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

Physical review. B, Condensed matter

Superconductivity in the two-component anyon gas at finite temperature

Jian Zhou, S. G. Chen

Published Apr 1, 1993• 2 citations
Publisher

Abstract

We show that the elementary excitation of the superconductive s-wave ground state in the two-component anyon gas is always accompanied by an angular-momentum-free, flux-free vortex. Finite-temperature superconductivity in the two-component anyon gas is similar to the two-dimension superfluid. There are two Thouless-Kosterlitz (TK) phase transitions.

DOI
10.1103/physrevb.47.8301

Related papers

The Finite Temperature s -Wave Superconductivity in the Two-Component Anyon Gas

Jian Wei Zhou, S.G. Chen

We discuss the BCS-like descriptions of the finite temperature s -wave superconductivity in the two-component anyon gas, and show that in the content of the BCS theory the long range gauge force can not be renormalized at the finite temperature T ≠ 0, and this singularity is inherent and can not be overcome by adding other interactions of any form. We attribute this to the fake vortex excitations, and show that an elementary excitation over the supercondutive s -wave ground state in the two-component anyon gas is always in company with the excitation of a fake vortex. The finite temperature superconductivity in the two-component anyon gas is similar with the two-dimensional superfluid. There are two KT phase transitions.

Communications in Theoretical Physics•Jun 1, 1993•0 citations

Vortex pairing in two-dimensional Bose gases

Christopher J. Foster, P. B. Blakie, Matthew J. Davis

Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.

arXiv:0912.1675•Physical Review A•Feb 24, 2010•64 citations

Singlet-pair superconductivity in the two-component anyon gas

Alexander V. Balatsky, Vadim Kalmeyer

We consider a gas of fractional-statistics particles constructed by binding flux \ifmmode\pm\else\textpm\fi{}\ensuremath{\pi} to fermions with charge \ifmmode\pm\else\textpm\fi{}1. In its ground state, the system is a superfluid condensate of s-wave pairs with no observable chirality.

Physical review. B, Condensed matter•Mar 1, 1991•10 citations

Superfluidity of the lattice anyon gas and topological invariance

Eduardo Fradkin

I consider a gas of ``free'' anyons with statistical parameter \ensuremath{\delta}, with hard cores, on a two-dimensional square lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a Chern-Simons gauge theory with coupling \ensuremath{\theta}=1/2\ensuremath{\delta}. At the semiclassical level, the system is found to be equivalent to a gas of fermions, with the same density, in an average effective magnetic field \ensuremath{\rho}/\ensuremath{\theta}. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If \ensuremath{\delta}=\ensuremath{\pi}/m and the density \ensuremath{\rho}=r/q, with m, r, and q integers, the system is a superfluid, provided that q is larger than twice the largest common factor of m and r. If q is even and the system is half filled, the state may be either a superfluid or a quantum Hall phase. For all other values of \ensuremath{\rho} and \ensuremath{\delta}, compatible with integer filling of the Landau bands, the system is in a quantum Hall phase. The dynamical stability of the superfluid state is ensured by the topological invariance of the quantized Hall conductance of the fermion problem. I find a close analogy between anyon superconductivity and the Schwinger mechanism. The effective Lagrangian for the low-energy modes coupled to the electromagnetic field is derived. The energies of fermion and flux states are logarithmically divergent, but finite for the anyon state. The system has flux quantization, a zero-temperature Hall effect with a quantized Hall conductance, Meissner effect, charged vortices, screening with induced magnetic fields for static charges, and different masses for the longitudinal and transverse components of the electromagnetic field.

Physical review. B, Condensed matter•Jul 1, 1990•67 citations

PHASE TRANSITIONS IN ULTRA-COLD TWO-DIMENSIONAL BOSE GASES

David A. W. Hutchinson, P. B. Blakie

We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.

arXiv:cond-mat/0602614•International Journal of Modern Physics B•Dec 15, 2006•7 citations

Quasiparticle and vortex in the anyon gas

弘之 森

We calculate a vortex current for some trial wave functions of an excited state of the anyon gas to show the identity of a quasiparticle with a vortex. We also give the energy of an excited state starting from the microscopic Hamiltonian and show that it is essentially the same as that of the vortex state of ordinary two-dimensional superfluids. A comment on anyons of intermediate statistics is given.

Physical review. B, Condensed matter•Mar 1, 1991•10 citations
We show that the elementary excitation of the superconductive s-wave ground state in the two-component anyon gas is always accompanied by an angular-momentum-free, flux-free vortex. Finite-temperature superconductivity in the two-component anyon gas is similar to the two-dimension superfluid. There are two Thouless-Kosterlitz (TK) phase transitions.
We discuss the BCS-like descriptions of the finite temperature s -wave superconductivity in the two-component anyon gas, and show that in the content of the BCS theory the long range gauge force can not be renormalized at the finite temperature T ≠ 0, and this singularity is inherent and can not be overcome by adding other interactions of any form. We attribute this to the fake vortex excitations, and show that an elementary excitation over the supercondutive s -wave ground state in the two-component anyon gas is always in company with the excitation of a fake vortex. The finite temperature superconductivity in the two-component anyon gas is similar with the two-dimensional superfluid. There are two KT phase transitions.
Recent experiments on ultracold Bose gases in two dimensions have provided evidence for the existence of the Berezinskii-Kosterlitz-Thouless (BKT) phase via analysis of the interference between two independent systems. In this work we study the two-dimensional quantum degenerate Bose gas at finite temperature using the projected Gross-Pitaevskii equation classical field method. Although this describes the highly occupied modes of the gas below a momentum cutoff, we have developed a method to incorporate the higher momentum states in our model. We concentrate on finite-sized homogeneous systems in order to simplify the analysis of the vortex pairing. We determine the dependence of the condensate fraction on temperature and compare this to the calculated superfluid fraction. By measuring the first order correlation function we determine the boundary of the Bose-Einstein condensate and BKT phases, and find it is consistent with the superfluid fraction decreasing to zero. We reveal the characteristic unbinding of vortex pairs above the BKT transition via a coarse-graining procedure. Finally, we model the procedure used in experiments to infer system correlations [Hadzibabic et al., Nature 441, 1118 (2006)], and quantify its level of agreement with directly calculated in situ correlation functions.
I consider a gas of ``free'' anyons with statistical parameter \ensuremath{\delta}, with hard cores, on a two-dimensional square lattice. Using a recently derived Jordan-Wigner transformation, I map this problem onto a gas of fermions on the same lattice coupled to a Chern-Simons gauge theory with coupling \ensuremath{\theta}=1/2\ensuremath{\delta}. At the semiclassical level, the system is found to be equivalent to a gas of fermions, with the same density, in an average effective magnetic field \ensuremath{\rho}/\ensuremath{\theta}. I consider the case in which an integer number of the Landau bands of the saddle-point problem are completely filled. If \ensuremath{\delta}=\ensuremath{\pi}/m and the density \ensuremath{\rho}=r/q, with m, r, and q integers, the system is a superfluid, provided that q is larger than twice the largest common factor of m and r. If q is even and the system is half filled, the state may be either a superfluid or a quantum Hall phase. For all other values of \ensuremath{\rho} and \ensuremath{\delta}, compatible with integer filling of the Landau bands, the system is in a quantum Hall phase. The dynamical stability of the superfluid state is ensured by the topological invariance of the quantized Hall conductance of the fermion problem. I find a close analogy between anyon superconductivity and the Schwinger mechanism. The effective Lagrangian for the low-energy modes coupled to the electromagnetic field is derived. The energies of fermion and flux states are logarithmically divergent, but finite for the anyon state. The system has flux quantization, a zero-temperature Hall effect with a quantized Hall conductance, Meissner effect, charged vortices, screening with induced magnetic fields for static charges, and different masses for the longitudinal and transverse components of the electromagnetic field.
We briefly review the theory of Bose-Einstein condensation in the two-dimensional trapped Bose gas and, in particular the relationship to the theory of the homogeneous two-dimensional gas and the Berezinskii-Kosterlitz-Thouless phase. We obtain a phase diagram for the trapped two-dimensional gas, finding a critical temperature above which the free energy of a state with a pair of vortices of opposite circulation is lower than that for a vortex-free Bose-Einstein condensed ground state. We identify three distinct phases which are, in order of increasing temperature, a phase coherent Bose-Einstein condensate, a vortex pair plasma with fluctuating condensate phase and a thermal Bose gas. The thermal activation of vortex-antivortex pair formation is confirmed using finite-temperature classical field simulations.