Abstract We discuss standard and tighter upper bounds on the critical temperature T c of two-dimensional superfluids and superconductors versus particle density n or filling factor ν for continuum and lattice systems from the Bardeen–Cooper–Schrieffer (BCS) to the Bose regime. We consider only one-band Hamiltonians, where the transition from the normal to the superfluid (superconducting) phase is governed by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism of vortex-antivortex binding, such that a direct relation between the superfluid density tensor and T c exists. The standard critical temperature upper bound T c up 1 is obtained from the Ferrell-Glover-Tinkham sum rule for the optical conductivity, which constrains the superfluid density tensor components. We demonstrate that it is imperative to consider at least the full effect of phase fluctuations of the order parameter for superfluidity (superconductivity) and use the renormalization group to obtain the phase-fluctuation critical temperature T c θ , a much tighter bound to the critical temperature supremum than T c up 1 over a wide range of densities or filling factors. We also discuss a fundamental difference between superfluids and superconductors in regards to the vortex core energy dependence on density. Going beyond phase fluctuations, we note that theories including modulus fluctuations of the order parameter or particle-hole fluctuations valid throughout the BCS-Bose evolution are still lacking, but the inclusion of these fluctuations can only produce a critical temperature that is lower than T c θ and thus produce an even tighter bound to the critical temperature supremum. We conclude by indicating that if the measured critical temperature exceeds T c θ in experiments involving two-dimensional single-band systems, then a non-BKT mechanism must be invoked to describe the superfluid (superconducting) transition.
Abstract We discuss standard and tighter upper bounds on the critical temperature T c of two-dimensional superfluids and superconductors versus particle density n or filling factor ν for continuum and lattice systems from the Bardeen–Cooper–Schrieffer (BCS) to the Bose regime. We consider only one-band Hamiltonians, where the transition from the normal to the superfluid (superconducting) phase is governed by the Berezinskii–Kosterlitz–Thouless (BKT) mechanism of vortex-antivortex binding, such that a direct relation between the superfluid density tensor and T c exists. The standard critical temperature upper bound T c up 1 is obtained from the Ferrell-Glover-Tinkham sum rule for the optical conductivity, which constrains the superfluid density tensor components. We demonstrate that it is imperative to consider at least the full effect of phase fluctuations of the order parameter for superfluidity (superconductivity) and use the renormalization group to obtain the phase-fluctuation critical temperature T c θ , a much tighter bound to the critical temperature supremum than T c up 1 over a wide range of densities or filling factors. We also discuss a fundamental difference between superfluids and superconductors in regards to the vortex core energy dependence on density. Going beyond phase fluctuations, we note that theories including modulus fluctuations of the order parameter or particle-hole fluctuations valid throughout the BCS-Bose evolution are still lacking, but the inclusion of these fluctuations can only produce a critical temperature that is lower than T c θ and thus produce an even tighter bound to the critical temperature supremum. We conclude by indicating that if the measured critical temperature exceeds T c θ in experiments involving two-dimensional single-band systems, then a non-BKT mechanism must be invoked to describe the superfluid (superconducting) transition.
We discuss standard and tighter upper bounds on the critical temperature Tc of two-dimensional (2D) superconductors and superfluids versus particle density n or filling factor ν for continuum and lattice systems from the Bardeen-Cooper-Schrieffer (BCS) to Bose regime. We discuss only one-band Hamiltonians, where the transition from the normal to superconducting (superfluid) phase is governed by Berezinskii-Kosterlitz-Thouless (BKT) mechanism of vortex-antivortex binding, such that a direct relation between the superfluid density tensor and Tc exists. We demonstrate that it is imperative to consider at least the full effect of phase fluctuations of order parameter for superconductivity (superfluidity) to establish tighter bounds. Using the renormalization group, we obtain phase-fluctuation critical temperature Tcθ, a much tighter upper bound to critical temperature supremum Tcsup than standard critical temperature upper bound Tcup1 from Ferrell-Glover-Tinkham sum rule. We go beyond textbook phase-fluctuation theories and show that chemical potential renormalization, order parameter equation, and Nelson-Kosterlitz relation need to be solved self-consistently and simultaneously with renormalization group flow equation to produce Tcθ over the entire BCS-Bose crossover. We note that an analytic theory including modulus fluctuations of the order parameter valid throughout the BCS-Bose evolution is still lacking, but the inclusion of modulus fluctuations can only produce a critical temperature lower than Tcθ and thus produce an even tighter bound to Tcsup. We conclude by indicating that if the measured critical temperature exceeds Tcθ in experiments involving 2D single-band systems, then a non-BKT mechanism must be invoked to describe the superconducting (superfluid) transition.
We discuss standard and tighter upper bounds on the critical temperature Tc of two-dimensional superconductors and superfluids versus particle density n or filling factor ν, under the assumption that the transition from the normal to the superconducting (superfluid) phase is governed by the Berezinskii-Kosterlitz-Thouless (BKT) mechanism of vortex-antivortex binding and a direct relation between the superfluid density tensor and Tc exists. The standard critical temperature upper bound Tcup1 is obtained from the Glover-Ferrell-Tinkham sum rule for the optical conductivity, which constrains the superfluid density tensor components. However, we show that Tcup1 is only useful in the limit of low particle/carrier density, where it may be close to the critical temperature supremum Tcsup . For intermediate and high particle/carrier densities, Tcup1 is far beyond Tcsup for any given interaction strength. We demonstrate that it is imperative to consider at least the full effects of phase fluctuations of the order parameter for superconductivity (superfluidity) to establish tighter bounds over a wide range of densities. Using the renormalization group, we obtain the critical temperature supremum for phase fluctuations Tc and show that it is a much tighter upper bound to Tcsup than Tcup1 for all particle/carrier densities. We conclude by indicating that if the Tc is exceeded in experiments involving single band systems, then a non-BKT mechanism must be invoked.
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 review aspects of the evolution from Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) in two dimensions, which have now become relevant in systems with low densities, such as gated superconductors Li xZrNCl, magic-angle twisted trilayer graphene, FeSe, FeSe1− xS x, and ultracold Fermi superfluids. We emphasize the important role played by chemical potentials in determining crossovers or topological quantum phase transitions during the BCS–BEC evolution in one-band and two-band superfluids and superconductors. We highlight that crossovers from BCS to BEC occur for pairing in nonnodal s-wave channels, whereas topological quantum phase transitions, in which the order parameter symmetry does not change, arise for pairing in any nodal higher angular momentum channels, such as d-wave. We conclude by discussing a few open questions regarding the BCS-to-BEC evolution in 2D, including modulus fluctuations of the order parameter, tighter upper bounds on critical temperatures, and the exploration of lattice effects in two-band superconductors and superfluids.
Abstract We discuss the evolution from Bardeen-Cooper-Schrieffer (BCS) to Bose superconductivity vs . carrier density n in two-dimensional (2D) gated superconductors and address the fundamental role that the interaction range plays in the Berezinskii-Kosterlitz-Thouless transition. We investigate the density dependence of the critical temperature ( T c ), superfluid density, order parameter modulus, chemical potential and pair size. Our most important finding is that it is absolutely essential to include classical and quantum phase fluctuations, as well as finite-ranged interactions to explain the non-monotonic behavior of T c vs . n and to guarantee that the upper bound on T c is not exceeded in 2D superconductors, as experimentally observed in (Nakagawa Y. et al. , Science , 372 (2021) 190), a lithium-intercalated layered nitride, and in magic-angle twisted trilayer graphene (Park J. M. et al. , Nature , 590 (2021) 249). Furthermore, we show that we can extract, from measurements of T c and the order parameter modulus, the effective mass of charge carriers and their interaction strength and range.
Understanding the material parameters that control the superconducting transition temperature T c is a problem of fundamental importance.In many novel superconductors phase fluctuations determine T c , rather than the collapse of the pairing amplitude.We derive rigorous upper bounds on the superfluid phase stiffness for multiband systems, valid in any dimension.This in turn leads to an upper bound on T c in two dimensions, which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry.Our bound is particularly useful for the strongly correlated regime of low-density and narrowband systems, where mean-field theory fails.For a simple parabolic band in 2D with Fermi energy E F , we find that k B T c ≤ E F =8, an exact result that has direct implications for the 2D BCS-BEC crossover in ultracold Fermi gases.Applying our multiband bound to magic-angle twisted bilayer graphene, we find that band structure results constrain the maximum T c to be close to the experimentally observed value.Finally, we discuss the question of deriving rigorous upper bounds on T c in 3D.