The Bardeen-Cooper-Schrieffer (BCS) condensation and the Bose-Einstein condensation (BEC) are the two extreme limits of the ground state of the paired fermion systems. We report crossover behavior from the BCS condensation to the BEC realized in the two-dimensional (2D) superconductor, electron doped layered material ZrNCl. The phase diagram, established by simultaneous experiments of resistivity and tunneling spectra under the ionic gating, demonstrates the pseudogap phase at the low doping regime. In the low carrier density limit, $T_{\rm BKT}$ (Berezinskii-Kosterlitz-Thouless transition temperature for 2D superconductors) scales as $T_{\rm BKT}/T_{\rm F} = 0.12$, where $T_{\rm F}$ is the Fermi temperature, which is consistent with the theoretical upper bound expected in the BCS-BEC crossover regime. The present results indicate that the gate-doped semiconductor provides an ideal platform for the 2D BCS-BEC crossover without any added complexity, such as magnetic orders and density waves.
The thermodynamic potential is calculated for a uniform superfluid gas of fermi atoms from the mean field BCS equations including corrections from induced interactions, Hartree-Fock energies and quasiparticle selfenergies. The entropy, specific heat and sound modes are calculated as function of temperature, density and interaction strength from the BCS to the unitarity limit and around the BCS-BEC crossover. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature.
Superconductivity in iron-based, magnesium diborides, and other novel superconducting materials has a strong multi-band and multi-gap character. Recent experiments support the possibillity for a BCS-BEC crossover induced by strong-coupling and proximity of the chemical potential to the band edge of one of the bands. Here we study the simplest theoretical model which accounts for the BCS-BEC crossover in a two-band superconductor, considering tunable interactions and tunable energy separations between the bands. Mean-field results for condensate fraction, correlation length, and superconducting…
We study the change in condensation energy from a single pair of fermionic atoms to a large number of pairs interacting via the reduced BCS potential. We find that the energy-saving due to correlations decreases when the pair number increases because the number of empty states available for pairing gets smaller ("moth-eaten effect"). However, this decrease dominates the 3D kinetic energy increase of the same amount of noninteracting atoms only when the pair number is a sizeable fraction of the number of states available for pairing. As a result, in BEC-BCS crossover of 3D systems, the condensa…
Based on a simple model of a layered superconductor with strong attractive interaction, we find that the separation of the pair-condensation temperature from the pair-formation temperature becomes more remarkable as the interlayer hopping gets smaller. We propose from this result the BCS-BEC crossover induced by the change in dimensionality, for instance, due to insertion of additional insulating layers or application of uniaxial pressure. The emergence of a pseudogap in the electronic density of states, which supports the idea of the dimensionality-induced BCS-BEC crossover, is also verified.
For the Cooper/BCS model interaction in superconductors (SCs) it is shown: a) how BCS-Bose crossover picture transition temperatures Tc, defined self-consistently by both the gap and fermion-number equations, require unphysically large couplings to differ significantly from the Tc of ordinary BCS theory defined without the number equation since here the chemical potential is assumed equal to the Fermi energy; how although ignoring either hole- or electron-Cooper-pairs in the recent "complete boson-fermion model": b) one obtains the precise BCS gap equation for all temperatures T, but c) only h…
We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter $1/k_Fa$, reaching their minimum value near unitarity. We find that, moving away from the weak coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.
Effects of superconducting fluctuation (SCF) on thermodynamic properties of electron systems in the so-called BCS-BEC-crossover regime are studied. As the attractive interaction between electrons becomes stronger upon approaching the BCS-BEC-crossover regime, importance of the mode coupling between SCF drastically increases. The enhanced mode coupling leads to lowering of both the zero-field superconducting critical temperature and the depairing field $B_\text{c2} (T)$. Consequently, SCF-induced contributions to the specific heat and the diamagnetic susceptibility can seemingly exceed the corr…
We study properties of excited states of an elongated Fermi superfluid along the BEC-BCS crossover including the unitarity limit. Analytic expressions for the sound velocity in an inhomogeneous as well as homogeneous Fermi superfluid along the crossover are obtained on the basis of the hydrodynamic theory. The complete excitation spectrum of axial quasiparticles with various discrete radial nodes are presented. We discuss the feasibility of measuring the sound velocity and the multibranch Bogoliubov spectrum experimentally.
The Bardeen-Cooper-Schrieffer (BCS) condensation and Bose-Einstein condensation (BEC) are the two limiting ground states of paired Fermion systems, and the crossover between these two limits has been a source of excitement for both fields of high temperature superconductivity and cold atom superfluidity. For superconductors, ultra-low doping systems like graphene and LixZrNCl successfully approached the crossover starting from the BCS-side. These superconductors offer new opportunities to clarify the nature of charged-particles transport towards the BEC regime. Here we report the study of vort…
We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half-filling where the electron-phonon coupling $g$ controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique. The dynamical effects induce distinct features such as absenceof the dispersion back-bending of Bogoliubov quasi-particles, non-monotonous coupling dependence of the pairing gap, and the soft phonon spectrum due to the Goldstone mode of local pair phase fluctuations. Also int…
Considering both "large-U" and "small-U" orbitals, it is found that the carriers of the high-Tc cuprates are polaron-like "stripons" carrying charge and located on stripe-like inhomogeneities, "quasi-electrons" carrying charge and spin, and "svivons" carrying spin and lattice distortion. This is shown to result in the observed anomalous spectroscopic and transport properties of the cuprates. Pairing results from transitions between pair states of stripons and quasi-electrons through the exchange of svivons, and a crossover occurs between BCS and Bose-Einstein condensation behaviors.
We investigate a mix-dimensional Fermi-Fermi mixture in which one species is confined in two-dimensional(2D) space while the other is free in three-dimensional space(3D). We determine the superfluid transition temperature $T_{c}$ for the entire BCS-BEC crossover including the important effects of noncondensed pairs. We find that the transition temperature reduces while the imbalance of mass is increased or lattice constant ($dz$) is reduced. In population imbalance case, the stability of superfluid is sharply destroyed by increasing the polarization.
Ultranarrow superconductors are in the strong quantum confinement regime with formation of multiple coherent condensates associated with the many subbands of the electronic structure. Here we analyze the multiband BCS-BEC crossover induced by the chemical potential tuned close to a subband bottom, in correspondence of a superconducting shape resonance. The evolution of the condensate fraction and of the pair correlation length in the ground state as functions of the chemical potential demonstrates the tunability of the BCS-BEC crossover for the condensate component of the selected subband. The…
First and second sound speeds are calculated for a uniform superfluid gas of fermi atoms as a function of temperature, density and interaction strength. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature. The sound modes and their dependence on density, scattering length and temperature are calculated in the BCS, molecular BEC and unitarity limits and a smooth crossover is extrapolated. It is found that first and second sound undergo avoided crossing on the BEC side due to mixing. Consequently, they are …
We consider the BCS-BEC crossover for a system of trapped Fermi atoms at finite temperature, both below and above the superfluid critical temperature, by including fluctuations beyond mean field. We determine the superfluid critical temperature and the pair-breaking temperature as functions of the attractive interaction between Fermi atoms, from the weak- to the strong-coupling limit (where bosonic molecules form as bound-fermion pairs). Density profiles in the trap are also obtained for all temperatures and couplings.
We show that in two-band $s$-wave superfluids it is possible to induce quantum phase transitions (QPTs) by tuning intraband and interband $s$-wave interactions, in sharp contrast to single-band $s$-wave superfluids, where only a crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensation (BEC) superfluidity occurs. For non-zero interband and attractive intraband interactions, we demonstrate that the ground state has always two interpenetrating superfluids possessing three spectroscopically distinct regions where pairing is qualitatively different: (I) BCS pairing in both b…
The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the critical temperature for the whole range in the scattering length $a$. On the BCS side for small negative $a$ we recover the Gorkov approximation, while on the BEC side of small positive $a$ the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields $T_c/T_F=0.264$. We also investigate the crossover from broad to narrow Feshbach resonan…
The quasiparticles of the high-T_c cuprates are found to consist of: polaron-like "stripons" carrying charge, and associated primarily with large-U orbitals in stripe-like inhomogeneities; "quasielectrons" carrying charge and spin, and associated with hybridized small-U and large-U orbitals; and "svivons" carrying spin and lattice distortion. It is shown that this electronic structure leads to the systematic behavior of spectroscopic and transport properties of the cuprates. High-T_c pairing results from transitions between pair states of stripons and quasielectrons through the exchange of svi…
We contrast {\it four} distinct versions of the BCS-Bose statistical crossover theory according to the form assumed for the electron-number equation that accompanies the BCS gap equation. The four versions correspond to explicitly accounting for two-hole-(2h) as well as two-electron-(2e) Cooper pairs (CPs), or both in equal proportions, or only either kind. This follows from a recent generalization of the Bose-Einstein condensation (GBEC) statistical theory that includes not boson-boson interactions but rather 2e- and also (without loss of generality) 2h-CPs interacting with unpaired electrons…
Superfluidity in coupled electron-hole sheets of bilayer graphene is predicted here to be multicomponent because of the conduction and valence bands. We investigate the superfluid crossover properties as functions of the tunable carrier densities and the tunable energy band gap $E_g$. For small band gaps there is a significant boost in the two superfluid gaps, but the interaction driven excitations from the valence to the conduction band can weaken the superfluidity, even blocking the system from entering the BEC regime at low densities. At a given larger density, a band gap $E_g\sim 40$-$60$ …
We investigate the BCS-BEC crossover taking into account an additional three-body interaction, which is essentially the scattering between the Cooper pairs and the newly formed bosons. We show that if the two-body interaction is attractive, the presence of this additional three-body term makes the crossover process a nonreversible one. Starting from a stable Bose-Einstein condensate (BEC) state, crossover to BCS can be achieved; but if the BCS state is the starting point, instead of a stable BEC region, what the system crosses over to is a metastable condensed state.
The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in a superconducting and Fermi superfluid medium is studied from the exact ground state wavefunction of the reduced BCS Hamiltonian. As the strength of the interaction increases, the ground state continuously evolves from a mixed-system of quasifree fermions and pair resonances (BCS), to pair resonances and quasibound molecules (pseudogap), and finally to a system of quasibound molecules (BEC). A single unified scenario arises where the Cooper-pair wavefunction has a unique functional form. Several exact analytic expressions, suc…
Strong evidence for pairing and superfluidity has recently been found in atomic Fermi gases at the BCS-BEC crossover both in collective modes and RF excitation energies. It is argued that the scale for the effective pairing gaps measured in RF experiments is set by the lowest quasiparticle in-gap excitation energies. These are calculated at the BCS-BEC crossover from semiclassical solutions to the Bogoliubov-deGennes equations. The strong damping of the radial breathing mode observed in the BCS limit occur when the lowest quasiparticle excitation energies coincide with the radial frequency, wh…
We study the effect of the induced interaction on the superfluid transition temperature of a Fermi gas with a BEC-BCS crossover. The Gorkov-Melik-Barkhudarov theory about the induced interaction is extended from the BCS side to the entire crossover, and the pairing fluctuation is treated in the approach by Nozières and Schmitt-Rink. At unitarity, the induced interaction reduces the transition temperature by about twenty percent. In the BCS limit, the transition temperature is reduced by a factor about 2.22, as found by Gorkov and Melik-Barkhudarov. Our result shows that the effect of the induc…
Predictions for the chemical potential and the excitation gap recently obtained by our diagrammatic theory for the BCS-BEC crossover in the superfluid phase are compared with novel Quantum Monte Carlo results at zero temperature now available in the literature. A remarkable agreement is found between the results obtained by the two approaches
In paired Fermi systems, strong many-body effects exhibit in the crossover regime between the Bardeen-Cooper-Schrieffer (BCS) and the Bose-Einstein condensation (BEC) limits. The concept of the BCS-BEC crossover, which is studied intensively in the research field of cold atoms, has been extended to condensed matters. Here, by analyzing the typical superconductors within the BCS-BEC phase diagram, we find that FeSe-based superconductors are prone to shift their positions in the BCS-BEC crossover regime by charge doping or substrate substitution, since their Fermi energies and the superconductin…
We discuss the superfluid wave function of an atomic Fermi gas, which can be measured in an atom shot noise correlation experiment. We note that it is qualitatively different in the BCS and Bose limits and on the basis of this we propose quantitative criteria to identify the crossover between the two regimes.
By using a Path Integral formalism, we study the fluctuating fields in the order parameter for a 3D uniform Fermi gas at T<Tc. The BCS-BEC crossover condition is included into the analysis in the framework of the usual s-wave scattering approximation. The general expressions for the temperature dependence of the partition function and the quadratic average in the fluctuations fields are explicitly established in terms of the BCS-Gor'kov correlation propagators.
Theoretical treatments of the BCS-BEC crossover need to provide as accurate as possible descriptions of the two regimes where the diluteness condition applies, either in terms of the constituent fermions (BCS limit) or of the composite bosons which form as bound-fermion pairs (BEC limit). This has to occur via a single fermionic theory that bridges across these two limiting representations. In this paper, we set up successive improvements of the fermionic theory, that result into composite bosons described at the level of either the Bogoliubov or the Popov approximations for point-like bosons.…
The collective mode frequencies in isotropic and deformed traps are calculated for general polytropic equation of states, $P\propto n^{γ+1}$, and expressed in terms of $γ$ and the trap geometry. For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the effective power $γ\simeq0.5-1.3$ is calculated from Jastrow type wave-function ansätze, and from the crossover model of Leggett. The resulting mode frequencies are calculated for these phases around the BCS-BEC crossover.
With reference to the broad and narrow Fano-Feshbach resonances of 6Li at about 822 G and 543 G, we show that for the broad resonance a molecular coupled-channel calculation can be mapped with excellent accuracy onto an effective single-channel problem with a contact interaction. This occurs for a wide enough range of the magnetic field, that the full BCS-BEC crossover can be realized with a typical trap. For the narrow resonance, the mapping onto a single-channel problem and the realization of the BCS-BEC crossover are restricted to too narrow a range of the magnetic field to obtain them in p…
We present a mean field approach based on pairs of fermionic atoms to describe condensates in the BEC-BCS crossover regime. By introducing an effective potential, the mean field equation allows us to calculate the chemical potential, the equation of states and the atomic correlation function. The results agree surprisingly well with recent quantum Monte Carlo calculations. We show that the smooth crossover from the bosonic mean field repulsion between molecules to the Fermi pressure among atoms is associated with the evolution of the atomic correlation function.
We calculate the parameters of the Ginzburg-Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg-Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg-Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical ro…
The main focus of this paper is a discussion of what might happen in a BCS superfluid when there is an imbalance between the two populations of fermionic particles forming Cooper pairs, having in mind the case of ultracold Fermi gases. In the last part the evolution in the BEC-BCS crossover of the collective mode arising in such a superfluid (with balanced atomic populations) is briefly considered.
We review the BCS-BEC crossover in relativistic Fermi systems, including the QCD matter at finite density. In the first part we study the BCS-BEC crossover in a relativistic four-fermion interaction model and show how the relativistic effect affects the BCS-BEC crossover. In the second part, we investigate both two-color QCD at finite baryon density and pion superfluid at finite isospin density, by using an effective Nambu--Jona-Lasinio model. We will show how the model describes the weakly interacting diquark and pion condensates at low density and the BEC-BCS crossover at high density.
We discuss an integrable model of interacting Fermions in one dimension, that allows an exact description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 Fermions to the Lieb-Liniger model of repulsive Bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from minus infinity to plus infinity while the system evolves from a BCS-like state through a Tonks gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and sp…
We present the Bogoliubov theory for the Bose-Einstein condensation of Feshbach molecules in a balanced Fermi mixture. Because the Bogoliubov theory includes (Gaussian) fluctuations, we can in this manner accurately incorporate both the two-body and many-body aspects of the BEC-BCS crossover that occurs near a Feshbach resonance. We apply the theory in particular to the very broad Feshbach resonance in atomic Li-6 at a magnetic field of B_0 = 834 G and find good agreement with experiments in that case. The BEC-BCS crossover for more narrow Feshbach resonances is also discussed.
We investigate the macroscopic quantum tunneling of fermionic superfluids in the two-dimensional BCS-BEC crossover by using an effective tunneling energy which explicitly depends on the condensate fraction and the chemical potential of the system. We compare the mean-field effective tunneling energy with the beyond-mean-field one finding that the mean-field tunneling energy is not reliable in the BEC regime of the crossover. Then we solve the Josephson equations of the population imbalance and the relative phase calculating the frequency of tunneling oscillation both in the linear regime and i…
We report on precision measurements of the frequency of the radial compression mode in a strongly interacting, optically trapped Fermi gas of Li-6 atoms. Our results allow for a test of theoretical predictions for the equation of state in the BEC-BCS crossover. We confirm recent quantum Monte-Carlo results and rule out simple mean-field BCS theory. Our results show the long-sought beyond-mean-field effects in the strongly interacting BEC regime.
We investigate the non-universal behavior of the BCS-BEC crossover model at the normal to superfluid transition. By using a finite temperature quantum field theoretical approach due to Nozieres and Schmitt-Rink and by making the effective range expansion of the effective two-body interaction we numerically calculate the crossover transition temperature as a function of the scattering length, $a_{F},$ and the effective range parameter, $r_{\mathrm{e}}.$ In an ultracold two-component atomic Fermi gas BCS-BEC crossover physics is expected to appear near magnetic-field-induced Feshbach resonances.…
We study the stationary Josephson effect for neutral fermions across the BCS-BEC crossover, by solving numerically the Bogoliubov-de Gennes equations at zero temperature. The Josephson current is found to be considerably enhanced for all barriers at about unitarity. For vanishing barrier, the Josephson critical current approaches the Landau limiting value which, depending on the coupling, is determined by either pair-breaking or sound-mode excitations. In the coupling range from the BCS limit to unitarity, a procedure is proposed to extract the pairing gap from the Landau limiting current.
The theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in the BCS (weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc…
We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasi-molecules with finite orbital angular momenta $L_z=\pm1,0$, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper-pairs and mol…
Theoretical predictions for the BCS-BEC crossover of trapped Fermi atoms are compared with recent experimental results for the density profiles of $^6$Li. The calculations rest on a single theoretical approach that includes pairing fluctuations beyond mean field. Excellent agreement with experimental results is obtained. Theoretical predictions for the zero-temperature chemical potential and gap at the unitarity limit are also found to compare extremely well with Quantum Monte Carlo simulations and with recent experimental results.
Using the coarse-grain averaged hydrodynamic approach, we calculate all low energy transverse excitation spectrum of a rotating Fermi superfluid containing vortex lattices for all regimes along the BEC-BCS crossover. In the fast rotating regime, the molecular BEC enters into the lowest Landau level, but the superfluid in the unitarity and the BCS regimes occupies many low-lying Landau levels. The difference between the breathing mode frequencies at the BEC and unitarity limit shrinks to zero as the rotation speed approaches the radial trap frequency, in contrast to the finite difference in the…
We discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields are critically analyzed in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover both in three spatial dimensions and in two spatial dimensions. The crucial role of pair fluctuations is investigated, and the beyond-mean-field Gaussian theory of the BCS-BEC crossover is compared with available experimental data of the two-dimensional u…
The work by Soares et al. [Phys. Rev. B 65, 174506 (2002)] investigates the BCS-BE crossover for d-wave pairing in the 2-dimensional attractive Hubbard model. Contrary to their claims, we found that a non-pairing region does not exist in the density vs coupling phase diagram. The gap parameter at T=0, as obtained by solving analytically as well as numerically the BCS equations, is in fact finite for any non-zero density and coupling, even in the weak-coupling regime.
We present a theory of a two-component atomic Fermi gas with tunable attractive contact interactions on a spherical shell going through the Bardeen-Cooper-Schrieffer (BCS) - Bose Einstein condensation (BEC) crossover, inspired by the realizations of spherical bubble traps for ultracold atoms in microgravity. The derivation follows the BCS-Leggett theory to obtain the gap and number equations. The BCS-BEC crossover can be induced by tuning the interaction, and the properly normalized gap and chemical potential exhibit universal behavior regardless of the planar or spherical geometry. Neverthele…
The crossover from Bardeen-Cooper-Schrieffer (BCS) superconductivity to Bose-Einstein condensation (BEC) is difficult to realize in quantum materials because, unlike in ultracold atoms, one cannot tune the pairing interaction. We realize the BCS-BEC crossover in a nearly compensated semimetal Fe$_{1+y}$Se$_x$Te$_{1-x}$ by tuning the Fermi energy, $ε_F$, via chemical doping, which permits us to systematically change $Δ/ ε_F$ from 0.16 to 0.5 were $Δ$ is the superconducting (SC) gap. We use angle-resolved photoemission spectroscopy to measure the Fermi energy, the SC gap and characteristic chang…
In this paper we present predictions for thermodynamic and transport properties of a BCS Bose-Einstein crossover theory, below Tc, which theory satisfies the reasonable constraints that it yield (i) the Leggett ground state and (ii) BCS theory at weak coupling and all temperatures. The nature of the strong coupling limit is inferred, along with the behavior of the Knight shift, superfluid density, and specific heat. Comparisons with existing data on short coherence length superconductors, such as organic and high Tc systems, are presented, which provide some support for the present picture.
We study thermodynamics of a two-species Feshbach-resonant atomic Fermi gas in a periodic potential, focusing in a deep optical potential where a tight binding model is applicable. We show that for more than half-filled band the gas exhibits a reentrant crossover with decreased detuning (increased attractive interaction), from a paired BCS superfluid to a Bose-Einstein condensate (BEC) of molecules of holes, back to the BCS superfluid, and finally to a conventional BEC of diatomic molecules. This behavior is associated with the non-monotonic dependence of the chemical potential on detuning and…
We report quantum Monte Carlo evidence of the existence of large gap superfluidity in electron-hole double layers over wide density ranges. The superfluid parameters evolve from normal state to BEC with decreasing density, with the BCS state restricted to a tiny range of densities due to the strong screening of Coulomb interactions, which causes the gap to rapidly become large near the onset of superfluidity. The superfluid properties exhibit similarities to ultracold fermions and iron-based superconductors, suggesting an underlying universal behavior of BCS-BEC crossovers in pairing systems.
We investigate the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of weakly-bound Cooper pairs to the Bose-Einstein Condensate (BEC) of strongly-bound molecular dimers in a gas of ultracold atoms loaded on a two-dimensional optical lattice. By using the the mean-field BCS equations of the emerging Hubbard model and the concept of off-diagonal-long-range-order for fermions we calculate analytically and numerically the pair binding energy, the energy gap and the condensate fraction of Cooper pairs as a function of interaction strength and filling fractor of atoms in the lattice at zero…
The BEC-BCS crossover in QCD at finite baryon and isospin chemical potentials is investigated in the Nambu--Jona-Lasinio model. The diquark condensation in two color QCD and the pion condensation in real QCD would undergo a BEC-BCS crossover when the corresponding chemical potential increases. We determined the crossover chemical potential as well as the BEC and BCS regions. The crossover is not triggered by increasing the strength of attractive interaction among quarks but driven by changing the charge density. The chiral symmetry restoration at finite temperature and density plays an importa…
The strongly-correlated regime of the BCS-BEC crossover can be realized by diluting a system of two-component fermions with a short-range attractive interaction. We investigate this system via a novel continuous-space-time diagrammatic determinant Monte Carlo method and determine the universal curve $T_c/ε_F$ for the transition temperature between the normal and the superfluid states as a function of the scattering length with the maximum on the BEC side. At unitarity, we confirm that $T_c/ε_F = 0.152(7)$.
We have considered the BCS-BEC crossover at T=0 in the framework of a lattice fermion model (the extended Hubbard model). We have analyzed the case of on-site hard core repulsion ($U=\infty$) and intersite attraction ($W<0$) in a 3D system with extended s-wave pairing symmetry. The mechanisms of density-driven and attraction-strength-driven crossover have been analyzed. We have obtained the ground state phase diagram. The analyzed quantities are: chemical potential, order parameter, coherence length and fraction of condensed particles.
We study the superconducting transition in a two-dimensional electron gas with strong Rashba spin-orbit coupling. We assume low electron density, such that only the majority spin band participates in the transition. We show that the superconducting transition follows either the Bose-Einstein condensation (BEC), or the Bardeen-Cooper-Schrieffer (BCS) scenarios, depending on the position of the chemical potential with respect to the bottom of the majority band, and the strength of the Coulomb repulsion between electrons. Hence, the BEC-BCS crossover in this system can be driven either by the cha…
