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     

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.     

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     

Interplay between spin-density-wave and superconducting states in quasi-one-dimensional conductors

The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a continuous crossover from a spin-density-wave state to unconventional superconductivity when deviations from perfect nesting of the Fermi surface exceed a critical value. Singlet pairing between electrons on neighboring stacks is found to be the most favorable symmetry for superconductivity. The consequences of non uniform spin-density-wave pairing on the structure of phase diagram within the crossover region is also discussed. Received 3 January 2001 and Received in final form 1st March 2001     

Electron-electron bound states in Maxwell-Chern-Simons-Proca QED <Emphasis Type="Bold">3</Emphasis>

We start from a parity-breaking MCS QED₃ model with spontaneous breaking of the gauge symmetry as a framework for evaluation of the electron-electron interaction potential and for attainment of numerical values for the e ^- e ^- - bound state. Three expressions ( V _eff , V _eff , V _eff ) are obtained according to the polarization state of the scattered electrons. In an energy scale compatible with condensed matter electronic excitations, these three potentials become degenerated. The resulting potential is implemented in the Schr?dinger equation and the variational method is applied to carry out the electronic binding energy. The resulting binding energies in the scale of 10-100 meV and a correlation length in the scale of 10-30 ? are possible indications that the MCS-QED₃ model adopted may be suitable to address an eventual case of e ^- e ^- pairing in the presence of parity-symmetry breakdown. The data analyzed here suggest an energy scale of 10-100 meV to fix the breaking of the U (1)-symmetry. Received 24 September 2002 / Received in final form 15 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: belich@cbpf.br RID="b" ID="b"e-mail: delcima@cbpf.br RID="c" ID="c"e-mail: manojr@cbpf.br RID="d" ID="d"e-mail: helayel@cbpf.br     

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     

Pairing mechanism in the doped Hubbard antiferromagnet: the 4×4 model as a test case

We introduce a local formalism, in terms of eigenstates of number operators, having well defined point symmetry, to solve the Hubbard model at weak coupling on a N × N square lattice (for even N). The key concept is that of W = 0 states, that are the many-body eigenstates of the kinetic energy with vanishing Hubbard repulsion. At half filling, the wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. Further, we state a general theorem which allows to find all the W = 0 pairs (two-body W = 0 singlet states). We show that, in special cases, this assigns the ground state symmetries at least in the weak coupling regime. The N = 4 case is discussed in detail. To study the doped half filled system, we enhance the group theory analysis of the 4×4 Hubbard model introducing an Optimal Group which explains all the degeneracies in the one-body and many-body spectra. We use the Optimal Group to predict the possible ground state symmetries of the 4×4 doped antiferromagnet by means of our general theorem and the results are in agreement with exact diagonalization data. Then we create W = 0 electron pairs over the antiferromagnetic state. We show analitycally that the effective interaction between the electrons of the pairs is attractive and forms bound states. Computing the corresponding binding energy we are able to definitely predict the exact ground state symmetry. Received 24 October 2000     

On-site repulsion as the source of pairing in carbon nanotubes and intercalated graphite

We show that different non-conventional superconductors have one fundamental feature in common: pair eigenstates of the Hamiltonian are repulsion-free, the W = 0 pairs. In extended Hubbard models, pairing can occur for reasonable parameter values. For (N, N) nanotubes the binding energy of the pair depends strongly on the filling and decreases towards a reduced but nonzero value for the graphite sheet N → ∞. Received 13 July 2002 Published online 29 November 2002     

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     

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.     

The possible origin of incommensurate spin textures in HTSC

An model of La_2-xSr_xCuO₄ explaining the features of incommensurate spin textures without any assumption of stripe formation is proposed. The foundations of this model are the mechanism of negative-U center formation proposed earlier and the concept of specific ordering of doped ions. It is shown that within the framework of the proposed model the features of “stripe” textures of La_2-xSr_xCuO₄ reflect exclusively the geometrical relations existing in a square lattice and the competition between different types of doped hole ordering.     

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     

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     

Superconductivity with s and p symmetries in an extended Hubbard model with correlated hopping

We consider a generalized Hubbard model with on-site and nearest-neighbour repulsions U and V respectively, and nearest-neighbour hopping for spin up (down) which depends on the total occupation n_b of spin down (up) electrons on both sites involved. The hopping parameters are t _AA , t_AB and t_BB for n _b =0,1,2 respectively. We briefly summarize results which support that the model exhibits s-wave superconductivity for certain parameters and extend them by studying the Berry phases. Using a generalized Hartree-Fock(HF) BCS decoupling of the two and three-body terms, we obtain that at half filling, for t _AB <t _AA =t _BB and sufficiently small U and V the model leads to triplet p-wave superconductivity for a simple cubic lattice in any dimension. In one dimension, the resulting phase diagram is compared with that obtained numerically using two quantized Berry phases (topological numbers) as order parameters. While this novel method supports the previous results, there are quantitative differences. Received: 2 February 1998 / Accepted: 17 March 1998     

Specific heat jump in non-Fermi superconductors

We derive the jump in the specific heat at T=T _c for a superconductor in a non-Fermi liquid model. We took into consideration the two possible limits in this problem: the spin-charge separation model for a Fermi liquid and the usual non-Fermi liquid model which satisfies the homogeneity relation for the spectral function , ). We also derive the order parameter behavior for these two cases in the vecinity of the critical temperature. Received: 25 January 1998 / Revised: 25 March 1998 / Accepted: 25 March 1998     

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     

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     

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     

“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