensate) in the BCS regime, both leading to dynamical instabilities of an exciton-BEC. Our result suggests that substantial region of the exciton-BEC phase in the phase diagram (in terms of the interaction strength and the decay rate) is unstable.

Optimized perturbation theory applied to the study of the thermodynamics and BEC-BCS crossover in the three-color Nambu–Jona-Lasinio model

The Nambu--Jona-Lasinio model with two flavors, three colors and diquark interactions is analyzed in the context of optimized perturbation theory (OPT). Corrections to the thermodynamical potential that go beyond the large-$N_c$ (LN) approximation are taken into account, and the region of the phase diagram corresponding to intermediate chemical potentials and very low temperatures is explored. The simultaneous presence of both the quark-antiquark and diquark condensates can cause the system to behave as a fluid composed of a Bose-Einstein condensate (BEC) or a color superconductor one, in the form of a Bardeen-Cooper-Schrieffer (BCS) superfluid. The BEC-BCS crossover is then studied in the nonperturbative OPT scheme. The results obtained in the context of the OPT method are then contrasted with those obtained in the LN approximation. We show that there are values for the coupling constants related to quark-quark and quark-antiquark interactions where the corrections beyond LN brought by the OPT method can influence the behavior of the diquark condensate and the effective quark mass as a function of the baryon chemical potential. These changes in the behavior of the phase structure of the model modify the location of the critical point related to the phase structure as a whole of the model. Also, when we impose the color neutrality condition, our results show that the nature of the phase transition can change as well, shifting the ratio of the quark-antiquark and quark-quark interactions to higher values in the OPT case as compared to the LN approximation.

Pure Goldstone mode in the quench dynamics of a confined ultracold Fermi gas in the BCS-BEC crossover regime

We present a numerical study of the dynamic response of a confined superfluid Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic time-dependent density-matrix approach within the full Bogoliubov-de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of a Goldstone mode of the BCS gap in a cigar-shaped $^6$Li gas. By analyzing this Goldstone mode over a wide range of parameters, we show that its excitation spectrum is gapless and that its main frequency is not fixed by the trapping potential but that it is determined by the details of the quench. Thus, we report the emergence of a pure Goldstone mode of the BCS gap that --in contrast to situations in many previous studies-- maintains its gapless excitation spectrum predicted by the Goldstone theorem. Furthermore, we observe that the size-dependent superfluid resonances resulting from the atypical BCS-BEC crossover have a direct impact on this Goldstone mode. Finally, we find that the interaction quench-induced Goldstone mode leads to a low-frequency in-phase oscillation of the single-particle occupations with complete inversion of the lowest-lying single-particle states which could provide a convenient experimental access to the pure gapless Goldstone mode.

Spin susceptibility and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $\chi_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $\chi_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a {\it uniform} Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from $\chi_{\rm t}(r,T)$, to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.

Snake instability of dark solitons across the BEC-BCS crossover: An effective-field-theory perspective

In the present article the snake instability mechanism for dark solitons in superfluid Fermi gases is studied in the context of a recently developed effective field theory [Eur. Phys. J. B 88, 122 (2015)]. This theoretical treatment has proven to be suitable to study stable dark solitons in quasi-1D setups across the BEC-BCS crossover. In this manuscript the nodal plane of the stable soliton solution is perturbed by adding a transverse modulation. The numerical solution of the system of coupled nonlinear differential equations describing the amplitude of the perturbation leads to the instability spectra which are calculated for a wide range of interaction regimes and compared to other theoretical predictions. The maximum transverse size that the atomic cloud can have in order to preserve the stability is estimated, and the effects of spin-imbalance on this critical length are examined, revealing a stabilization of the soliton with increasing imbalance.

Effective-range dependence of two-dimensional Fermi gases

The Feshbach resonance provides precise control over the scattering length and effective range of interactions between ultracold atoms. We propose the ultratransferable pseudopotential to model effective interaction ranges $\ensuremath{-}1.5\ensuremath{\le}{k}_{\mathrm{F}}^{2}{R}_{\mathrm{eff}}^{2}\ensuremath{\le}0$, where ${R}_{\mathrm{eff}}$ is the effective range and ${k}_{\text{F}}$ is the Fermi wave vector, describing narrow to broad Feshbach resonances. We develop a mean-field treatment and exploit the pseudopotential to perform a variational and diffusion Monte Carlo study of the ground state of the two-dimensional Fermi gas, reporting on the ground-state energy, contact, condensate fraction, momentum distribution, and pair-correlation functions as a function of the effective interaction range across the BEC-BCS crossover. The limit ${k}_{\mathrm{F}}^{2}{R}_{\mathrm{eff}}^{2}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ is a gas of bosons with zero binding energy, whereas $ln({k}_{\mathrm{F}}a)\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ corresponds to noninteracting bosons with infinite binding energy.

Ground state properties of a two-dimensional Fermi superfluid with anisotropic spin–orbit coupling

In this study, we performed a theoretical investigation of the ground state properties of a two-dimensional ultra-cold Fermi superfluid with anisotropic spin–orbit coupling (SOC). In the absence of the Zeeman field, the system evolved from a weak coupling BCS regime to a strongly interacting BEC regime (BCS–BEC crossover) with increases in either the two-particle interaction strength or the SOC parameters. We focused on the behaviors of the pairing parameter and density of states (DOS) when the anisotropic parameter of the SOC increased. Surprisingly, we discovered that the gap parameter decreased as the anisotropic parameters increased, but the DOS at the Fermi surface exhibited non-monotonic behavior as a function of the anisotropic parameter. In the presence of the Zeeman field, we considered a particular type of topological phase transition by obtaining the analytical result for the topological invariant and we related this directly to the quantum phase transition with a sudden change in the ground state wave-function. The effects of higher partial wave pairing terms on this topological phase transition were also considered in this study.

Nonlocal equation for the superconducting gap parameter

The properties are considered in detail of a non-local (integral) equation for the superconducting gap parameter, which is obtained by a coarse-graining procedure applied to the Bogoliubov-deGennes (BdG) equations over the whole coupling-vs-temperature phase diagram associated with the superfluid phase. It is found that the limiting size of the coarse-graining procedure, which is dictated by the range of the kernel of this integral equation, corresponds to the size of the Cooper pairs over the whole coupling-vs-temperature phase diagram up to the critical temperature, even when Cooper pairs turn into composite bosons on the BEC side of the BCS-BEC crossover. A practical method is further implemented to solve numerically this integral equation in an efficient way, which is based on a novel algorithm for calculating the Fourier transforms. Application of this method to the case of an isolated vortex, throughout the BCS-BEC crossover and for all temperatures in the superfluid phase, helps clarifying the nature of the length scales associated with a single vortex and the kinds of details that are in practice disposed off by the coarse-graining procedure on the BdG equations.

Phonon effects in the excitonic condensation induced in the extended Falicov-Kimball model

A ground state of the excitonic condensate in the 2D extended Falicov-Kimball model involving the coupling of electrons and vibrational degrees of freedom has been investigated. Adapting the unrestricted Hartree-Fock approximation, we have derived a set of explicitly self-consistent equations determining both an excitonic order parameter and a lattice distortion when both the electron-phonon coupling and the electron-electron interaction are treated on an equal footing. A ground-state phase diagram of the excitonic condensate depending on the model parameters is constructed. The phase diagram shows us that a window of the excitonic condensate with lattice distortion increases when increasing the electron-phonon coupling or moving up the f-electron level, whereas, it is confined in between two critical values of the Coulomb interaction. The Coulomb interaction and the electron-phonon coupling have been affirmed to act together in establishing the excitonic condensate phase with lattice distortion in dichalcogenide systems. The BCS-BEC crossover of the excitonic condensation in the systems is also addressed.

S+is superconductivity with incipient bands: Doping dependence and STM signatures

Motivated by the recent observations of small Fermi energies and comparatively large superconducting gaps, present also on bands not crossing the Fermi energy (incipient bands) in iron-based superconductors, we analyse the doping evolution of superconductivity in a four-band model across the Lifshitz transition including BCS-BEC crossover effects on the shallow bands. Similar to the BCS case we find that with hole doping the phase difference between superconducting order parameters of the hole bands changes from $0$ to $\pi$ through an intermediate $s+is$ state breaking time-reversal symmetry. The transition however occurs in the region where electron bands are incipient and chemical potential renormalization in the superconducting state leads to a significant broadening of the $s+is$ region. We further present the qualitative features of the $s+is$ state that can be observed in scanning tunnelling microscopy (STM) experiments also taking incipient bands into account.

Effect of electron irradiation on the pseudogap temperature dependence of YBa $$_2$$ 2 Cu $$_3$$ 3 O $$_{7-\delta }$$ 7 - δ single crystals

The effect of electron irradiation on the basal-plane conductivity $$\sigma (T)$$ of YBa $$_2$$ Cu $$_3$$ O $$_{7-\delta }$$ single crystals is investigated. The excess conductivity $$\Delta \sigma (T)$$ has been revealed to obey an exponential temperature dependence in the broad temperature range $$T_f< T < T^*$$ , where $$T_f$$ is the transition temperature from the pseudogap state to the regime of fluctuation conductivity. The description of the excess conductivity by the relation $$\Delta \sigma (T) \propto (1-T/T^*)\exp (\Delta ^*_{ab}/T)$$ can be interpreted in terms of the mean-field theory where $$T^*$$ is the mean-field transition temperature to the pseudogap state and $$\Delta ^*(T)$$ is satisfactory described within the framework of the BCS-BEC crossover theory. In all, electron irradiation of the YBa $$_2$$ Cu $$_3$$ O $$_{7-\delta }$$ single crystals has been revealed to lead to an expansion of the temperature range of the pseudogap state, thereby narrowing the range of the linear dependence of $$\rho (T)$$ in the ab-plane.

Correlation length and universality in the BCS-BEC crossover for energy-dependent resonance superfluidity

We consider the BCS-BEC crossover of a quantum Fermi gas at T = 0 in the presence of an energy-dependent Fano-Feshbach resonance, driving the system from broad to narrow limits. We choose a minimal microscopic potential reproducing the two-particle resonance physics in terms of the scattering length a and the effective range R ∗ representing the resonance width, and solve the BCS mean-field equations varying a, R ∗ and the density. We show that the condensate fraction manifests a universal behavior when the correlation length, measuring the pair size, is used as the crossover parameter. Generally, a negative effective range has the effect of stretching the crossover region between the two extreme regimes, as evidenced by the behavior of the chemical potential. These results can be useful in view of the more recent perspectives of realizing narrow resonances also by optical means and amenable as a base quantum Monte Carlo simulations.

A nucleon-pair and boson coexistent description of nuclei**Supported by National Natural Science Foundation of China (11375080, 11675071), the U.S. National Science Foundation (OCI-0904874 and ACI-1516338), U. S. Department of Energy (DE-SC0005248), the Southeastern Universities Research Association, the China-U. S. Theory Institute for Physics with Exotic Nuclei (CUSTIPEN) (DE-SC0009971), and the LSU–LNNU joint research program (9961) is acknowledged

We study a mixture of s-bosons and like-nucleon pairs with the standard pairing interaction outside an inert core. Competition between the nucleon-pairs and s-bosons is investigated in this scenario. The robustness of the BCS-BEC coexistence and crossover phenomena are examined through an analysis of pf-shell nuclei with realistic single-particle energies, in which two configurations with Pauli blocking of nucleon-pair orbits due to the formation of the s-bosons is taken into account. When the nucleon-pair orbits are considered to be independent of the s-bosons, the BCS-BEC crossover becomes smooth, with the number of the s-bosons noticeably more than that of the nucleon-pairs near the half-shell point, a feature that is demonstrated in the pf-shell for several values of the standard pairing interaction strength. As a further test of the robustness of the BCS-BEC coexistence and crossover phenomena in nuclei, results are given for values of even-even 102–130Sn with 100Sn taken as a core and valence neutron pairs confined within the 1d5/2, 0g7/2, 1d3/2, 2s1/2, 1h11/2 orbits in the nucleon-pair orbit and the s-boson independent approximation. The results indicate that the B(E2) values are reproduced well.

Research on the Thermodynamic Property of Weakly Interacting Fermi Gases Through N-E-V Distribution and Pseudopotential Method

As the experiments of quantum system are conducted in the external field where the volume, energy and particle number are variable, the thermodynamic property of weakly interacting Fermi system is studied in this paper through the statistical distribution (N-E-V distribution) of a completely open system where the volume, energy and particle number are variable. Firstly, analytical expressions of internal energy, the equation of state, entropy and heat capacity expressed by Fermi integral are worked out. On that basis, the analytical expression and results of numerical calculation of the above thermodynamic quantities in extremely low temperature conditions can be known. Then, comparison between the calculations of N-E-V distribution and pseudopotential method (the volume and particle number remain the same) is drawn. The results show that the calculation of N-E-V distribution always makes up for the deviation of that of pseudopotential method. Besides, the most special thing about the calculation derived from N-E-V distribution is that the temperature variation curve of internal energy and that in the ideal Fermi system intersect. The characteristics of energy transfer between “attractive force” and “repulsive force” at the intersection temperature tc, which indicates that there is a phase transition. The intersection temperature does not change with the scattering length a (a0 repulsive force). Moreover, the intersection temperature of all weakly interacting Fermi system is 0.184 times as large as Fermi temperature, which is within the range of temperature for BEC and BCS phase transition and BEC-BCS crossover.

Local photoemission spectra and effects of spatial inhomogeneity in the BCS-BEC-crossover regime of a trapped ultracold Fermi gas

We theoretically investigate single particle excitations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-Condensation) crossover regime of an ultracold Fermi gas. Including strong pairing fluctuations within a $T$-matrix approximation, as well as effects of a harmonic trap potential in the local density approximation, we calculate the local photoemission spectrum in the normal state. Recently, JILA group has measured this quantity in a $^{40}$K Fermi gas, in order to examine homogeneous single-particle properties of this system. Comparing our results with this experiment, we show that, this attempt indeed succeeds under the JILA's experimental condition. However, we also find that the current local photoemission spectroscopy still has room for improvement, in order to examine the pseudogap phenomenon predicted in the BCS-BEC crossover region. Since ultracold Fermi gases are always in a trap, our results would be useful in applying this system to various homogeneous Fermi systems, as a quantum simulator.

Possible Fano resonance for high-Tc multi-gap superconductivity in p-Terphenyl doped by K at the Lifshitz transition

Recent experiments have reported the emergence of high-temperature superconductivity with critical temperature Tc between 43 K and 123 K in a potassium-doped aromatic hydrocarbon para-Terphenyl or p-Terphenyl. This achievement provides the record for the highest Tc in an organic superconductor overcoming the previous record of Tc = 38 K in Cs3C60 fulleride. Here we propose that the driving mechanism is the quantum resonance between superconducting gaps near a Lifshitz transition which belongs to the class of Fano resonances called shape resonances. For the case of p-Terphenyl our numerical solutions of the multigap equation shows that high Tc is driven by tuning the chemical potential by K doping and it appears only in a narrow energy range near a Lifshitz transition. At the maximum critical temperature, Tc = 123 K, the condensate in the appearing new small Fermi surface pocket is in the BCS-BEC crossover while the Tc drops below 0.3 K where it is in the BEC regime. Finally, we predict the experimental results which can support or falsify our proposed mechanism: a) the variation of the isotope coefficient as a function of the critical temperature and b) the variation of the gaps and their ratios 2Δ/Tc as a function of Tc.

Topological superfluids and the BEC-BCS crossover in the attractive Haldane-Hubbard model

Motivated by the recent realization of the Haldane model in shaking optical lattice, we investigate the effects of attractive interaction and BEC-BCS crossover in this model at and away from half filling. We show that, contrary to the usual s-wave BEC-BCS crossover in the lattice, a topological superfluid with Chern number C=2 appears in an extended region of phase space for intermediate strength of the attractive interaction in the interaction-density plane. When inversion symmetry is broken, a new gapless topological state is realized. We also investigate the fluctuations in these superfluid phases and show that the Anderson-Bogoliubov mode is quadratic due to time-reversal symmetry breaking and the existence of an undamped Leggett mode in the strong coupling limit.