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Electrical conductivity in the strong‐coupling non‐half‐filled band Hubbard model
Author(s) -
Ihle D.
Publication year - 1978
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220860133
Subject(s) - condensed matter physics , hubbard model , electrical resistivity and conductivity , conductivity , singularity , discontinuity (linguistics) , coulomb , coupling (piping) , physics , electronic band structure , electron , van hove singularity , materials science , fermi level , quantum mechanics , mathematics , mathematical analysis , superconductivity , metallurgy
Abstract The chemical potential μ and the electrical dc conductivity σ in the one‐dimensional Hubbard model in the strong‐coupling region U ≫ t ( U intra‐atomic Coulomb energy, – t nearest‐neighbour hopping integral) are calculated as functions of temperature and electron density n . In the non‐half‐filled band case n ≠ 1 the Bari‐Kaplan approximation lim (σ/ t 2 ) is shown to yield an unphysical singularity in the dc conductivity at T = 0 which is connected with the discontinuity of the zero‐temperature chemical potential at n = 1. An improved calculation for n ≠ 1 going beyond the Bari‐Kaplan approximation (i.e. taking into account the band terms in μ and σ/ t 2 ) yields a finite zero‐temperature conductivity which is proportional to the first power in t . For small deviations from the half‐filled band case the conductivity as a function of increasing temperature subsequently shows a metal‐like behaviour, a semiconductor‐like behaviour, and a repeated decrease at high temperatures.