Physical Review Letters

Pairing in two dimensions

Stefan Schmitt-Rink, Chandra Mohan Varma, Andrei E. Ruckenstein

Published Jul 24, 1989• 158 citations

Abstract

A two-dimensional Fermi gas with an attractive s-wave interaction is shown to display a finite number of bound fermion pairs at all densities and temperatures. We study the chemical equilibrium between bound and ionized fermion pairs by including single-pair fluctuations in the free energy. While this turns out to be sufficient to drive the critical temperature for the onset of long-range order to zero, higher-order processes must be invoked to describe correctly the low-temperature regime.

DOI: 10.1103/physrevlett.63.445

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Physical Review Letters

Pairing in two dimensions

Stefan Schmitt-Rink, Chandra Mohan Varma, Andrei E. Ruckenstein

Published Jul 24, 1989• 158 citations

Publisher

Abstract

DOI: 10.1103/physrevlett.63.445

Related papers

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Sergei V. Traven

It is demonstrated that the interaction between fluctuations of the pairing field in a two-dimensional (2D) dilute attractive Fermi gas stabilizes the low-temperature phase of the system. This result, which is valid for all values of the "coupling parameter" $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}$ (where ${\ensuremath{\varepsilon}}_{0}$ is the two-fermion binding energy and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy), then allows one to conclude that a 2D dilute attractive Fermi gas is superfluid at small but finite temperature.It is demonstrated that the interaction between fluctuations of the pairing field in a two-dimensional (2D) dilute attractive Fermi gas stabilizes the low-temperature phase of the system. This result, which is valid for all values of the "coupling parameter" $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}$ (where ${\ensuremath{\varepsilon}}_{0}$ is the two-fermion binding energy and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy), then allows one to conclude that a 2D dilute attractive Fermi gas is superfluid at small but finite temperature.

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Superconductivity in a two-dimensional Fermi gas: Evolution from Cooper pairing to Bose condensation

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Theja N. De Silva

We study pairing of an interacting three-component Fermi gas in two dimensions. By using a mean-field theory to decouple the interactions between different pairs of Fermi components, we study the free energy landscapes as a function of various system parameters including chemical potentials, binding energies, and temperature. We find that the $s$ -wave pairing channel is determined by both chemical potentials and the interaction strengths between the three available channels. We find a second-order thermal phase transition and a series of first-order quantum phase transitions for a homogenous system as we change the parameters. In particular, for symmetric parameters, we find the simultaneous existence of three superfluid orders as well as re-entrant quantum phase transitions as we tune the parameters.We study pairing of an interacting three-component Fermi gas in two dimensions. By using a mean-field theory to decouple the interactions between different pairs of Fermi components, we study the free energy landscapes as a function of various system parameters including chemical potentials, binding energies, and temperature. We find that the $s$-wave pairing channel is determined by both chemical potentials and the interaction strengths between the three available channels. We find a second-order thermal phase transition and a series of first-order quantum phase transitions for a homogenous system as we change the parameters. In particular, for symmetric parameters, we find the simultaneous existence of three superfluid orders as well as re-entrant quantum phase transitions as we tune the parameters.

arXiv:0901.3770Physical Review AJul 31, 200912 citations

{k}_{F}

${\ensuremath{\xi}}_{0}$\ensuremath{\sim}O(1)], a striking feature of the high-

{T}_{c}

materials. We find that a two-body bound state in vacuum is a necessary and sufficient condition for an s-wave pairing instability. We also find that the existence of such a bound state in a higher-angular-momentum (l>0) channel is not a necessary condition for an l-wave pairing instability. We further investigate using a variational ansatz the evolution from a state with large overlapping Cooper pairs (

{k}_{F}

${\ensuremath{\xi}}_{0}$\ensuremath{\gg}1) to one with Bose condensation of composite bosons (

{k}_{F}

${\ensuremath{\xi}}_{0}$\ensuremath{\ll}1). For the s-wave case an exact solution of the variational equations shows a smooth crossover from one regime to the other at T=0. The p-wave solution has a weak singularity when the chemical potential goes through zero, which is the bottom of the band. We show, quite generally, independent of the dimensionality and of model details, that the gap--to--single-particle excitations is nodeless, even if the anisotropic pair wave function has nodes, when the coupling is strong enough that the chemical potential is negative.

l

channels. It has been found that the onset of the superconducting phase can occur at temperatures

(>100\mathrm{nK})

of the same order of magnitude as the Fermi temperature $(\ensuremath{\sim}300\mathrm{nK}),$ and the energy gap in the excitation spectrum is a small fraction $(\ensuremath{\sim}1%)$ of the Fermi energy.

s

-wave pairing channel is determined by both chemical potentials and the interaction strengths between the three available channels. We find a second-order thermal phase transition and a series of first-order quantum phase transitions for a homogenous system as we change the parameters. In particular, for symmetric parameters, we find the simultaneous existence of three superfluid orders as well as re-entrant quantum phase transitions as we tune the parameters.