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Journal of the Physical Society of Japan

A Model of Superconductors on a Lattice

Tohru Morita

Published Nov 15, 1990• 0 citations
Publisher

Abstract

We study a model fermion system on a lattice, which is expected to show the superconductor state, the normal state and the antiferromagnetic state, as we vary the number density of particles and the temperature. The phase transition between the superconductor state and the normal state is investigated in the “molecular-field approximation” with the aid of the cluster variation method.

DOI
10.1143/jpsj.59.4096

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Modern Physics Letters B•Nov 20, 1993•2 citations
We study a model fermion system on a lattice, which is expected to show the superconductor state, the normal state and the antiferromagnetic state, as we vary the number density of particles and the temperature. The phase transition between the superconductor state and the normal state is investigated in the “molecular-field approximation” with the aid of the cluster variation method.
The numerical method was developed that combines the variational cluster approximation and the exact diagonalization techniques to solve Hubbard models of various dimensionality, number of orbitals, and lattice geometry. The developed method was tested on the one-band Hubbard model; antiferromagnetic ordering and the superconducting phase were observed, in accordance with known results obtained by other techniques. The method may be successfully used for studying properties of high-temperature superconductors.
In the model considered, the nonlocal interaction of the fermions in different sublattices of a bipartite lattice is introduced. It can also be regarded as local interaction of fermions with opposite ``hypercharge''. The corresponding term in the Hamiltonian is SU(4)-invariant and appears to be the most tractable version of the SO(5)-invariant model that unifies antiferromagnetic and d-wave superconducting order parameters. The model has been studied primarily in the weak interaction limit and in the mean field approximation. Near the half-filling the antiferromagnetic critical temperature has a peak. However, the superconducting transition takes place when the Fermi surface crosses the area where the density of states is of order of inverse coupling coefficient. Thus, in mean-field approximation, there exist an interval of values of the chemical potential, for which the system is a superconductor for arbitrary high temperatures. The temperature dependence of specific heat, Hall coefficient, and DC conductivity in the normal phase agrees with that experimentally observed in high-TcT_cTc​ cuprates.
Dilute gases of 2-component fermions are of great interest in atomic and nuclear physics. When interactions are strong enough so that a bound state is at threshold, universal behavior is expected. Lattice field theory provides a first principles approach to the study of strongly interacting systems such as this through Monte Carlo simulation. Results of exploratory simulations are presented here. In particular, the finite temperature phase transition between superfluid and normal states is studied. We present first results for the critical temperature T_c and describe the future work necessary to determine T_c as a function of interaction strength.
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.