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arXiv:2401.06054 · Physical review. B./Physical review. B

Finite-size effects in the two-dimensional BCS-BEC crossover

M. Lanaro, Giacomo Bighin, Luca Dell’Anna, Luca Salasnich

Published Mar 18, 2024• 1 citation
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Abstract

We study the finite-size effects on the BCS-BEC crossover in two dimensions, occurring in confined fermionic superfluids. We analyze several thermodynamic properties, such as the chemical potential, the energy gap, and the superfluid density, taking into account unavoidable quantum fluctuations, and, by means of the renormalization group procedure, we detect the putative Berezinskii-Kosterlitz-Thouless phase transition at finite size.

DOI
10.1103/physrevb.109.104511

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We study the finite-size effects on the BCS-BEC crossover in two dimensions, occurring in confined fermionic superfluids. We analyze several thermodynamic properties, such as the chemical potential, the energy gap, and the superfluid density, taking into account unavoidable quantum fluctuations, and, by means of the renormalization group procedure, we detect the putative Berezinskii-Kosterlitz-Thouless phase transition at finite size.
We study finite-temperature properties of a two-dimensional superfluid made of ultracold alkali-metal atoms in the BCS-BEC crossover. We investigate the region below the critical temperature TBKT{T}_{\mathrm{BKT}}TBKT​ of the Berezinskii-Kosterlitz-Thouless phase transition where there is quasicondensation by analyzing the effects of phase and amplitude fluctuations of the order parameter. In particular, we calculate the superfluid fraction, the sound velocity, and the quasicondensate fraction as a function of the temperature and of the binding energy of fermionic pairs.
The role of fluctuations is enhanced in lower dimensionality systems: in a two dimensions offdiagonal long-range order is destroyed by the fluctuations at any finite temperature, drastically modifying the critical properties with respect to the three-dimensional counterpart.Recently two-dimensional systems of interacting fermions have been the subject of Montecarlo studies and experimental investigations, in particular an ultracold gas of attractive fermions with a widely tunable interaction due to a Feshbach resonance has been realized and the Berezinskii-Kosterlitz-Thouless transition has been observed.The present work deals with the theoretical description of an ultracold Fermi gas: we discuss the role of Gaussian fluctuations of the order parameter in the equation of state, in particular we take into account the first sound velocity, showing that the inclusion of order parameter fluctuations is needed in order to get the correct composite-boson limit in the strong-coupling regime.The theory is also compared with experimental data.Finally we focus on the superfluid density in the weak-coupling, intermediate and strong-coupling regimes at finite temperature, through which the Berezinskii-Kosterlitz-Thouless critical temperature is obtained.
We analyze the theoretical derivation of the beyond-mean-field equation of state for two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover. We show that at zero temperature our theory — considering Gaussian fluctuations on top of the mean-field equation of state — is in very good agreement with experimental data. Subsequently, we investigate the superfluid density at finite temperature and its renormalization due to the proliferation of vortex–antivortex pairs. By doing so, we determine the Berezinskii–Kosterlitz–Thouless (BKT) critical temperature — at which the renormalized superfluid density jumps to zero — as a function of the inter-atomic potential strength. We find that the Nelson–Kosterlitz criterion overestimates the BKT temperature with respect to the renormalization group equations, this effect being particularly relevant in the intermediate regime of the crossover.
We use the functional renormalization group approach with partial bosonization in the particle-particle channel to study the effect of order parameter fluctuations on the BCS-Bose-Einstein condensate (BEC) crossover of superfluid fermions in three dimensions. Our approach is based on a new truncation of the vertex expansion where the renormalization group flow of bosonic two-point functions is closed by means of Dyson-Schwinger equations and the superfluid order parameter is related to the single-particle gap via a Ward identity. We explicitly calculate the chemical potential, the single-particle gap, and the superfluid order parameter at the unitary point and compare our results with experiments and previous calculations.
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.
The two-species Fermi gas with attractive short-range interactions in two spatial dimensions provides a paradigmatic system for the understanding of strongly correlated Fermi superfluids in two dimensions. It is known to exhibit a BEC to BCS crossover as a function of ln(k_{F}a), where a is the scattering length, and to undergo a Berezinskii-Kosterlitz-Thouless superfluid transition below a critical temperature T_{c}. However, the extent of a pseudogap regime in the strongly correlated regime of ln(k_{F}a)∼1, in which pairing correlations persist above T_{c}, remains largely unexplored with controlled theoretical methods. Here, we use finite-temperature auxiliary-field quantum Monte Carlo methods on discrete lattices in the canonical ensemble formalism to calculate thermodynamical observables in the strongly correlated regime. We extrapolate to continuous time and the continuum limit to eliminate systematic errors and present results for particle numbers ranging from N=42 to N=162. We estimate T_{c} by a finite-size scaling analysis, and observe clear pseudogap signatures above T_{c} and below a temperature T^{*} in both the spin susceptibility and free-energy gap. We also present results for the contact, a fundamental thermodynamic property of quantum many-body systems with short-range interactions.