Bardeen–Cooper–Schrieffer Bose–Einstein Condensation Crossover Research Articles

Finite-range effect in the two-dimensional density-induced BCS–BEC crossover

Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.

Real-space BCS-BEC crossover in FeSe monolayers

The quantum many-body states in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover regime are of long-lasting interest. Here we report direct spectroscopic evidence of BCS-BEC crossover in real space in a FeSe monolayer thin film by using spatially resolved scanning tunneling spectra. The crossover is driven by the shift of band structure relative to the Fermi level. The theoretical calculation based on a two-band model qualitatively reproduces the measured spectra in the whole crossover range. In addition, the Zeeman splitting of the quasiparticle states is found to be consistent with the characteristics of a condensate. Our work paves the way to study the exotic states of BCS-BEC crossover in a two-dimensional crystalline material at the atomic scale.

Excitonic condensation state in the assistance of the adiabatic and anti-adiabatic phonons

The excitonic condensate in semimetal and semiconducting materials with the assistance of the phonons in both the adiabatic and anti-adiabatic regimes has been investigated. In the framework of the random phase approximation, we analyse the static excitonic susceptibility function once the electrons and holes are described in the extended Falicov–Kimball model involving the electron–phonon interaction. The excitonic condensate transition point is detected as a divergence of the susceptibility function. The complex phase diagrams exhibit the significant impact of the adiabatic phonons on the stability of the excitonic condensation state. In contrast, phonons in the anti-adiabatic regime play a less role in the formation and the condensation of the excitons. Depending on the temperature or the external pressure, the excitonic condensate stability and its Bardeen–Cooper–Schrieffer–Bose–Einstein condensation crossover in the systems are also discussed in detail.

Superconductivity of the FeSe/SrTiO3 Interface in View of BCS–BEC Crossover**Supported by the National Key R&D Program of China under Grant Nos 2017YFA0303600, 2016YFA0300600 and 2016YFA0202300, the National Natural Science Foundation of China under Grant No 11634016, the Strategic Priority Research Program (B) of Chinese Academy of Sciences under Grant No XDB07030100, the Research Program of Beijing Academy of Quantum Information

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 superconducting gap sizes are comparable. Especially at the interface of single-layer FeSe on SrTiO3 substrate, the superconductivity is relocated closer to the crossover unitary than other doped FeSe-based materials, indicating that the pairing interaction is effectively modulated. We further show that hole-doping can drive the interfacial system into the phase with possible pre-paired electrons, demonstrating its flexible tunability within the BCS–BEC crossover regime.

Impurity-induced Shiba bound state in the BCS–BEC crossover regime of two-dimensional Fermi superfluid**Project supported by the National Key R&D Program of China (Grant No. 2017YFA0206302).

For a two-dimensional ultra-cold Fermi superfluid with an effective static magnetic impurity, we theoretically investigated the variation of the Yu–Shiba–Rusinov (YSR) bound state in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover regime. Within the framework of mean-field theory, analytical results of the YSR bound state energy were obtained as a function of the interaction parameters. First, when the background Fermi superfluid system stays in the weakly interacting BCS regime, we found that the YSR bound state energy is linearly dependent on the gap parameter with its coefficient slightly different from previous results. Second, we discovered re-entrance phenomena for the YSR state and an upper bound of the strength of the interaction between the paired atoms. By carefully analyzing the bound state energy as a function of the interaction parameters, we obtained a phase diagram showing the existence of the YSR state. Finally, we concluded that the re-entrance phenomena and the critical point can be easily experimentally detected through measurement of radio-frequency spectroscopy and density of states using current experimental techniques.

Multi-regulator functional renormalization group for many-fermion systems

We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.

Zero-Temperature Properties of a Strongly Interacting Superfluid Fermi Gas in the BCS–BEC Crossover Region

We investigate thermodynamic properties and effects of quantum fluctuations in the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover region of a superfluid Fermi gas in the low-temperature limit. Including strong-coupling corrections within the framework of an extended T-matrix approximation, we numerically compute the isothermal compressibility $$\chi _n$$ . While quantum fluctuation effects on $$\chi _n$$ in the strong-coupling BEC regime are explained by the quantum depletion due to a repulsive interaction between tightly bound molecules, effects of self-energy shift on the Fermi chemical potential are found to enhance $$\chi _n$$ in the weak-coupling BCS region. We also show that the calculated $$\chi _n$$ agrees well with the recent experiment on a $$^6$$ Li Fermi gas done from the weak-coupling region to the unitarity limit. Our result would be useful for the study of many-body quantum corrections in the BCS–BEC crossover region of a strongly interacting Fermi superfluid.

BCS–BEC Crossover in Two-Dimensional Attractive Hubbard Model under Magnetic Field

The Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover in the two-dimensional attractive Hubbard model under the magnetic field is discussed at the half-filling at T=0 K on the basis of the formalism of Eagles and Leggett. It is shown that the so-called Fulde-Ferrel-Larkin-Ovchinikov-like state with a non-zero center-of-mass wave vector ${\bf q}\not=0$ is not stabilized in the weak-coupling (BCS) region, while such a state with ${\bf q}\not=0$ is stabilized against that with ${\bf q}=0$ even in a wide strong-coupling (BEC) region where di-fermion molecules are formed. The physical implication of this surprising result is discussed.

THE EFFECTS OF THE BEYOND MEAN FIELD CORRECTIONS OF FERMI SUPERFLUID GAS IN A DOUBLE-WELL POTENTIAL

By considering the contribution of the higher-order term representing the lowest approximation of beyond mean field corrections, we investigate a superfluid Fermi gas confined in a double-well potential in Bose–Einstein Condensation (BEC) side of the Bardeen–Cooper–Schrieffer (BCS) to BEC crossover. Two limited cases of deep BEC regime and BEC regime of BCS–BEC crossover, corresponding to the two-body scattering length a sc is small enough and large enough, respectively. We derive a simple two-mode model that could depict the dynamics effectively. With making thorough analysis on the two-mode model and its corresponding classical Hamiltonian, we find that the Josephson oscillation or self-trapping phenomenon could emerge at certain parameters. We find three kinds of the phase states: Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST) and running-phase-type self-trapping (RPTST). The dependence of these three phase states on the dimensionless interaction parameter y = 1/(kFa sc ) and the initial system energy are given in this paper.

BCS–BEC crossover in a trapped Fermi super-fluid using a density-functional equation

We derive a generalized time-dependent Galilean-invariant density-functional (DF) equation appropriate to study the stationary and non-stationary properties of a trapped Fermi super-fluid in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover. This equation is equivalent to a quantum hydrodynamical equation for a Fermi super-fluid. The bulk chemical potential of this equation has the proper (model-independent) dependence on the Fermi–Fermi scattering length in the BCS and BEC limits. We apply this DF equation to the study of the stationary density profile and size of a cigar-shaped Fermi super-fluid of 6Li atoms, and the results are in good agreement with the experiment of Bartenstein et al in the BCS–BEC crossover. We also apply the DF equation to the study of axial and radial breathing oscillation and our results for these frequencies are in good agreement with experiments in the BCS–BEC crossover.

Relativistic BCS–BEC crossover of a two-species Fermi gas with number density asymmetry at zero temperature

We systematically study relativistic two-species fermions with tunable attractive interactions and number-density asymmetry at zero temperature. In general, a Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC)–relativistic BEC (RBEC) crossover is observed. A generalized BCS ground state and its stability are analyzed. The homogeneous superfluid phase can become unstable and we consider phase separation in real space for neutral systems. In the nonrelativistic limit, our results are consistent with well-known results. In addition to a BCS–BEC crossover similar to that in the nonrelativistic case, in the strongly attractive regime gapless excitations of antifermions and a RBEC state are observed. We address how different phases respond to number density asymmetry and present predictive phase diagrams of BCS–BEC–RBEC crossover.

BCS-BEC crossover and thermodynamics in asymmetric nuclear matter with pairings in isospinI=0andI=1channels

The Bardeen/Cooper/Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover and phase diagram for asymmetric nuclear superfluid with pairings in isospin $I=0$ and $I=1$ channels are investigated at the mean-field level by using a density-dependent nucleon-nucleon potential. Induced by the in-medium nucleon mass and density-dependent coupling constants, neutron-proton Cooper pairs could be in BEC state at sufficiently low density, but there is no chance for the BEC formation of neutron-neutron and proton-proton pairs at any density and asymmetry. We calculate the phase diagram in asymmetry-temperature plane for weakly interacting nuclear superfluid and find that including the $I=1$ channel changes significantly the phase structure at low temperature. There appears a new phase with both $I=0$ and $I=1$ pairings at low temperature and low asymmetry, and the gapless state in any phase with $I=1$ pairing is washed out and all excited nucleons are fully gapped.

Collective Modes of a Quasi-Two-Dimensional Superfluid FermiGas in BCS-BEC Crossover

We investigate the collective modes of a quasi-two-dimensional (Q2D)superfluid Fermi gas in Bardeen–Cooper–Schrieffer Bose–Einsteincondensation (BCS-BEC) crossover. For solving a generalizedGross–Pitaevskii equation by using a time-dependent variational method,we take a trial wavefunction with the form of hybrid Gaussian-parabolictype, which not only reflects the Q2D character of the system and alsoallows an essentially analytical approach of the problem. We present aQ2D criterion that is valid for various superfluid regimes and displaysclearly the relation between the maximum condensed particle number andthe parameters of trapping potential as well as atom–atom interaction.We show that due to the small particle number in the Q2D condensate, thecontribution to oscillating frequencies by the quantum pressure in thestrong confinement direction is significant and hence a Thomas–Fermiapproximation can not be used.

BCS–BEC crossover in one-dimensional integrable model

Abstract The crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid with singlet pairs to Bose–Einstein condensation (BEC) of molecules is studied in one dimension. By use of the nested Bethe ansatz method, the ground state properties of spin-1/2 fermions interacting through attractive δ-function are analyzed explicitly for strong and weak couplings. Based on those results, we confirm a crossover picture, that is, in the BEC regime (strong couplings) the system is described by molecules with weak repulsion while in the BCS regime (weak couplings) it behaves as the weakly attractive fermions.