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Chinese Physics B

Effects of electron correlation on superconductivity in the Hatsugai–Kohmoto model*

Huai-Shuang Zhu, Qiang Han

Published Mar 5, 2021• 8 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/abec36

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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.
Multiband superconductivity gives rise to a rich landscape of possible pairing states. Here we study superconductivity emerging from a half-filled normal state in a two-orbital extension of the Hatsugai-Kohmoto model, an exactly solvable model of correlated electrons with momentum-local interactions, which provides a minimal framework to explore the interplay of strong correlations, orbital structure and pairing symmetry. For a system with point-group symmetry D4h\rm D_{4h}D4h​, we classify the symmetry-allowed superconducting gap structures, taking into account spin, orbital and momentum degrees of freedom. We further compute the critical temperature and the superconducting order parameter for selected pairing channels as functions of interaction and pairing strength within a mean-field treatment. Our results provide a systematic framework for analyzing superconductivity in the orbital Hatsugai-Kohmoto model and extend symmetry-based approaches to correlated multiband settings.
A theoretical study of BCS pairing in an extended Hubbard model with on-site repulsion (U) and a BCS pairing field (V) is presented. Treating the effect of U in the Gutzwiller approximation, we study the effect of increasing U in the Fermi-liquid phase, on the BCS pairing due to V. It is found that the superconducting energy gap (\ensuremath{\Delta}) is strongly enhanced in the correlated metallic phase near half-filling of the band due to the localization effects of U. Further, the ground state is found to be superconducting even when \ensuremath{\Vert}V\ensuremath{\Vert}U, contrary to the prediction in a Hartree-Fock treatment.
The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.
The understanding of the mechanisms responsible for superconductivity in strongly correlated systems is an interesting and important subject in condensed matter physics. Several theoretical proposals were considered for these systems. The Coulomb interaction between electrons allow a new approach to study this problem. In this paper, we use a usual Hubbard model with a local repulsive interaction to describe a 2D system. The system of equations are solved using the Green's functions method, within a Hubbard-I mean field approximation, which allows to treat the strong interaction limit. We consider both cases of attractive and repulsive interactions and obtain the zero temperature phase diagram of the model. Our results show, in the repulsive case, the existence of a superconducting ground state mediated by the kinetic electronic energy and described by a non-local order parameter. A minimum value of the repulsive interaction UminU_{min}Umin​ is required to create a pairing state. At finite temperatures, for strong interactions, the critical temperature TcT_cTc​ shows a saturation similar to the Bose-Einstein condensation observed for strong attractive interactions.
We study superconductivity in the extended Hubbard model with a strong on-site repulsion U and weak attractive density-density interaction Vij{\mathit{V}}_{\mathit{ij}}Vij​. The electron correlation effects, beyond the weak-coupling regime of U, are included approximately by employing Hubbard decoupling approximations. The formulas for superconducting transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ of the present approach are compared to those obtained with the strong-coupling expansion and slave-boson techniques. The methods share some common features. We discuss behavior of Tc{\mathit{T}}_{\mathit{c}}Tc​ for superconducting phases with s- and d-wave symmetry of the superconducting order parameter. In contrast to the mean-field treatment of U, we find that the strong on-site repulsion does not destroy superconductivity induced by ${\mathit{V}}_{\mathit{ij}}$0 even when U\ensuremath{\gg}|${\mathit{V}}_{\mathit{ij}}$|. \textcopyright{} 1996 The American Physical Society.
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.