Perturbation expansion for 2-D Hubbard model

We develop an efficient method to calculate the third-order corrections to the self-energy of the hole-doped two-dimensional Hubbard model in space-time representation. Using the Dyson equation we evaluate the renormalized spectral function in various parts of the Brillouin zone and find significant modifications with respect to the second-order theory even for rather small values of the coupling constant U. The spectral function becomes unphysical for $U \simeq W$, where W is the half-width of the conduction band. Close to the Fermi surface and for U<W, the single-particle spectral weight is reduced in a finite energy interval around the Fermi energy. The increase of U opens a gap between the occupied and unoccupied parts of the spectral function.Comment: 17 pages, 11 Postscript figures, Phys. Rev. B, accepte

Many Body Correlation Corrections to Superconducting Pairing in Two Dimensions.

We demonstrate that in the strong coupling limit (the superconducting gap $\Delta$ is as large as the chemical potential $\mu$), which is relevant to the high-$T_c$ superconductivity, the correlation corrections to the gap and critical temperature are about 10\% of the corresponding mean field approximation values. For the weak coupling ($\Delta \ll \mu$) the correlation corrections are very large: of the order of 100\% of the corresponding mean field values.Comment: LaTeX 12 page

Andreev experiments on superconductor/ferromagnet point contacts

Andreev reflection is a smart tool to investigate the spin polarisation P of the current through point contacts between a superconductor and a ferromagnet. We compare different models to extract P from experimental data and investigate the dependence of P on different contact parameters.Comment: 14 pages, 5 figures, accepted for publication in Fizika Nizkikh Temperatu

Reversing non-local transport through a superconductor by electromagnetic excitations

Superconductors connected to normal metallic electrodes at the nanoscale provide a potential source of non-locally entangled electron pairs. Such states would arise from Cooper pairs splitting into two electrons with opposite spins tunnelling into different leads. In an actual system the detection of these processes is hindered by the elastic transmission of individual electrons between the leads, yielding an opposite contribution to the non-local conductance. Here we show that electromagnetic excitations on the superconductor can play an important role in altering the balance between these two processes, leading to a dominance of one upon the other depending on the spatial symmetry of these excitations. These findings allow to understand some intriguing recent experimental results and open the possibility to control non-local transport through a superconductor by an appropriate design of the experimental geometry.Comment: 6 pages, 3 figure

Microscopic Theory of Josephson Mesoscopic Constrictions

We present a microscopic theory for the d.c. Josephson effect in model mesoscopic constrictions. Our method is based on a non-equilibrium Green function formalism which allows for a self-consistent determination of the order parameter profile along the constriction. The various regimes defined by the different length scales (Fermi wavelength $\lambda_F$, coherence length $\xi_0$ and constriction length $L_C$) can be analyzed, including the case where all these lengths are comparable. For the case $\lambda_F \tilde{<} (L_C,\xi_0)$ phase oscillations with spatial period $\lambda_F/2$ can be observed. In the case of $L_C>\xi_0$ solutions with a phase-slip center inside the constriction can be found, in agreement with previous phenomenological theories.Comment: 4 pages (RevTex 3.0), 3 postscript figures available upon request, 312456-C

Supercurrent flow through an effective double barrier structure

Supercurrent flow is studied in a structure that in the Ginzburg-Landau regime can be described in terms of an effective double barrier potential. In the limit of strongly reflecting barriers, the passage of Cooper pairs through such a structure may be viewed as a realization of resonant tunneling with a rigid wave function. For interbarrier distances smaller than $d_0=\pi\xi(T)$ no current-carrying solutions exist. For distances between $d_0$ and $2d_0$, four solutions exist. The two symmetric solutions obey a current-phase relation of $\sin(\Delta\varphi/2)$, while the two asymmetric solutions satisfy $\Delta\varphi=\pi$ for all allowed values of the current. As the distance exceeds $nd_0$, a new group of four solutions appears, each contaning $(n-1)$ soliton-type oscillations between the barriers. We prove the inexistence of a continuous crossover between the physical solutions of the nonlinear Ginzburg-Landau equation and those of the corresponding linearized Schr\"odinger equation. We also show that under certain conditions a repulsive delta function barrier may quantitatively describe a SNS structure. We are thus able to predict that the critical current of a SNSNS structure vanishes as $\sqrt{T'_c-T}$, where $T'_c$ is lower than the bulk critical temperature.Comment: 20 pages, RevTex, to appear in Phys. Rev. B, 6 figures on request at [email protected]

Non-equilibrium current noise in mesoscopic disordered SNS junctions

Current noise in superconductor-normal metal-superconductor (SNS) junctions is calculated within the scattering theory of multiple Andreev reflections (MAR). It is shown that the noise exhibits subharmonic gap singularities at $eV=2\Delta/n$, $n=1,2,...$ both in single-mode junctions with arbitrary transparency $D$ and in multi-mode disordered junctions. The subharmonic structure is superimposed with monotonic increase of the effective transferred charge $q^*=S_I(0)/2I$ with decreasing bias voltage. Other features of the noise include a step-like increase of $q^*$ in junctions with small $D$, and a divergence $S_I(0) \propto V^{-1/2}$ at small voltages and excess noise $S_{ex} = 2eI_{ex}$, where $I_{ex}$ is the excess current, at large voltages, in junctions with diffusive transport.Comment: 5 page

Investigation of the Two-Particle-Self-Consistent Theory for the Single-Impurity Anderson Model and an Extension to the Case of Strong Correlation

The two-particle-self-consistent theory is applied to the single-impurity Anderson model. It is found that it cannot reproduce the small energy scale in the strong correlation limit. A modified scheme to overcome this difficulty is proposed by introducing an appropriate vertex correction explicitly. Using the same vertex correction, the self-energy is investigated, and it is found that under certain assumptions it reproduces the result of the modified perturbation theory which interpolates the weak and the strong correlation limits.Comment: 5 pages, 7 figures, submitted to J. Phys. Soc. Jp

Strong-coupling scenario of a metamagnetic transition

We investigate the periodic Anderson model in the presence of an external magnetic field, using dynamical mean-field theory in combination with the modified perturbation theory. A metamagnetic transition is observed which exhibits a massive change in the electronic properties. These are discussed in terms of the quasiparticle weight and densities of states. The results are compared with the experimental results of the metamagnetic transition in CeRu_2Si_2.Comment: 5 pages, 3 figures, to appear in PR

Magnetic phase diagram of the Hubbard model

The competition between commensurate and incommensurate spin-density-wave phases in the infinite-dimensional single-band Hubbard model is examined with quantum Monte Carlo simulation and strong and weak coupling approximations. Quantum fluctuations modify the weak-coupling phase diagram by factors of order unity and produce remarkable agreement with the quantum Monte Carlo data, but strong-coupling theories (that map onto effective Falicov-Kimball models) display pathological behavior. The single-band model can be used to describe much of the experimental data in Cr and its dilute alloys with V and Mn.Comment: 12 pages plus 3 uuencoded postscript figures, ReVTe