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12 pages, 1433 KiB

Open AccessArticle

Low-Lying Collective Excitations of Superconductors and Charged Superfluids

by Serghei Klimin, Jacques Tempere and Hadrien Kurkjian

Condens. Matter 2023, 8(2), 42; https://doi.org/10.3390/condmat8020042 - 3 May 2023

Cited by 1 | Viewed by 1927

We investigate theoretically the momentum-dependent frequency and damping of low-lying collective excitations of superconductors and charged superfluids in the BCS–BEC crossover regime. The study is based on the Gaussian pair-and-density fluctuation method for the propagator of Gaussian fluctuations of the pair and density [...] Read more.

We investigate theoretically the momentum-dependent frequency and damping of low-lying collective excitations of superconductors and charged superfluids in the BCS–BEC crossover regime. The study is based on the Gaussian pair-and-density fluctuation method for the propagator of Gaussian fluctuations of the pair and density fields. Eigenfrequencies and damping rates are determined in a mutually consistent nonperturbative way as complex poles of the fluctuation propagator. Particular attention is paid to new features with respect to preceding theoretical studies, which were devoted to collective excitations of superconductors in the far BCS regime. We find that at a sufficiently strong coupling, new branches of collective excitations appear, which manifest different behavior as functions of the momentum and the temperature. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors VII)

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12 pages, 328 KiB

Open AccessArticle

Rabi Coupled Fermions in the BCS–BEC Crossover

by Luca Dell’Anna, Federico De Bettin and Luca Salasnich

Condens. Matter 2022, 7(4), 59; https://doi.org/10.3390/condmat7040059 - 22 Oct 2022

Viewed by 1957

Abstract

We investigate the three-dimensional BCS–BEC crossover in the presence of a Rabi coupling, which strongly affects several properties of the system, such as the chemical potential, the pairing gap and the superfluid density. We determine the critical interaction strength, below which the system [...] Read more.

We investigate the three-dimensional BCS–BEC crossover in the presence of a Rabi coupling, which strongly affects several properties of the system, such as the chemical potential, the pairing gap and the superfluid density. We determine the critical interaction strength, below which the system is normal also at zero temperature. Finally, we calculate the effect of the Rabi coupling on the critical temperature of the superfluid-to-normal phase transition by using different theoretical schemes. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors VII)

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10 pages, 824 KiB

Open AccessReview

First and Second Sound in Two-Dimensional Bosonic and Fermionic Superfluids

by Luca Salasnich, Alberto Cappellaro, Koichiro Furutani, Andrea Tononi and Giacomo Bighin

Symmetry 2022, 14(10), 2182; https://doi.org/10.3390/sym14102182 - 17 Oct 2022

Cited by 1 | Viewed by 2073

Abstract

We review our theoretical results of the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the

U (1)

symmetry, there is the coexistence of first and [...] Read more.

We review our theoretical results of the sound propagation in two-dimensional (2D) systems of ultracold fermionic and bosonic atoms. In the superfluid phase, characterized by the spontaneous symmetry breaking of the

U (1)

symmetry, there is the coexistence of first and second sound. In the case of weakly-interacting repulsive bosons, we model the recent measurements of the sound velocities of

^{39}

K atoms in 2D obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless (BKT) superfluid-to-normal transition temperature. In particular, we perform a quite accurate computation of the superfluid density and show that it is reasonably consistent with the experimental results. For superfluid attractive fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover. In the low-temperature regime, we reproduce the recent measurements of first-sound speed with

^{6}

Li atoms. We also predict that there is mixing between sound modes only in the finite-temperature BEC regime. Full article

(This article belongs to the Special Issue Symmetry and Pauli Exclusion Principle)

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12 pages, 709 KiB

Open AccessArticle

Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

by Filippo Pascucci, Andrea Perali and Luca Salasnich

Condens. Matter 2021, 6(4), 49; https://doi.org/10.3390/condmat6040049 - 1 Dec 2021

Cited by 2 | Viewed by 3254

Abstract

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 [...] Read more.

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 rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-Linear Phenomena in Superfluids and Superconductors VI)

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59 pages, 608 KiB

Open AccessFeature PaperArticle

Critical Temperature in the BCS-BEC Crossover with Spin-Orbit Coupling

by Luca Dell’Anna and Stefano Grava

Condens. Matter 2021, 6(2), 16; https://doi.org/10.3390/condmat6020016 - 30 Apr 2021

Cited by 3 | Viewed by 4165

Abstract

We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a [...] Read more.

We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature

T_{c}

over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find

T_{c}

along the crossover in the presence of a spin–orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive

T_{c}

is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin–orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors III)

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13 pages, 392 KiB

Open AccessArticle

Effect of Mismatched Electron-Hole Effective Masses on Superfluidity in Double Layer Solid-State Systems

by Sara Conti, Andrea Perali, François M. Peeters and David Neilson

Condens. Matter 2021, 6(2), 14; https://doi.org/10.3390/condmat6020014 - 7 Apr 2021

Cited by 2 | Viewed by 3102

Abstract

Superfluidity has been predicted and now observed in a number of different electron-hole double-layer semiconductor heterostructures. In some of the heterostructures, such as GaAs and Ge-Si electron-hole double quantum wells, there is a strong mismatch between the electron and hole effective masses. We [...] Read more.

Superfluidity has been predicted and now observed in a number of different electron-hole double-layer semiconductor heterostructures. In some of the heterostructures, such as GaAs and Ge-Si electron-hole double quantum wells, there is a strong mismatch between the electron and hole effective masses. We systematically investigate the sensitivity to unequal masses of the superfluid properties and the self-consistent screening of the electron-hole pairing interaction. We find that the superfluid properties are insensitive to mass imbalance in the low density BEC regime of strongly-coupled boson-like electron-hole pairs. At higher densities, in the BEC-BCS crossover regime of fermionic pairs, we find that mass imbalance between electrons and holes weakens the superfluidity and expands the density range for the BEC-BCS crossover regime. This permits screening to kill the superfluid at a lower density than for equal masses. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors III)

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9 pages, 599 KiB

Open AccessArticle

Hidden Pseudogap and Excitation Spectra in a Strongly Coupled Two-Band Superfluid/Superconductor

by Hiroyuki Tajima, Pierbiagio Pieri and Andrea Perali

Condens. Matter 2021, 6(1), 8; https://doi.org/10.3390/condmat6010008 - 7 Feb 2021

Cited by 1 | Viewed by 3300

Abstract

We investigate single-particle excitation properties in the normal state of a two-band superconductor or superfluid throughout the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein-condensation (BEC) crossover, within the many-body T-matrix approximation for multichannel pairing fluctuations. We address the single-particle density of states and the spectral [...] Read more.

We investigate single-particle excitation properties in the normal state of a two-band superconductor or superfluid throughout the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein-condensation (BEC) crossover, within the many-body T-matrix approximation for multichannel pairing fluctuations. We address the single-particle density of states and the spectral functions consisting of two contributions associated with a weakly interacting deep band and a strongly interacting shallow band, relevant for iron-based multiband superconductors and multicomponent fermionic superfluids. We show how the pseudogap state in the shallow band is hidden by the deep band contribution throughout the two-band BCS-BEC crossover. Our results could explain the missing pseudogap in recent scanning tunneling microscopy experiments in FeSe superconductors. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors III)

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4 pages, 185 KiB

Open AccessPerspective

The Role of the Short Coherence Length in Unconventional Superconductors

by Guy Deutscher

Condens. Matter 2020, 5(4), 77; https://doi.org/10.3390/condmat5040077 - 1 Dec 2020

Cited by 5 | Viewed by 3212

Abstract

A short coherence length is a distinctive feature of many cases of unconventional superconductivity. While in conventional superconductors, it is many orders of magnitude larger than the basic inter-particle distance, a short coherence length is common to superconductors as diverse as the cuprates, [...] Read more.

A short coherence length is a distinctive feature of many cases of unconventional superconductivity. While in conventional superconductors, it is many orders of magnitude larger than the basic inter-particle distance, a short coherence length is common to superconductors as diverse as the cuprates, the picnites and granular superconductors. We dwell particularly on the last, because their simple chemical structure makes them a favorable material for exploring fundamental phenomena such as the Bardeen-Cooper Schrieffer (BCS)-to-Bose–Einstein condensation cross-over and the effect of the vicinity of a Mott metal-to-insulator transition. Full article

(This article belongs to the Special Issue From Quantum Paraelectric/Ferroelectric Perovskite Oxides to High Temperature Superconducting Copper Oxides -- In Honor of Professor K.A. Müller for His Lifework)

20 pages, 579 KiB

Open AccessArticle

BCS-BEC Crossover Effects and Pseudogap in Neutron Matter

by David Durel and Michael Urban

Universe 2020, 6(11), 208; https://doi.org/10.3390/universe6110208 - 13 Nov 2020

Cited by 7 | Viewed by 2452

Abstract

Due to the large neutron–neutron scattering length, dilute neutron matter resembles the unitary Fermi gas, which lies half-way in the crossover from the BCS phase of weakly coupled Cooper pairs to the Bose–Einstein condensate of dimers. We discuss crossover effects in analogy with [...] Read more.

Due to the large neutron–neutron scattering length, dilute neutron matter resembles the unitary Fermi gas, which lies half-way in the crossover from the BCS phase of weakly coupled Cooper pairs to the Bose–Einstein condensate of dimers. We discuss crossover effects in analogy with the T-matrix theory used in the physics of ultracold atoms, which we generalize to the case of a non-separable finite-range interaction. A problem of the standard Nozières–Schmitt-Rink approach and different ways to solve it are discussed. It is shown that in the strong-coupling regime, the spectral function exhibits a pseudo-gap at temperatures above the critical temperature

T_{c}

. The effect of the correlated density on the density dependence of

T_{c}

is found to be rather weak, but a possibly important effect due to the reduced quasiparticle weight is identified. Full article

(This article belongs to the Special Issue Superfluidity and Superconductivity in Neutron Stars)

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13 pages, 684 KiB

Open AccessArticle

Dispersion and Damping of Phononic Excitations in Fermi Superfluid Gases in 2D

by Lars-Paul Lumbeeck, Jacques Tempere and Serghei Klimin

Condens. Matter 2020, 5(1), 13; https://doi.org/10.3390/condmat5010013 - 25 Feb 2020

Cited by 4 | Viewed by 2814

Abstract

We calculate the sound velocity and the damping rate of the collective excitations of a 2D fermionic superfluid in a non-perturbative manner. Specifically, we focus on the Anderson–Bogoliubov excitations in the BEC-BCS crossover regime, as these modes have a sound-like dispersion at low [...] Read more.

We calculate the sound velocity and the damping rate of the collective excitations of a 2D fermionic superfluid in a non-perturbative manner. Specifically, we focus on the Anderson–Bogoliubov excitations in the BEC-BCS crossover regime, as these modes have a sound-like dispersion at low momenta. The calculation is performed within the path-integral formalism and the Gaussian pair fluctuation approximation. From the action functional, we obtain the propagator of the collective excitations and determine their dispersion relation by locating the poles of this propagator. We find that there is only one kind of collective excitation, which is stable at

T = 0

and has a sound velocity of

v_{F} / \sqrt{2}

for all binding energies, i.e., throughout the BEC-BCS crossover. As the temperature is raised, the sound velocity decreases and the damping rate shows a non-monotonous behavior: after an initial increase, close to the critical temperature

T_{C}

the damping rate decreases again. In general, higher binding energies provide higher damping rates. Finally, we calculate the response functions and propose that they can be used as another way to determine the sound velocity. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors II)

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7 pages, 1173 KiB

Open AccessArticle

The Dirac Spectrum and the BEC-BCS Crossover in QCD at Nonzero Isospin Asymmetry

by Bastian B. Brandt, Francesca Cuteri, Gergely Endrődi and Sebastian Schmalzbauer

Particles 2020, 3(1), 80-86; https://doi.org/10.3390/particles3010007 - 4 Feb 2020

Cited by 12 | Viewed by 2767

Abstract

For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and

\bar{d}

Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the [...] Read more.

For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and

\bar{d}

Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at

μ_{I} \geq m_{π} / 2

by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential). Full article

(This article belongs to the Special Issue Selected Papers from “Theory of Hadronic Matter under Extreme Conditions”)

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14 pages, 588 KiB

Open AccessArticle

BCS-BEC Crossover and Pairing Fluctuations in a Two Band Superfluid/Superconductor: A T Matrix Approach

by Hiroyuki Tajima, Andrea Perali and Pierbiagio Pieri

Condens. Matter 2020, 5(1), 10; https://doi.org/10.3390/condmat5010010 - 21 Jan 2020

Cited by 15 | Viewed by 4093

Abstract

We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as [...] Read more.

We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as the critical temperature, chemical potential, and momentum distributions undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan’s contact to a two band system and report the two contacts for different pair-exchange couplings. The present results are compared with those obtained by the simpler Nozières–Schmitt–Rink approximation. We confirm a pronounced enhancement of the critical temperature due to the multiband configuration, as well as to the pair-exchange coupling. Full article

(This article belongs to the Special Issue Fluctuations and Highly Non-linear Phenomena in Superfluids and Superconductors II)

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19 pages, 3341 KiB

Open AccessReview

Fermi-Bose Mixtures and BCS-BEC Crossover in High-T_c Superconductors

by Maxim Yu. Kagan and Antonio Bianconi

Condens. Matter 2019, 4(2), 51; https://doi.org/10.3390/condmat4020051 - 3 Jun 2019

Cited by 25 | Viewed by 5603

Abstract

In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC (Bardeen Cooper Schrieffer–Bose Einstein) crossover compared with the strong-coupling approach, which can serve as the cornerstones on the way from high-temperature to [...] Read more.

In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC (Bardeen Cooper Schrieffer–Bose Einstein) crossover compared with the strong-coupling approach, which can serve as the cornerstones on the way from high-temperature to room-temperature superconductivity in pressurized metallic hydrides. We discuss some key theoretical ideas and mechanisms proposed for unconventional superconductors (cuprates, pnictides, chalcogenides, bismuthates, diborides, heavy-fermions, organics, bilayer graphene, twisted graphene, oxide hetero-structures), superfluids and balanced or imbalanced ultracold Fermi gases in magnetic traps. We build a bridge between unconventional superconductors and recently discovered pressurized hydrides superconductors H₃S and LaH₁₀ with the critical temperature close to room temperature. We discuss systems with a line of nodal Dirac points close to the Fermi surface and superconducting shape resonances, and hyperbolic superconducting networks which are very important for the development of novel topological superconductors, for the energetics, for the applications in nano-electronics and quantum computations. Full article

(This article belongs to the Special Issue From cuprates to Room Temperature Superconductors)

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12 pages, 779 KiB

Open AccessArticle

Goldstone and Higgs Hydrodynamics in the BCS–BEC Crossover

by Luca Salasnich

Condens. Matter 2017, 2(2), 22; https://doi.org/10.3390/condmat2020022 - 20 Jun 2017

Cited by 4 | Viewed by 4373

Abstract

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 [...] Read more.

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 ultracold Fermi superfluid. Full article

(This article belongs to the Special Issue Control and Enhancement of Quantum Coherence in Nanostructured Materials)

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