Effective interactions and superconductivity in the t-J model in the large-N limit

The feasibility of a perturbation expansion for Green's functions of the t-J model directly in terms of X-operators is demonstrated using the Baym-Kadanoff functional method. As an application we derive explicit expressions for the kernel of the linearized equation for the superconducting order parameter in leading order of a 1/N expansion. The linearized equation is solved numerically on a square lattice taking instantaneous and retarded contributions into account. Classifying the order parameter according to irreducible representations of the point group C_4v of the square lattice and according to even or odd parity in frequency we find that a reasonably strong instability occurs only for even frequency pairing with d-wavelike symmetry. The corresponding transition temperature T_c is where t is the nearest-neighbor hopping integral. The underlying effective interaction consists of an attractive, instantaneous term and a retarded term due to charge and spin fluctuations. The latter is weakly attractive at low frequencies below ,strongly repulsive up to and attractive towards even higher energies. T_c increases with decreasing doping until a d-wavelike bond-order wave instability is encountered near optimal doping at for J=0.3. T_c is essentially linear in J and rather insensitive to an additional second-nearest neighbor hopping integral t'. A rather striking property of T_c is that it is hardly affected by the soft mode associated with the bond-order wave instability or by the Van Hove singularity in the case with second-nearest neighbor hopping. This unique feature reflects the fact that the solution of the gap equation involves momenta far away from the Fermi surface (due to the instantaneous term) and many frequencies (due to the retarded term) so that singular properties in momentum or frequency are averaged out very effectively. Received: 16 June 1998 / Accepted: 14 July 1998     

Antiferromagnetism and superconductivity in a model with extended pairing interactions

The competition between antiferromagnetism and the d + id superconducting state is studied in a model with near and next near neighbour interactions in the absence of any on-site repulsion. A mean field study shows that it is possible to have simultaneous occurrence of an antiferromagnetic and a singlet d + id superconducting state in this model. In addition, such a coexistence generates a triplet d + id superconducting order parameter with centre of mass momentum Q = (π,π) dynamically having the same orbital symmetry as the singlet superconductor. Inclusion of next nearest neighbour hopping in the band stabilises the d_xy superconducting state away from half filling, the topology of the phase diagram, though, remains similar to the near neighbour model. In view of the very recent observation of a broad region of coexistence of antiferromagnetic and unconventional superconducting states in organic superconductors, the possibility of observation of the triplet state has been outlined. Received 30 November 2000 and Received in final form 27 March 2001     

Consequences of charge imbalance in superconductors within the theory of hole superconductivity

The theory of hole superconductivity proposes that the fundamental asymmetry between electrons and holes in solids is responsible for superconductivity. Here we point out a remarkable consequence of this theory: a tendency for negative charge to be expelled from the bulk of the superconductor towards the surface. Experimentally observable consequences of this physics are discussed.     

d-wave superconductivity in the hubbard model

The superconducting instabilities of the doped repulsive 2D Hubbard model are studied in the intermediate to strong coupling regime with the help of the dynamical cluster approximation. To solve the effective cluster problem we employ an extended noncrossing approximation, which allows for a transition to the broken symmetry state. At sufficiently low temperatures we find stable d-wave solutions with off-diagonal long-range order. The maximal T(c) approximately 150 K occurs for a doping delta approximately 20% and the doping dependence of the transition temperatures agrees well with the generic high- T(c) phase diagram.     

On the boson-fermion model of superconductivity

Summary The existence of pair excitations in a Fermi gas interacting via a short-range attractive potential is investigated. Within the ladder approximation to the Bethe-Salpeter equation for the effective two-particle interaction, evidence of pair excitation is found at energies slightly larger than the chemical potential. The link between those excitations and a boson-fermion model of superconductivity (Phys. Lett. A,196 (1995) 359) is discussed. In particular it is shown that the charge carrier density dependence of the pair excitation (boson) energy, assumed phenomenologically in the boson-fermion model, is consistent with the properties of the interacting Fermi gas studied. These results give support to the microscopic origin of the phenomenological boson-fermion model of superconductivity. Within the polaron-bipolaron theory the assumption that bosons and fermions can be described as mobile particles has found support in ref.[6] where the small bipolaron (boson) delocalization is discussed and in ref.[7] where the large polaron delocalization is analysed.     

One-dimensional two-band model of superconductivity

The interband Fermi surface nesting in the system of the title is shown to extremely magnify the effect of the exchange-like interaction which elevates the superconducting transition temperature T_c by reducing the suppressing effect of the Coulomb interaction and in some cases drives superconductivity by itself. This magnification is through the processes expressed by the ladder and bubble diagrams including the interband Coulomb and exchange interactions in addition to the above one. The divergence of the present ladder diagram is new in the parameter-dependence and easier to occur than the known one taking account of the interband Coulomb interaction only. How this effective magnification of the above interaction elevates T_c is roughly discussed. Relevance to the high T_c of the YBa₂Cu₃O_y superconductors is argued.     

The symmetries of the Manton superconductivity model

The symmetries and conserved quantities of Manton’s modified superconductivity model with non-relativistic Maxwell–Chern–Simons dynamics (also related to the Quantized Hall Effect) are obtained in the “Kaluza–Klein type” framework of Duval et al.     

Microscopic model of superconductivity in carbon nanotubes

We propose the model of a manifold of one-dimensional interacting electron systems to account for the superconductivity observed in ropes of nanotubes. We rely on the strong suppression of single-particle hopping between neighboring nanotubes in a disordered rope and conclude that the tunneling takes place in pairs of electrons, which are formed within each nanotube due to the existence of large superconducting correlations. Our estimate of the transition temperature is consistent with the values that have been measured experimentally in ropes with about 100 metallic nanotubes.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.