Superconductivity in weakly correlated electron systems

We study the influence of the short-ranged Hubbard correlation U between the conduction electrons on the Cooper pair formation in normal (s-wave) superconductors. The Coulomb correlation is considered within the standard second order perturbation theory, which becomes exact in the weak coupling limit but goes beyond the simple Hartree-Fock treatment by yielding a finite lifetime of the quasiparticles at finite temperature. An attractive pairing interaction V, which may be mediated by the standard electron-phonon mechanism, is considered between nearest neighbor sites. A critical value for the attractive interaction is required to obtain a superconducting state. For finite temperature a gapless superconductivity is obtained due to the finite lifetime of the quasiparticles, i.e. the Coulomb correlation has a pair-breaking influence. The energy gap and depend very sensitively on U, V and band filling n and develop a maximum away from half filling as function of n. The ratio varies with n, being higher than the BCS value near half filling and reaching the BCS value for lower n. Received 17 February 1999     

Appearance of anisotropic non s-wave superconductivity above the critical pressure of antiferromagnetic CeRhIn5

We have carried out ¹¹⁵In nuclear quadrupole resonance (NQR) measurements in CeRhIn₅. At ambient pressure, CeRhIn₅ undergoes an antiferromagnetic AF phase transition at K. The ¹¹⁵In NQR spectrum has shown the appearance of a small internal field in the direction perpendicular to the tetragonal c-axis. With application of a hydrostatic pressure, the AF state is suppressed and the superconductivity appears just above the critical pressure (P = 17 kbar). The nuclear spin lattice relaxation rate 1/T₁ of ¹¹⁵In measured at P = 27 kbar indicates the occurrence of the superconductivity in the nearly AF region. In the superconducting state, 1/T₁ has no Hebel-Slichter coherence peak just below of 2 K and has a power law T-dependence (T³) down to 300 mK. This is consistent with anisotropic superconductivity, with line nodes in the superconducting energy gap: non-s-wave superconductivity occurs in CeRhIn₅. Received 5 July 2000     

Pairing in the Hubbard model: the Cu O cluster versus the Cu-O plane

We study the Cu₅O₄ cluster by exact diagonalization of a three-band Hubbard model and show that bound electron or hole pairs are obtained at appropriate fillings, and produce superconducting flux quantization. The results extend earlier cluster studies and illustrate a canonical transformation approach to pairing that we have developed recently for the full plane. The quasiparticles that in the many-body problem behave like Cooper pairs are W =0 pairs, that is, two-hole eigenstates of the Hubbard Hamiltonian with vanishing on-site repulsion. The cluster allows W =0 pairs of d symmetry, due to a spin fluctuation, and ssymmetry, due to a charge fluctuation. Flux quantization is shown to be a manifestation of symmetry properties that hold for clusters of arbitrary size. Received 23 July 1999     

Superconductors with topological order

We propose a mechanism of superconductivity in which the order of the ground state does not arise from the usual Landau mechanism of spontaneous symmetry breaking but is rather of topological origin. The low-energy effective theory is formulated in terms of emerging gauge fields rather than a local order parameter and the ground state is degenerate on topologically non-trivial manifolds. The simplest example of this mechanism of superconductivity is concretely realized as global superconductivity in Josephson junction arrays.     

A microscopic model for the intrinsic Josephson tunneling in high- superconductors

A quantitative analysis of a microscopic model for the intrinsic Josephson effect in high-temperature superconductors based on interlayer tunneling is presented both within a mean-field BCS evaluation and a numerically essentially exact Quantum Monte-Carlo study. The pairing correlations in the CuO₂-planes are modelled by a 2D Hubbard model with attractive interaction, a model which accounts well for some of the observed features such as the short planar coherence length. The stack of Hubbard planes is arranged on a torus, which is threaded by a magnetic flux. The current perpendicular to the planes is calculated as a function of applied flux (i.e. the phase), and - after careful elimination of finite-size effects due to single-particle tunneling - found to display a sinusoidal field dependence in accordance with interlayer Josephson tunneling. Studies of the temperature dependence of the supercurrent reveal at best a mild elevation of the Josephson transition temperature compared to the planar Kosterlitz-Thouless temperature. These and other results on the dependence of the model parameters are compared with a standard BCS evaluation. Received: 24 February 1998 / Revised: 28 April 1998 / Accepted: 23 June 1998     

Triplet superconductivity in a 1D itinerant electron system with transverse spin anisotropy

In this paper we study the ground state phase diagram of a one-dimensional t-J-U model away from half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With increasing ferromagnetic exchange transitions into a ferrometallic and then a spin gapped triplet superconducting phase take place.     

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     

From semiconductors to superconductors: a simple model for pseudogaps

We consider a two-dimensional semiconductor with a local attraction among the carriers. We study the ground state of this system as a function of the semiconductor gap. We find a direct transition from a superconducting to an insulating phase for no doping at a critical value, the single particle excitations being always gapped. For finite doping we find a smooth crossover. We calculate the critical temperature due to both the particle excitations and the Berezinkii-Kosterlitz-Thouless transition. Received 8 December 1998     

Dual model for magnetic excitations and superconductivity in UPd 2 Al 3

The Heavy Fermion state in UPd₂Al₃ may be approximately described by a dual model where two of the three U-5 f electrons are in a localized state split by the crystalline electric field into two low lying singlets with a splitting energy Δ≃ 6 meV. The third 5 f electron has itinerant character and forms the Heavy Electron bands. Inelastic neutron scattering and tunneling experiments suggest that magnetic excitons, the collective propagating crystal field excitations of the localized 5 f electrons, mediate superconducting (sc) pairing in UPd₂Al₃. A theory for this novel mechanism is developed within a nonretarded approach. A model for the magnetic exciton bands is analyzed and compared with experiment. The sc pair potential which they mediate is derived and the gap equations are solved. It is shown that this mechanism favors an odd parity state which is nondegenerate due to the combined symmetry breaking by the crystalline electric field and the AF order parameter. A hybrid model including the spin fluctuation contribution to the pairing is also discussed. Received 22 October 2001 and Received in final form 28 February 2002     

The modes of an ultra-cold strongly magnetized charged Bose gas

The modes of a strongly magnetized charged Bose gas are presented for ultra-low temperatures. For longitudinal oscillations propagating parallel to the magnetic field the dispersion relation is found to be dominated by the one-dimensional field-free plasmon dispersion relation as found by Alexandrov, Beere and Kabanov recently in reference [1], while for propagation perpendicular to the magnetic field they are found to be influenced by the cyclotron motion of the particles. Dispersion relations for these modes known as Bernstein modes are given near the cyclotron frequency and its first two harmonics. The dispersion relations for transverse modes in the system are then presented for the cases of photon propagation perpendicular and parallel to the direction of the magnetic field. Received: 3 July 1997 / Revised: 12 August 1997 / Accepted: 4 November 1997     

“W = 0” pairing in Cu-O clusters and in the plane

The Cu-O plane and the clusters that possess the same C_4v symmetry around a Cu ion have 2-hole eigenstates of the kinetic energy with vanishing on-site repulsion (W=0 pairs). Cluster calculations by exact diagonalisation show that these are the quasiparticles that lead to a paired ground state, and have superconducting flux-quantisation properties. Here, we extend the theory to the full plane, and show that the W=0 quasiparticles are again the natural explanation of superconducting flux-quantisation. Moreover, by a new approach which is exact in principle, we calculate the effective interaction between two holes added to the ground state of the repulsive three-band Hubbard model. To explain how a noninteracting electron gas becomes a superconductor when switching the local Coulomb interaction, we obtain a closed-form analytic expression including the effects of all virtual transitions to 4-body intermediate states (exchange of an electron-hole pair). Our scheme is ready to include other interactions which are not considered in the Hubbard model but may be important. In the plane, the W=0 pairs have ¹ B ₂ and ¹ A ₂ symmetry. The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid, while it is repulsive for triplet pairs. From , we derive an integral equation for the pair eigenfunction; the binding energy of the pairs is in the range of tens of meV. However, our symmetry-based method is far more general than the model. Received 18 December 1998     

Renormalized quasiparticles in antiferromagnetic states of the Hubbard model

We analyze the properties of the quasiparticle excitations of metallic antiferromagnetic states in a strongly correlated electron system. The study is based on dynamical mean field theory (DMFT) for the infinite dimensional Hubbard model with antiferromagnetic symmetry breaking. Self-consistent solutions of the DMFT equations are calculated using the numerical renormalization group (NRG). The low energy behavior in these results is then analyzed in terms of renormalized quasiparticles. The parameters for these quasiparticles are calculated directly from the NRG derived self-energy, and also from the low energy fixed point of the effective impurity model. From these the quasiparticle weight and the effective mass are deduced. We show that the main low energy features of the k-resolved spectral density can be understood in terms of the quasiparticle picture. We also find that Luttinger's theorem is satisfied for the total electron number in the doped antiferromagnetic state.     

Magnon-mediated binding between holes in an antiferromagnet

The long-range forces between holes in an antiferromagnet are due to magnon exchange. The one-magnon exchange potential between two holes is proportional to cos(2 ϕ)/r ² where r is the distance vector of the holes and ϕ is the angle between r and an axis of the square crystal lattice. One-magnon exchange leads to bound states of holes with antiparallel spins resembling d-wave symmetry.     

Nature of correlations in the atomic limit of the boson fermion model

Using the equation of motion technique for Green's functions we derive the exact solution of the boson fermion model in the atomic limit. Both (fermion and boson) subsystems are characterised by the effective three level excitation spectra. We compute the spectral weights of these states and analyse them in detail with respect to all possible parameters. Although in the atomic limit there is no true phase transition, we notice that upon decreasing temperature some pairing correlations start to appear. Their intensity is found to be proportional to the depleted amount of the fermion nonbonding state. We notice that pairing correlations behave in a fashion observed for the optimally doped and underdoped high T_c superconductors. We try to identify which parameter of the boson fermion model can possibly correspond to the actual doping level. This study clarifies the origin of pairing correlations within the boson fermion model and may elucidate how to apply it for interpretation of experimental data. Received 31 January 2003 / Received in final form 18 March 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: doman@kft.umcs.lublin.pl     

The screened polarons

We present a theory of polarons incorporating the screening of the Coulomb interaction, and we apply this theory to the case of anisotropic ionic crystals as the perovskites. We show that the “screened polarons" cannot be treated individually: all the polarons present in the material are coupled via the screening. We also show that, in the frame of this theory of large-scale polarons, the bipolarons are excluded and replaced by pairs of polarons; we propose to associate the pseudogap experimentally observed in perovskites with the binding energy of these pairs. Finally we suggest that the existence of the polarons pairs poses in new terms the problem of a polaronic theory of superconductivity. Received 9 December 1998 and Received in final form 2 March 2000     

Small bipolarons in the 2-dimensional Holstein-Hubbard model. I. The adiabatic limit

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction , which tends to break them, generates many different ground-states. There are four domains in the phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small , large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large , large g); or 3) be a “quadrisinglet state” which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron. Received 10 December 1998     

General spectral function expressions of a 1D correlated model

We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of pseudofermion operators such that the spectral functions can be written as a convolution of pseudofermion dynamical correlation functions. Our results are valid for all finite energy and momentum values and are used elsewhere in the study of the unusual finite-energy properties of quasi-one-dimensional compounds and the new quantum systems of ultra-cold fermionic atoms on an optical lattice.     

Two-parameter extended Hubbard Hamiltonian with supersymmetry

We investigate under which circumstances extended Hubbard models, including bond-charge, exchange, and pair-hopping terms, are invariant under gl (2,1) superalgebra. This happens for a two-parameter Hamiltonian which includes as particular cases the t - J, the EKS and the one-parameter BGLZ Hamiltonians, all integrable in one dimension. We show that the two parameter Hamiltonian can be recasted as the sum of the BGLZ Hamiltonian plus the graded permutation operator of electronic states on neighbouring sites. The integrability of the corresponding one-dimensional model is discussed. Received: 17 February 1998 / Received in final form: 6 March 1998 / Accepted: 17 April 1998     

Symmetry breaking induced by a magnetic field in a quasi-two-dimensional d-wave superconductor

A model of quasi-two-dimensional d-wave superconductor, with strong nesting properties of the Fermi surface is considered. The orbital effect of a moderate magnetic field applied perpendicularly to the conducting planes is studied in the mean field approximation. It is shown that the field can induce a time reversal symmetry breaking SDW order coexisting with the superconducting order and can open a gap over the whole Fermi surface. The anomalies recently observed in the heat conductivity in might be ascribed to this effect. Received 7 May 1999 and Received in final form 13 August 1999