Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

Superconducting States with the Lattice Distortion in the Extended Hubbard Model

Eiji Miyai, Masa-aki Ozaki

Published Apr 10, 1997• 0 citations
Publisher

Abstract

We give group theoretical classification of superconducting (SC) states with a single SC order parameter in the extended Hubbard model with uniform lattice distortion on the two-dimensional square lattice, by using the mean field approach. We obtain two singlet SCs (s-wave and d-wave) and eight triplet SCs by decomposing the pairing interaction into irreducible components (A1g, B1g and Eu) of point symmetry D4h. We show that in the singlet SC state with a single SC order parameter (s-wave or d-wave) no anisotropic lattice distortion occurs. In the case of triplet SC states, two SC states among eight must be accompanied with anisotropic lattice distortion. The symmetry of SC order parameter uniquely determines the lattice symmetry. We have performed numerical calculations for these SC states, and shown the possibility that one of the SC states with anisotropic lattice distortion becomes most stable of all SC states in the extended Hubbard model. We also discuss singlet SC states with multiple SC order parameters (s-wave and d-wave). It is shown that the anisotropic distortion must occur in (s+d)-SC states and not in (s+id)-SC state.

DOI
10.1142/s0217979297000587

Related papers

SUPERCONDUCTING CLASSES IN THE EXTENDED HUBBARD MODEL

Masa-aki Ozaki, Eiji Miyai, Tomoaki Konishi +1 more

This paper describes group theoretical classification of superconducting states (SC) in the extended Hubbard model with on-site repulsion (U), nearest neighbor attraction (V) and nearest neighbour exchange interaction (J) on the two-dimensional square lattice using the mean field approach. By decomposing the pairing interaction into irreducible parts; A1g, B1g and Eu of D4h point symmetry, we have derived two singlet SCs (s-wave and d-wave) from A1g and B1g, eight triplet SCs from Eu. The first three types of triplet SC have pairing by electrons with antiparallel spin, the second two types have pairing by electrons with equal spin and the last three types are non-unitary and have pairing by only up-spin electrons. We showed that three non-unitary states have to be accompanied with a ferromagnetic order from the structure of the maximal little groups. We performed numerical studies for these SCs. For parameters and electron density favorable for the ferromagnetic order, a non-unitary SC coexistent with ferromagnetism is most stable.

International Journal of Modern Physics B•May 30, 1996•1 citation

Spin singlet and triplet superconductivity in the extended Hubbard model with anisotropic exchange interaction

Yoshiki Hori, Akira Goto

We study the effect of the nearest neighbor anisotropic exchange interaction on superconductivity in extended Hubbard model in a square lattice. This Hamiltonian is one of a base model to describe various effects on triplet superconductors, e.g. Sr 2 RuO 4 , because the ferromagnetic exchange is advantagous for triplet pairing. Within a one-band meanfield approximation, we calculate the critical temperatures of spin singlet and triplet superconductivity. We obtain a phase diagram in the longitudinal vs transverse exchange couplings and we show how the stable pairing state is controlled by the anisotropy of the exchange interaction.

Journal of Physics Conference Series•Mar 1, 2009•2 citations

Group Theoretical Analysis of the Vortex Lattice States in the Attractive Hubbard Model

Makiko Ozaki, M. Yamazaki, G. Akira +1 more

This paper describes a group theoretical classification of superconducting states (vortex lattice states) in a unifom magnetic field of the extended Hubbard model with on-site attraction (U<0), or nearest-neighbor attraction (V<0) on a two-dimensional square lattice. Using symmetries of the magnetic translation and the tetragonal rotation of the system, we obtain invariance groups of vortex lattice states. When the magnetic flux φ through a unit cell of the crystal lattice is φ0/p2 (φ0=ch/2e is the flux quantum, p is an integer) we obtained three types of symmorphic tetragonal vortex lattice states, in which the center of point rotations is at a lattice site of the crystal lattice, corresponding to the irreducible representation of the tetragonal symmetry D4. For these three states, locations and winding numbers of vortex lines are determined by the symmetries of their invariance group. From these three symmorphic states we derived three (two) types of non-symmorphic vortex lattice states in which the center of point rotations is at the center of a plaquette (link) of the crystal lattice. We show that d-wave, s-wave and p-wave local order parameters inevitably coexist due to the invariance magnetic translation group L of the vortex lattice state. From the irreducible projective representations (two-dimensional) of L, we show that all energy bands of the quasiparticles are at least doubly degenerate.

Progress of Theoretical Physics•Aug 1, 1998•5 citations

Pairing symmetry in a two-orbital Hubbard model on a square lattice

Katsunori Kubo

We investigate superconductivity in a two-orbital Hubbard model on a square lattice by applying fluctuation exchange approximation. In the present model, the symmetry of the two orbitals are assumed to be that of an $s$ orbital. Then, we find that an $s$-wave spin-triplet orbital-antisymmetric state and a $p$-wave spin-singlet orbital-antisymmetric state appear when Hund's rule coupling is large. These states are prohibited in a single-orbital model within states with even frequency dependence, but allowed for multiorbital systems. We also discuss pairing symmetry in other models which are equivalent to the two-orbital Hubbard model except for symmetry of orbitals. Finally, we show that pairing states with a finite total momentum, even without a magnetic field, are possible in a system with two Fermi surfaces.

arXiv:cond-mat/0702624•Physical Review B•Jun 14, 2007•117 citations

Anisotropic superconductivity driven by kinematic interaction

V. A Ivanov

We have analysed the effect of kinematic pairing on the symmetry of superconducting order parameter for a square lattice in the frame of the strongly correlated Hubbard model. It is argued that in the first perturbation order the kinematic interaction renormalizes the Hubbard-I dispersions and provides at low doping the mixed singlet ( s + s *)-wave superconductivity, giving way at higher doping to the triplet p -wave superconductivity. The obtained phase diagram depends only on the hopping integral parameter. The influence of the Coulomb repulsion on the kinematic superconducting pairing has been estimated. The ( s + s *)-wave gap and the thermodynamic critical magnetic field have been derived.

Europhysics Letters (EPL)•Nov 1, 2000•4 citations

Superfluid properties of the extended Hubbard model with intersite electron pairing

R. Micnas, B. Tobijaszewska

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.

Journal of Physics Condensed Matter•Oct 3, 2002•28 citations
We give group theoretical classification of superconducting (SC) states with a single SC order parameter in the extended Hubbard model with uniform lattice distortion on the two-dimensional square lattice, by using the mean field approach. We obtain two singlet SCs (s-wave and d-wave) and eight triplet SCs by decomposing the pairing interaction into irreducible components (A1g, B1g and Eu) of point symmetry D4h. We show that in the singlet SC state with a single SC order parameter (s-wave or d-wave) no anisotropic lattice distortion occurs. In the case of triplet SC states, two SC states among eight must be accompanied with anisotropic lattice distortion. The symmetry of SC order parameter uniquely determines the lattice symmetry. We have performed numerical calculations for these SC states, and shown the possibility that one of the SC states with anisotropic lattice distortion becomes most stable of all SC states in the extended Hubbard model. We also discuss singlet SC states with multiple SC order parameters (s-wave and d-wave). It is shown that the anisotropic distortion must occur in (s+d)-SC states and not in (s+id)-SC state.
This paper describes group theoretical classification of superconducting states (SC) in the extended Hubbard model with on-site repulsion (U), nearest neighbor attraction (V) and nearest neighbour exchange interaction (J) on the two-dimensional square lattice using the mean field approach. By decomposing the pairing interaction into irreducible parts; A1g, B1g and Eu of D4h point symmetry, we have derived two singlet SCs (s-wave and d-wave) from A1g and B1g, eight triplet SCs from Eu. The first three types of triplet SC have pairing by electrons with antiparallel spin, the second two types have pairing by electrons with equal spin and the last three types are non-unitary and have pairing by only up-spin electrons. We showed that three non-unitary states have to be accompanied with a ferromagnetic order from the structure of the maximal little groups. We performed numerical studies for these SCs. For parameters and electron density favorable for the ferromagnetic order, a non-unitary SC coexistent with ferromagnetism is most stable.
We study the effect of the nearest neighbor anisotropic exchange interaction on superconductivity in extended Hubbard model in a square lattice. This Hamiltonian is one of a base model to describe various effects on triplet superconductors, e.g. Sr 2 RuO 4 , because the ferromagnetic exchange is advantagous for triplet pairing. Within a one-band meanfield approximation, we calculate the critical temperatures of spin singlet and triplet superconductivity. We obtain a phase diagram in the longitudinal vs transverse exchange couplings and we show how the stable pairing state is controlled by the anisotropy of the exchange interaction.
This paper describes a group theoretical classification of superconducting states (vortex lattice states) in a unifom magnetic field of the extended Hubbard model with on-site attraction (U<0), or nearest-neighbor attraction (V<0) on a two-dimensional square lattice. Using symmetries of the magnetic translation and the tetragonal rotation of the system, we obtain invariance groups of vortex lattice states. When the magnetic flux φ through a unit cell of the crystal lattice is φ0/p2 (φ0=ch/2e is the flux quantum, p is an integer) we obtained three types of symmorphic tetragonal vortex lattice states, in which the center of point rotations is at a lattice site of the crystal lattice, corresponding to the irreducible representation of the tetragonal symmetry D4. For these three states, locations and winding numbers of vortex lines are determined by the symmetries of their invariance group. From these three symmorphic states we derived three (two) types of non-symmorphic vortex lattice states in which the center of point rotations is at the center of a plaquette (link) of the crystal lattice. We show that d-wave, s-wave and p-wave local order parameters inevitably coexist due to the invariance magnetic translation group L of the vortex lattice state. From the irreducible projective representations (two-dimensional) of L, we show that all energy bands of the quasiparticles are at least doubly degenerate.
We investigate superconductivity in a two-orbital Hubbard model on a square lattice by applying fluctuation exchange approximation. In the present model, the symmetry of the two orbitals are assumed to be that of an sss orbital. Then, we find that an sss-wave spin-triplet orbital-antisymmetric state and a ppp-wave spin-singlet orbital-antisymmetric state appear when Hund's rule coupling is large. These states are prohibited in a single-orbital model within states with even frequency dependence, but allowed for multiorbital systems. We also discuss pairing symmetry in other models which are equivalent to the two-orbital Hubbard model except for symmetry of orbitals. Finally, we show that pairing states with a finite total momentum, even without a magnetic field, are possible in a system with two Fermi surfaces.
We have analysed the effect of kinematic pairing on the symmetry of superconducting order parameter for a square lattice in the frame of the strongly correlated Hubbard model. It is argued that in the first perturbation order the kinematic interaction renormalizes the Hubbard-I dispersions and provides at low doping the mixed singlet ( s + s *)-wave superconductivity, giving way at higher doping to the triplet p -wave superconductivity. The obtained phase diagram depends only on the hopping integral parameter. The influence of the Coulomb repulsion on the kinematic superconducting pairing has been estimated. The ( s + s *)-wave gap and the thermodynamic critical magnetic field have been derived.
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.