Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9709034 · Journal of Experimental and Theoretical Physics

Pseudogap phase formation in the crossover from Bose-Einstein condensation to BCS superconductivity

V. P. Gusynin, В. М. Локтев, Sergei G. Sharapov

Published Apr 1, 1999• 28 citations
arXivHTMLPDF

Abstract

A phase diagram for a 2D metal with variable carrier density has been derived. It consists of a normal phase, where the order parameter is absent: a so-called “abnormal normal” phase where this parameter is also absent but the mean number of composite bosons (bound pairs) exceeds the mean number of free fermions; a pseudogap phase where the absolute value of the order parameter gradually increases but its phase is a random value, and finally a superconducting (here Berezinskii-Kosterlitz-Thouless) phase. The characteristic transition temperatures between these phases are found. The chemical potential and paramagnetic susceptibility behavior as functions of the fermion density and the temperature are also studied. An attempt is made to qualitatively compare the resulting phase diagram with the features of underdoped high-T c superconducting compounds above their critical temperature.

DOI
10.1134/1.558845

Related papers

Pseudogap Phase Formation in the Crossover from Bose-Einstein Condensation to BCS Superconductivity in Low-Dimensional Systems

V. P. Gusynin, Vadim M. Loktev, Rachel M. Quick +1 more

A phase diagram for a two-dimensional metal with variable carrier density has been studied using the modulus-phase representation for the order parameter in fully microscopic treatment. This amounts to splitting the degrees of freedom into neutral fermion and charged boson degrees of freedom. Although true long range order is forbidden in two dimensions, long range order for the neutral fermions is possible since this does not violate any continuous symmetry. The phase fluctuations associated with the charged degrees of freedom destroy long range order in the full system as expected. The presence of the neutral order parameter gives rise to new features in the superconducting condensate formation in low-dimensional systems. The resulting phase diagram contains a new phase which lies above the superconducting (here Berezinskii–Kosterlitz–Thouless) phase and below the normal (Fermi-liquid) phase. We identify this phase with the pseudogap phase observed in underdoped high-T c superconducting compounds above their critical temperature. We also find that the phase diagram persists even in the presence of weak 3-dimensionalisation.

arXiv:cond-mat/9803142•International Journal of Modern Physics B•Dec 20, 1998•2 citations

Phase diagram of a 2D metal system with a variable number of carriers

V. P. Gusynin, В. М. Локтев, Sergei G. Sharapov

It is shown that the phase diagram of a 2D metal undergoing a superconducting transition consists of regions of a normal phase where the modulus of the order parameter is absent, an “anomalous normal” phase where the modulus of the order parameter is different from zero but the phase of the order parameter is a random quantity, and a Berezinskii-Kosterlitz-Thouless phase. The characteristic temperatures of transitions between the phases and the behavior of the chemical potential as a function of the fermion density and temperature are found.

Journal of Experimental and Theoretical Physics Letters•Jan 1, 1997•44 citations

On the Boson–Fermion resonant model on a lattice

R. Micnas

We review briefly the properties of a mixture of mutually interacting bosons (bound electron pairs) and itinerant fermions on a lattice (the boson–fermion model). The calculations of the superconducting phase transition temperature () and the phase diagram are the main concern. The self-consistent -matrix method is applied to determine the superconducting critical temperature from a pseudogap phase. The method takes into account the pairing fluctuations effects. The -matrix results for are given for a three-dimensional (3-D) cubic lattice with tight-binding dispersion of electrons and standard bosons, and they are also compared with those of the BCS- mean-field approximation. Our results describe the BCS-Bose-Einstein condensation crossover in the boson–fermion mixture with resonant interaction. The energy scales involved in the pseudogap formation are also analysed.

arXiv:1912.04094•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Nov 21, 2014•4 citations

Strong Pairing in two dimensions: Pseudogap and other phenomena

Xiaoyu Wang, Qijin Chen, K. Levin

This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii-Kosterlitz-Thouless (BKT) temperature $T_{\text{BKT}}$ as a function of \emph{attractive} pairing strength by associating it with the onset of quasi-condensation in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established Quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS-BEC crossover theory for fermions, leads to non-monotonic behavior for $T_{\text{BKT}}$ as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that $T_{\text{BKT}}$ has an absolute maximum of the order of $0.1 E_F$. We discuss how our results compare with those derived from the Nelson Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in $T_\text{BKT}$ followed by an often dramatic decrease before the system enters the BEC regime.

•Jul 13, 2019•0 citations

Crossover from BCS Theory to Bose–Einstein Condensation

Mohit Randeria

This article gives a detailed review of our current theoretical understanding of the crossover from cooperative Cooper pairing to independent bound-state formation and Bose–Einstein condensation in Fermi systems with increasing attractive interactions. Introduction There are two well-known paradigms for understanding the phenomena of superconductivity and superfluidity: (I) BCS theory [1], in which the normal state is a degenerate Fermi liquid that undergoes a pairing instability at a temperature T c ≪ ε f , the degeneracy scale. The formation of Cooper pairs and their condensation (macroscopic occupation of a single quantum state) both occur simultaneously at the transition temperature T c . (II) Bose–Einstein condensation (BEC) of bosons at a T c of the order of their degeneracy temperature. At a fundamental level these bosons (for example, 4 He or excitons) are invariably composite objects made up of an even number of fermions. The composite particles form at some very high temperature scale of the order of their dissociation temperature T dissoc , and these “pre-formed” bosons then condense at the BEC T c ≪ T dissoc . In most cases of experimental interest the system under consideration clearly falls into one category or the other. For instance, 3 He is a Fermi superfluid described by (I) whereas 4 He is a Bose superfluid (II). Essentially all cases of superconductivity in metals that we understand reasonably well are much closer to (I) than to (II), as evidenced by the existence of fermionic quasiparticles above T c .

Cambridge University Press eBooks•Apr 6, 1995•158 citations

DISORDERED SUPERCONDUCTORS: A SIMPLE MODEL MANIFESTING PSEUDOGAP AND BCS-BEC CROSSOVER

Poulumi Dey, Saurabh Basu

The effect of random on-site disorder on s-wave (BCS) superconductors described by a two dimensional negative-U Hubbard model is studied using Bogoliubov-de Gennes (BdG) method. The mean field pairing amplitudes become spatially inhomogeneous at large values of disorder where the system breaks up into superconducting islands with large pairing amplitudes, separated by insulating strips. The amplitude fluctuations are correctly accounted for via BdG calculations, however it misses phase fluctuations which are inherent to low dimensions. The phase fluctuations affect superconducting properties strongly, and the effect is more pronounced in the limit of large disorder. We provide a close estimate of the actual transition temperature, Tcby incorporating phase fluctuations about the inhomogeneous BdG state. This is obtained by relating the jump in renormalized Ds(obtained from a self consistent Harmonic approximation on a phase-only Hamiltonian) at the Kosterlitz-Thouless (KT) transition and the KT transition temperature, TKTobtained from Ds(T) = (2/π)TKTas temperature tends to TKTfrom below. This yields opening of a large region sandwiched between [Formula: see text] (obtained by the vanishing of [Formula: see text]) and TKTwhere there is no phase coherence between the pairs, however amplitude correlations continue to exist, reminiscent of a pseudogap phase in high-Tcsuperconductors which is marked by short ranged preformed pairs without any definite phase relation between them. Further, the appearance of the superconducting islands from a homogeneous phase indicates the evolution of a system consisting of large and overlapping pairs to one that contains short and tightly bound pairs - a scenario termed as BCS-BEC crossover. We have investigated in details the crossover phenomenon as a function of disorder and confirmed it's existence at small values of electron concentration, however, absent at larger densities.

International Journal of Modern Physics B•Aug 20, 2009•1 citation
A phase diagram for a 2D metal with variable carrier density has been derived. It consists of a normal phase, where the order parameter is absent: a so-called “abnormal normal” phase where this parameter is also absent but the mean number of composite bosons (bound pairs) exceeds the mean number of free fermions; a pseudogap phase where the absolute value of the order parameter gradually increases but its phase is a random value, and finally a superconducting (here Berezinskii-Kosterlitz-Thouless) phase. The characteristic transition temperatures between these phases are found. The chemical potential and paramagnetic susceptibility behavior as functions of the fermion density and the temperature are also studied. An attempt is made to qualitatively compare the resulting phase diagram with the features of underdoped high-T c superconducting compounds above their critical temperature.
A phase diagram for a two-dimensional metal with variable carrier density has been studied using the modulus-phase representation for the order parameter in fully microscopic treatment. This amounts to splitting the degrees of freedom into neutral fermion and charged boson degrees of freedom. Although true long range order is forbidden in two dimensions, long range order for the neutral fermions is possible since this does not violate any continuous symmetry. The phase fluctuations associated with the charged degrees of freedom destroy long range order in the full system as expected. The presence of the neutral order parameter gives rise to new features in the superconducting condensate formation in low-dimensional systems. The resulting phase diagram contains a new phase which lies above the superconducting (here Berezinskii–Kosterlitz–Thouless) phase and below the normal (Fermi-liquid) phase. We identify this phase with the pseudogap phase observed in underdoped high-T c superconducting compounds above their critical temperature. We also find that the phase diagram persists even in the presence of weak 3-dimensionalisation.
It is shown that the phase diagram of a 2D metal undergoing a superconducting transition consists of regions of a normal phase where the modulus of the order parameter is absent, an “anomalous normal” phase where the modulus of the order parameter is different from zero but the phase of the order parameter is a random quantity, and a Berezinskii-Kosterlitz-Thouless phase. The characteristic temperatures of transitions between the phases and the behavior of the chemical potential as a function of the fermion density and temperature are found.
We review briefly the properties of a mixture of mutually interacting bosons (bound electron pairs) and itinerant fermions on a lattice (the boson–fermion model). The calculations of the superconducting phase transition temperature () and the phase diagram are the main concern. The self-consistent -matrix method is applied to determine the superconducting critical temperature from a pseudogap phase. The method takes into account the pairing fluctuations effects. The -matrix results for are given for a three-dimensional (3-D) cubic lattice with tight-binding dispersion of electrons and standard bosons, and they are also compared with those of the BCS- mean-field approximation. Our results describe the BCS-Bose-Einstein condensation crossover in the boson–fermion mixture with resonant interaction. The energy scales involved in the pseudogap formation are also analysed.
This paper addresses the transition from the normal to the superfluid state in strongly correlated two dimensional fermionic superconductors and Fermi gases. We arrive at the Berezinskii-Kosterlitz-Thouless (BKT) temperature TBKTT_{\text{BKT}}TBKT​ as a function of \emph{attractive} pairing strength by associating it with the onset of quasi-condensation in the normal phase. Our approach builds on a criterion for determining the BKT transition temperature for atomic gases which is based on a well established Quantum Monte Carlo analysis of the phase space density. This latter quantity, when derived from BCS-BEC crossover theory for fermions, leads to non-monotonic behavior for TBKTT_{\text{BKT}}TBKT​ as a function of the attractive interaction or inverse scattering length. In Fermi gases, this implies a robust superconducting dome followed by a long tail from the flat BEC asymptote, rather similar to what is observed experimentally. For lattice systems we find that TBKTT_{\text{BKT}}TBKT​ has an absolute maximum of the order of 0.1EF0.1 E_F0.1EF​. We discuss how our results compare with those derived from the Nelson Kosterlitz criterion based on the mean field superfluid density and the approach to the transition from below. While there is agreement in the strict mean-field BCS regime at weak coupling, we find that at moderate pairing strength bosonic excitations cause a substantial increase in TBKTT_\text{BKT}TBKT​ followed by an often dramatic decrease before the system enters the BEC regime.
This article gives a detailed review of our current theoretical understanding of the crossover from cooperative Cooper pairing to independent bound-state formation and Bose–Einstein condensation in Fermi systems with increasing attractive interactions. Introduction There are two well-known paradigms for understanding the phenomena of superconductivity and superfluidity: (I) BCS theory [1], in which the normal state is a degenerate Fermi liquid that undergoes a pairing instability at a temperature T c ≪ ε f , the degeneracy scale. The formation of Cooper pairs and their condensation (macroscopic occupation of a single quantum state) both occur simultaneously at the transition temperature T c . (II) Bose–Einstein condensation (BEC) of bosons at a T c of the order of their degeneracy temperature. At a fundamental level these bosons (for example, 4 He or excitons) are invariably composite objects made up of an even number of fermions. The composite particles form at some very high temperature scale of the order of their dissociation temperature T dissoc , and these “pre-formed” bosons then condense at the BEC T c ≪ T dissoc . In most cases of experimental interest the system under consideration clearly falls into one category or the other. For instance, 3 He is a Fermi superfluid described by (I) whereas 4 He is a Bose superfluid (II). Essentially all cases of superconductivity in metals that we understand reasonably well are much closer to (I) than to (II), as evidenced by the existence of fermionic quasiparticles above T c .
The effect of random on-site disorder on s-wave (BCS) superconductors described by a two dimensional negative-U Hubbard model is studied using Bogoliubov-de Gennes (BdG) method. The mean field pairing amplitudes become spatially inhomogeneous at large values of disorder where the system breaks up into superconducting islands with large pairing amplitudes, separated by insulating strips. The amplitude fluctuations are correctly accounted for via BdG calculations, however it misses phase fluctuations which are inherent to low dimensions. The phase fluctuations affect superconducting properties strongly, and the effect is more pronounced in the limit of large disorder. We provide a close estimate of the actual transition temperature, Tcby incorporating phase fluctuations about the inhomogeneous BdG state. This is obtained by relating the jump in renormalized Ds(obtained from a self consistent Harmonic approximation on a phase-only Hamiltonian) at the Kosterlitz-Thouless (KT) transition and the KT transition temperature, TKTobtained from Ds(T) = (2/π)TKTas temperature tends to TKTfrom below. This yields opening of a large region sandwiched between [Formula: see text] (obtained by the vanishing of [Formula: see text]) and TKTwhere there is no phase coherence between the pairs, however amplitude correlations continue to exist, reminiscent of a pseudogap phase in high-Tcsuperconductors which is marked by short ranged preformed pairs without any definite phase relation between them. Further, the appearance of the superconducting islands from a homogeneous phase indicates the evolution of a system consisting of large and overlapping pairs to one that contains short and tightly bound pairs - a scenario termed as BCS-BEC crossover. We have investigated in details the crossover phenomenon as a function of disorder and confirmed it's existence at small values of electron concentration, however, absent at larger densities.