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arXiv:1902.08316 · Journal of Physics Condensed Matter

Mixed temperature-dependent order parameters in the extended Hubbard model

Joel Hutchinson, Frank Marsiglio

Published Nov 5, 2020• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1361-648x/abc801

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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.
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.
We study an extended Hubbard model with on-site repulsion and nearest-neighbors attraction which tries to mimic some of the experimental features of doped cuprates in the superconducting state. We draw and discuss the phase diagram as a function of the effective interactions among electrons for a wide range of doping concentrations. We locate the region which is relevant for the cuprates setting some constraints on the parameters which may be used in this kind of effective model. We also study the effects of temperature and orthorombicity on the symmetry and magnitude of the gap function, and map the model onto a simpler linearized Hamiltonian, which produces similar phase diagrams.
The paper examines part of the ground state diagram of the extended Hubbard model, with the on-site attraction U < 0 and intersite repulsion W > 0 in the presence of charge density waves, superconducting and η-superconducting order parameters.We show the possibility of the stabilization of the mixed state, with all three nonzero order parameters, in the model with nearest neighbor interactions.The other result of the paper is application of the exact solution of the Schrödinger equation for the two--electron bound state, as an additional bound for the phase diagram of the model, resulting in the partial suppression of the superconducting state of the s-wave symmetry, in favor of the normal state phase.
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.
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.
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.