Abstract Collective excitations in the superconducting state of an extended Hubbard model with an intrasite attraction are investigated using the random phase approximation method. The results for the energy of gapless excitations are consistent with the well known result of Anderson in the limit of weak attraction and the result of the perturbation theory (with respect to the band term) in the limit of strong attraction. Investigating the dependence of the excitation energy on the density of electrons in the band conditions are found of instability of the singlet superconducting state with respect to the disordered state (for attractive intersite interactions) and to the charge ordered superconducting state (for intersite repulsion).
Abstract Collective excitations in the superconducting state of an extended Hubbard model with an intrasite attraction are investigated using the random phase approximation method. The results for the energy of gapless excitations are consistent with the well known result of Anderson in the limit of weak attraction and the result of the perturbation theory (with respect to the band term) in the limit of strong attraction. Investigating the dependence of the excitation energy on the density of electrons in the band conditions are found of instability of the singlet superconducting state with respect to the disordered state (for attractive intersite interactions) and to the charge ordered superconducting state (for intersite repulsion).
By use of a diagrammatic method we determine the density-density response functions in the random-phase approximation (RPA) and the collective-excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state. The energy of the collective modes, given by the poles of these response functions, is found to be a linear function of the wave vector (for small k and short-range intersite interaction) with the velocity interpolating smoothly between the weak- (\ensuremath{\propto}2zt, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\ll}2zt) and strong-coupling (\ensuremath{\propto}zt2/\ensuremath{\Vert}U\ensuremath{\Vert}, \ensuremath{\Vert}U\ensuremath{\Vert}\ensuremath{\gg}2zt) limits. The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong-coupling limit. The numerical analysis for a two-dimensional (2D) square lattice shows the occurrence of a rotonlike minima near the zone boundary. In the weak-coupling regime we find that apart from a commensurate charge-density-wave (CDW) instability, an increase in the intersite Coulomb repulsion can give rise to a CDW incommensurate with the lattice period, away from half-filling. The resulting phase diagram for the 2D square lattice, including a singlet superconducting ground state, electronic-droplet formation, and CDW's, is determined. Finally, the effects of a long-range Coulomb interaction are analyzed briefly and it is shown that the energy of collective excitations evolves smoothly from the weak- to the strong-coupling limit for a 2D lattice.
We discuss the density-density response functions and the collective excitation spectrum for the extended Hubbard model with on-site attraction and arbitrary electron density, in the superconducting ground state.For the short-range intersite interaction we find the sound wave-like modes with the velocity interpolating smoothly between the weak (v 2Zt, |UD <2Zt) and strong coupling (v > 2Zt) limits.The latter agrees with the results obtained from an effective pseudospin Hamiltonian valid in the strong coupling limit.In the weak coupling regime, we obtain that apart from a commensurate charge density wave instability, an increase in the intersite Coułomb repulsion can give rise to a charge density wave incommensurate with the lattice period, away from half-frlling.The ground state phase diagram for 2D square lattice, including singlet superconducting ground state, electronic droplet formation, and charge density waves is determined.It is also shown that the energy of collective excitations evolves smoothly from weak to strong coupling limit for a 2D lattice, in the case of a long-range Coulomb interaction.Finally, the mode coupling effects in the frequency behavior of the density-density response functions are analyzed.
We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.
We study the normal (non-superconducting) phase of attractive Hubbard model within dynamical mean field theory (DMFT) using numerical renormalization group (NRG) as impurity solver. Wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by BCS approximation, up to the strong-coupling region, where superconducting transition is described by Bose-condensation of compact Cooper pairs, which are formed at temperatures much exceeding superconducting transition temperature. We calculate density of states, spectral density and optical conductivity in the normal phase for this wide range of U, including the disorder effects. Also we present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. Disorder influence on the critical temperature Tc is rather weak, suggesting in fact the validity of Anderson theorem, with the account of the general widening of the conduction band due to disorder.
In this paper, we analyze a simple extended Hubbard model with an intermediate on-site interaction (both repulsive and attractive) and a weak intersite attractive interaction. Following Hubbard decoupling approximations and introducing Hubbard subband operators, we obtain a generalized gap function for singlet s-wave pairing that explicitly depends on the Hubbard subband energies. For the on-site repulsive-interaction case, we find that the superconductivity is not destroyed in the intermediate-interaction regime, contrary to the prediction of a Hartree-Fock mean-field treatment. The essential consequence of the on-site repulsion is the formation of the Hubbard subbands separated by the Mott-Hubbard gap, and it is within these subbands that pairing induced by the intersite interaction occurs. For the attractive on-site interaction case, the on-site pairing amplitude is found to be proportional to the bandwidth, and the gap function has contributions from both on-site and intersite pairing. The relevance of the model to high-temperature superconductivity is discussed.
We study the normal (non-superconducting) phase of attractive Hubbard model within dynamical mean field theory (DMFT) using numerical renormalization group (NRG) as impurity solver. Wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by BCS approximation, up to the strong-coupling region, where superconducting transition is described by Bose-condensation of compact Cooper pairs, which are formed at temperatures much exceeding superconducting transition temperature. We calculate density of states, spectral density and optical conductivity in the normal phase for this wide range of U, including the disorder effects. Also we present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. Disorder influence on the critical temperature Tc is rather weak, suggesting in fact the validity of Anderson theorem, with the account of the general widening of the conduction band due to disorder.