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:0802.1271

Superconductivity from four Fermion complexes

Kleinert, P.

Published Feb 11, 2008• 0 citations
arXivHTMLPDF

Abstract

Superconductivity is studied for a fermionic system with attractive four-body interaction. Applying a Green function approach, the gap equation is derived. From the solution, the transition temperature is calculated. Under the condition that the respective coupling constants are comparable, the transition temperature of four-fermion complexes is considerably larger than the corresponding BCS value.

DOI
10.48550/arxiv.0802.1271

Related papers

Phase fluctuations and single-fermion spectral density in 2d systems with attraction

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

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green’s function, its spectral density, and the density of states are derived in the approximation where the coupling between the spin and charge degrees of freedom is neglected. The resulting single-particle Green’s function clearly demonstrates a non-Fermi-liquid behavior. The results show that as the temperature increases through the 2D critical temperature, the widths of the quasiparticle peaks broaden significantly.

arXiv:cond-mat/9811207•Journal of Experimental and Theoretical Physics•Jun 1, 2000•19 citations

Properties of a Fermi liquid at the superfluid transition in the crossover region between BCS superconductivity and Bose-Einstein condensation

R. Haussmann

The self-consistent equations, which have been derived recently as a microscopic model for the crossover between BCS superconductivity and Bose-Einstein condensation in a three-dimensional interacting Fermi system [R. Haussmann, Z. Phys. B 91, 291 (1993)], are solved numerically by repeated Fourier transformation. We find a superfluid transition temperature ${\mathit{T}}_{\mathit{c}}$ which increases monotonically with increasing attractive coupling strength. Furthermore, we determine the chemical potential \ensuremath{\mu}, the fermion distribution function n(k), and the complex effective mass 2${\mathit{m}}^{\mathrm{*}}$ of the fermion pairs at T=${\mathit{T}}_{\mathit{c}}$. The bound fermion pairs cause a power-law tail \ensuremath{\sim}${\mathit{k}}^{\mathrm{\ensuremath{-}}4}$ in n(k) for large k and behave as short-living quasiparticles in the crossover region, which is indicated by a large imaginary part of 2${\mathit{m}}^{\mathrm{*}}$.

Physical review. B, Condensed matter•May 1, 1994•245 citations

Phase fluctuations and Non-Fermi Liquid Properties of 2D Fermi-system with attraction

V. P. Gusynin, В. М. Локтев, R. M. Quick +1 more

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.

•Jan 1, 1999•1 citation

Pairing and superconducting properties of 2D Fermi systems with attraction

Eduard V. Gorbar, V. P. Gusynin, В. М. Локтев

Proceeding from a microscopic model Hamiltonian for a system of Fermi particles with attraction, we have derived an effective Lagrangian, which allows analysis of the superconducting properties of the system for arbitrary fermion concentrations. Exact solution of the equations for the gap and the chemical potential enables us to examine the crossover from the regime of local pairs and superfluidity to the Cooper pairing and the BCS-like superconductivity. It is shown that the physical parameter that demarcates the regions of exotic and normal behavior is the fermion bound state energy. The expressions derived suggest that in the region of relatively low concentrations the parameters of a 2D metal correspond to a type-II superconductor.

Low Temperature Physics•Nov 1, 1993•8 citations

PHASE FLUCTUATIONS AND NON-FERMI LIQUID PROPERTIES OF 2D FERMI-SYSTEM WITH ATTRACTION

V. P. Gusynin, VADIM M. LOKTEV, RACHEL M. QUICK +1 more

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.

arXiv:cond-mat/9906407•International Journal of Modern Physics B•Dec 20, 1999•1 citation

The green’s functions of superconductivity- A review

MI Imo

We present some basic Green’s functions of superconductivity, making emphasis on their geneology and analytic properties. From calculations, we note that the temperature dependence of the Green’s functions for fermionic (and bosonic) systems limits and defines the extent of their applications and results. Furthermore, the Gorkov interaction term of the four field fermion operators, is examined and interpreted in terms of the Landau condensate. Finally we show that the Gorkov interaction under a certain condition sustains superconductivity and spin density wave in the system.KEYWORDS: Green’s functions, Bethe-Salpeter equation, Landau condensate, superconductivity, spin density wave.

Global Journal of Pure and Applied Sciences•Jul 15, 2013•0 citations
Superconductivity is studied for a fermionic system with attractive four-body interaction. Applying a Green function approach, the gap equation is derived. From the solution, the transition temperature is calculated. Under the condition that the respective coupling constants are comparable, the transition temperature of four-fermion complexes is considerably larger than the corresponding BCS value.
The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green’s function, its spectral density, and the density of states are derived in the approximation where the coupling between the spin and charge degrees of freedom is neglected. The resulting single-particle Green’s function clearly demonstrates a non-Fermi-liquid behavior. The results show that as the temperature increases through the 2D critical temperature, the widths of the quasiparticle peaks broaden significantly.
The self-consistent equations, which have been derived recently as a microscopic model for the crossover between BCS superconductivity and Bose-Einstein condensation in a three-dimensional interacting Fermi system [R. Haussmann, Z. Phys. B 91, 291 (1993)], are solved numerically by repeated Fourier transformation. We find a superfluid transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ which increases monotonically with increasing attractive coupling strength. Furthermore, we determine the chemical potential \ensuremath{\mu}, the fermion distribution function n(k), and the complex effective mass 2m∗{\mathit{m}}^{\mathrm{*}}m∗ of the fermion pairs at T=Tc{\mathit{T}}_{\mathit{c}}Tc​. The bound fermion pairs cause a power-law tail \ensuremath{\sim}${\mathit{k}}^{\mathrm{\ensuremath{-}}4}$ in n(k) for large k and behave as short-living quasiparticles in the crossover region, which is indicated by a large imaginary part of 2m∗{\mathit{m}}^{\mathrm{*}}m∗.
The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.
Proceeding from a microscopic model Hamiltonian for a system of Fermi particles with attraction, we have derived an effective Lagrangian, which allows analysis of the superconducting properties of the system for arbitrary fermion concentrations. Exact solution of the equations for the gap and the chemical potential enables us to examine the crossover from the regime of local pairs and superfluidity to the Cooper pairing and the BCS-like superconductivity. It is shown that the physical parameter that demarcates the regions of exotic and normal behavior is the fermion bound state energy. The expressions derived suggest that in the region of relatively low concentrations the parameters of a 2D metal correspond to a type-II superconductor.
The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction has been studied. Analytic expressions for the fermion Green function, its spectral density and the density of states are derived. The resultant single-particle Green function clearly demonstrates non-Fermi liquid behavior. The results show that as the temperature increases through the 2D critical temperature the width of the quasiparticle peaks broadens significantly. At the same time one retains the gap in quasiparticle spectrum. The spectral density for the dynamical fluctuations can also be obtained. Clearly the dynamical fluctuations fill the gap giving the observed pseudogap behaviour.
We present some basic Green’s functions of superconductivity, making emphasis on their geneology and analytic properties. From calculations, we note that the temperature dependence of the Green’s functions for fermionic (and bosonic) systems limits and defines the extent of their applications and results. Furthermore, the Gorkov interaction term of the four field fermion operators, is examined and interpreted in terms of the Landau condensate. Finally we show that the Gorkov interaction under a certain condition sustains superconductivity and spin density wave in the system.KEYWORDS: Green’s functions, Bethe-Salpeter equation, Landau condensate, superconductivity, spin density wave.