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arXiv:cond-mat/9808279 · Philosophical Magazine B

Superconductivity in the extended hubbard model with more than nearest-neighbour contributions

Zsolt Szabó, Zsolt Gulácsi

Published Dec 1, 1997• 7 citations
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Abstract

Superconducting phase diagram of the extended Hubbard model supplemented with interaction and hopping terms exceeding the nearest-neighbour distance in range is analysed systematically at different band filling and temperature values in a mean-field approximation. The obtained results clearly emphasize the importance of next-nearest-neighbour terms in developing the main superconducting phases of different symmetries at a given point of the phase diagram; in particular, critical temperatures TT , zero temperature gap amplitude values Δ0, Δ0/T c ratios, doping and temperature dependences are all strongly influenced by next-nearest-neighbour contributions.

DOI
10.1080/01418639708243138

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Philosophical Magazine B•Nov 1, 1997•2 citations
Superconducting phase diagram of the extended Hubbard model supplemented with interaction and hopping terms exceeding the nearest-neighbour distance in range is analysed systematically at different band filling and temperature values in a mean-field approximation. The obtained results clearly emphasize the importance of next-nearest-neighbour terms in developing the main superconducting phases of different symmetries at a given point of the phase diagram; in particular, critical temperatures TT , zero temperature gap amplitude values Δ0, Δ0/T c ratios, doping and temperature dependences are all strongly influenced by next-nearest-neighbour contributions.
Superconducting phases of the extended Hubbard model has been investigated in the weak-coupling limit at different temperatures and doping levels in the presence of on-site, nearest-neighbour and next-nearest-neighbour couplings. The main result is the occurrence of stable pairing states of different symmetries depending on the tunable parameters of the model; attractive nearest-neighbour couplings give rise to a stable superconducting state having dxr y2 symmetry, while attractive next-nearest-neighbour interactions favour pairing states of dxy symmetry.
Abstract The extended Hubbard model can host s-wave, d-wave and p-wave superconducting phases depending on the values of the on-site and nearest-neighbour interactions. Upon detailed examination of the free energy functional of the gap in this model, we show that these symmetries are often dependent on temperature. The critical points of this functional are constrained by symmetry and allow us to formulate stringent conditions on the temperature profile of the gap function, applicable to other models as well. We discuss the finite temperature phase diagram of the extended Hubbard model, and point out the existence of symmetry transitions below T c . Understanding the nature of these transitions is crucial to assessing the symmetry of unconventional superconductors.
The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e., the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1d=1d=1 and $d=\ensuremath{\infty},$ by means of the (broken symmetry) Hartree-Fock approximations and, for $d=\ensuremath{\infty},$ by the slave-boson mean-field method. For d=1,d=1,d=1, at half filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0q=0q=0 and q=Qq=Qq=Q $(\ensuremath{\eta}$ pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings shrinks with increasing lattice dimensionality d and for $d=\ensuremath{\infty}$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.
We study the superfluid properties of short-coherence-length superconductors described by the extended Hubbard model with on-site repulsive and intersite attractive interaction. We have analysed the superfluid stiffness and thermodynamic properties of the model versus electron concentration and pairing interaction on a two-dimensional square lattice with nearest- and next-nearest-neighbour hopping. The effects of phase fluctuations on anisotropic superconductivity of extended s-and d x 2 − y 2 -wave type were examined within the Kosterlitz–Thouless (KT) scenario. The KT critical temperatures were determined and compared with those from the BCS–Hartree–Fock approximation. The Uemura-type plots, i.e. the critical temperature versus zero-temperature phase stiffness, were obtained for both extended s- and d-wave pairings. The states with mixed (s ∗ and d x 2 − y 2 ) symmetry, and in particular the time-reversal breaking state of s + id symmetry, were analysed and the phase diagrams taking into account these states are presented. We also briefly discuss the crossover from BCS to local pair superconductivity for the d x 2 − y 2 -wave pairing. A comparison of the theoretical results with the experimental data, in particular those of T c versus λ −2 (0), for high- T c cuprate superconductors is made.
We calculate the magnetic phase diagram of the Hubbard model for a Bethe lattice with nearest-neighbour (NN) hopping t 1 and next-nearest-neighbour (NNN) hopping t 2 in the limit of infinite coordination. We use the amplitude t 2 / t 1 of the NNN hopping to tune the density of states (DOS) of the non-interacting system from a situation with particle–hole symmetry to an asymmetric one with van-Hove singularities at the lower ( t 2 / t 1 >0) respectively upper ( t 2 / t 1 <0) band edge for large enough | t 2 / t 1 |. For this strongly asymmetric situation, we find rather extended parameter regions with ferromagnetic states and regions with antiferromagnetic states.