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Physical review. B, Condensed matter

Electron correlations in quasi-one-dimensional electron systems: Intrinsic superconductivity

N. Nafari, B. Davoudi

Published Jan 15, 1998• 8 citations
Publisher

Abstract

In this paper, we study correlations in quasi-one-dimensional electron systems. To account for the short-range correlations we have used a ladder approximation (LA), and to account for the long-range correlations we have used the Singwi, Tosi, S\"olander, and Land (STLS) scheme. After solving the integral equation appearing in the LA and solving the set of self-consistent equations of the STLS scheme, we join the resulting static structure factor in the large- and small-$q$ limit smoothly. We then calculate the pair-correlation functions, the ground-state energy, the screened potential, and the plasmon dispersion relation. Our pair-correlation function remains positive everywhere (for ${r}_{s}<~6.5$) and its value at the origin, $g(0),$ is compared with the results of other calculational schemes. The screened potential is repulsive for ${r}_{s}<~2$ and shows a weak attractive part for ${r}_{s}>2.$ We have argued that in these systems the $s$-wave intrinsic superconductivity is absent. Finally, the quantities calculated in this paper are compared with the results of other calculational schemes.

DOI
10.1103/physrevb.57.2447

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In this paper, we study correlations in quasi-one-dimensional electron systems. To account for the short-range correlations we have used a ladder approximation (LA), and to account for the long-range correlations we have used the Singwi, Tosi, S"olander, and Land (STLS) scheme. After solving the integral equation appearing in the LA and solving the set of self-consistent equations of the STLS scheme, we join the resulting static structure factor in the large- and small-qqq limit smoothly. We then calculate the pair-correlation functions, the ground-state energy, the screened potential, and the plasmon dispersion relation. Our pair-correlation function remains positive everywhere (for rs< 6.5{r}_{s}<~6.5rs​< 6.5) and its value at the origin, g(0),g(0),g(0), is compared with the results of other calculational schemes. The screened potential is repulsive for rs< 2{r}_{s}<~2rs​< 2 and shows a weak attractive part for rs>2.{r}_{s}>2.rs​>2. We have argued that in these systems the sss-wave intrinsic superconductivity is absent. Finally, the quantities calculated in this paper are compared with the results of other calculational schemes.
Understanding how electrons form pairs in the presence of strong electron correlations demands going beyond the BCS paradigm. We study a correlated superconducting model where the correlation effects are accounted for by a U term local in momentum space. The electron correlation is treated exactly while the electron pairing is treated approximately using the mean-field theory. The self-consistent equation for the pair potential is derived and solved. Somewhat contrary to expectation, a weak attractive U comparable to the pair potential can destroy the superconductivity, whereas for weak to intermediate repulsive U , the pair potential can be enhanced. The fidelity of the mean-field ground state is calculated to describe the strength of the elelectron correlation. We show that the pair potential is not equal to the single-electron superconducting gap for the strongly correlated superconductors, in contrast to the uncorrelated BCS limit.
In this second work in a series of papers the coupled-cluster or exp(S)\mathrm{exp}(S)exp(S) formalism is applied to the problem of ground-state correlations in the one-component Fermi plasma. The main approximation employed is the so-called SUB2 approximation for the two-body subsystem correlation operator S2{S}_{2}S2​ which provides a measure of the two-particle---two-hole component in the true ground-state wave function, and in which the coupling to larger subsystems is neglected. The SUB2 equations for Fermi systems are brought into tractable form by a "state-averaging" procedure which we develop by analogy with the comparable Bose equations, and which is shown by comparison with earlier exact results to be accurate in the metallic density regime at about the 1% level. Our final results for metallic densities include the completely integrated and self-consistent effects of the terms which by themselves generate (i) the random-phase approximation (RPA) and its associated exact long-range screening effects, (ii) the extra random-phase approximation exchange terms necessary to keep the RPA explicitly antisymmetric, (iii) the self-consistent particle-particle ladders (LAD) that describe two-particle scattering within the many-body medium and which describe the exact short-range behavior, (iv) a class of particle-hole ladder terms, and (v) the self-consistent hole-potential terms. Particular attention is paid to the important effects caused by the interference at intermediate separations of the long-range RPA and the short-range LAD effects. By comparison with recent and essentially exact stochastic simulations of the many-body Schr\"odinger equation, our results are seen to be accurate to about 1% for metallic densities, and hence to provide what is probably the currently best microscopic description available for this system. We show also that even in the low-density limit the SUB2 approximation provides a good "translationally-invariant-solid" description of both charged Fermi and Bose systems in this exact Wigner crystal regime.
The dielectric response of a quasi-one-dimensional system of interacting electrons has been investigated. In the authors' model the particles move freely in one direction and are tightly bound in the transverse direction. Calculation of the Coulomb matrix elements leads to an effective one-dimensional electron-electron interaction nu (q) which is less singular for small q than the 1/q 2 potential assumed by previous authors. As a result, the excitonic instability which they find even for a rigid positive background does not arise in their calculation. The calculations are based on the approximation of Singwi, Tosi, Land and Sjolander (1968). As expected in this approach, the pair correlation function at small distances remains positive over a much larger range of densities than that for which the compressibility sum rule is satisfied. The static dielectric function is negative around q=2k F , which suggests the possibility of charge ordering when the background is allowed to be polarisable. If nu (q) is replaced by a delta -function potential, a numerical calculation of the energy for the exact solution of Yang may be made. On comparison with the result obtained with the method of Singwi et al. it is found that the approximate scheme gives good correlation energies for high densities.
We have evaluated the density-density response of the two-dimensional electron gas at zero temperature by solving the Dyson equation for the particle-hole Green's function, including exchange Coulomb matrix elements and short-range contributions in the ladder approximation. We study the effect of these correlations on the total energy, compressibility per particle, local field factor G ( q ), static structure factor and pair-correlation function. Results are compared with the normal random-phase approximation, local field theories and quantum Monte Carlo calculations.
We study the one-dimensional electron gas with parabolic dispersion and a repulsive delta-function interaction potential. Using the ladder theory we obtain analytical results for the ground-state energy and the compressibility which are in agreement with exact results for weak and strong coupling. We calculate the short- and the long-distance behaviour of the pair-correlation function g(z) and derive critical exponents from . We evaluate the connection between the local-field correction and critical exponents.