Gap States in Dilute Magnetic Alloy Superconductors

We study states in the superconducting gap induced by magnetic impurities using self-consistent quantum Monte Carlo with maximum entropy and formally exact analytic continuation methods. The magnetic impurity susceptibility has different characteristics for T_{0} \alt T_{c0} and T_{0} \agt T_{c0} ($T_{0}$: Kondo temperature, $T_{c0}$: superconducting transition temperature) due to the crossover between a doublet and a singlet ground state. We systematically study the location and the weight of the gap states and the gap parameter as a function of $T_{0}/T_{c0}$ and the concentration of the impurities.Comment: 4 pages in ReVTeX including 4 encapsulated Postscript figure

Competition between electron-phonon attraction and weak Coulomb repulsion

The Holstein-Hubbard model is examined in the limit of infinite dimensions. Conventional folklore states that charge-density-wave (CDW) order is more strongly affected by Coulomb repulsion than superconducting order because of the pseudopotential effect. We find that both incommensurate CDW and superconducting phases are stabilized by the Coulomb repulsion, but, surprisingly, the commensurate CDW transition temperature is more robust than the superconducting transition temperature. This puzzling feature is resolved by a detailed analysis of perturbation theory.Comment: 13 pages in ReVTex including 3 encapsulated postscript files (embedded in the text). The encapsulated postscript files are compressed and uuencoded after the TeX file

The anharmonic electron-phonon problem

The anharmonic electron-phonon problem is solved in the infinite-dimensional limit using quantum Monte Carlo simulation. Charge-density-wave order is seen to remain at half filling even though the anharmonicity removes the particle-hole symmetry (and hence the nesting instability) of the model. Superconductivity is strongly favored away from half filling (relative to the charge-density-wave order) but the anharmonicity does not enhance transition temperatures over the maximal values found in the harmonic limit.Comment: 5 pages typeset in ReVTeX. Four encapsulated postscript files include

Role of the van Hove Singularity in the Quantum Criticality of the Hubbard Model

A quantum critical point (QCP), separating the non-Fermi liquid region from the Fermi liquid, exists in the phase diagram of the 2D Hubbard model [Vidhyadhiraja et. al, Phys. Rev. Lett. 102, 206407 (2009)]. Due to the vanishing of the critical temperature associated with a phase separation transition, the QCP is characterized by a vanishing quasiparticle weight. Near the QCP, the pairing is enhanced since the real part of the bare d-wave p-p susceptibility exhibits algebraic divergence with decreasing temperature, replacing the logarithmic divergence found in a Fermi liquid [Yang et. al, Phys. Rev. Lett. 106, 047004 (2011)]. In this paper we explore the single-particle and transport properties near the QCP. We focus mainly on a van Hove singularity (vHS) coming from the relatively flat dispersion that crosses the Fermi level near the quantum critical filling. The flat part of the dispersion orthogonal to the antinodal direction remains pinned near the Fermi level for a range of doping that increases when we include a negative next-near-neighbor hopping t' in the model. For comparison, we calculate the bare d-wave pairing susceptibility for non-interacting models with the usual two-dimensional tight binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a vHS that completely describes the critical algebraic behavior of the bare d-wave pairing susceptibility. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz Law are examined in the Fermi liquid, marginal Fermi liquid, and pseudo-gap doping regions. A negative next-near-neighbor hopping t' increases the doping region with marginal Fermi liquid character. Both T and negative t' are relevant variables for the QCP, and both the transport and the motion of the vHS with filling suggest that they are qualitatively similar in their effect.Comment: 15 pages, 17 figure

Correlation and surface effects in Vanadium Oxides

Recent photoemission experiments have shown strong surface modifications in the spectra from vanadium oxides as (V,Cr)_2O_3 or (Sr,Ca)VO_3. The effective mass is enhanced at the surface and the coherent part of the surface spectrum is narrowed as compared to the bulk. The quasiparticle weight is more sensitive at the surface than in the bulk against bandwidth variations. We investigate these effects theoretically considering the single-band Hubbard model for a film geometry. A simplified dynamical mean-field scheme is used to calculate the main features of the interacting layer-dependent spectral function. It turns out that the experimentally confirmed effects are inherent properties of a system of strongly correlated electrons. The reduction of the weight and the variance of the coherent part of the surface spectrum can be traced back to the reduced surface coordination number. Surface correlation effects can be strongly amplified by changes of the hopping integrals at the surface.Comment: to appear in PRB; 8 pages, 6 figure

Weak-coupling expansions for the attractive Holstein and Hubbard models

Weak-coupling expansions (conserving approximations) are carried out for the attractive Holstein and Hubbard models (on an infinite-dimensional hypercubic lattice) that include all bandstructure and vertex correction effects. Quantum fluctuations are found to renormalize transition temperatures by factors of order unity, but may be incorporated into the superconducting channel of Migdal-Eliashberg theory by renormalizing the phonon frequency and the interaction strength.Comment: 10 pages, (five figures available from the author by request) typeset with ReVTeX, preprint NSF-ITP-93-10

Iterated perturbation theory for the attractive Holstein and Hubbard models

A strictly truncated (weak-coupling) perturbation theory is applied to the attractive Holstein and Hubbard models in infinite dimensions. These results are qualified by comparison with essentially exact Monte Carlo results. The second order iterated perturbation theory is shown to be quite accurate in calculating transition temperatures for retarded interactions, but is not as accurate for the self energy or the irreducible vertex functions themselves. Iterated perturbation theory is carried out thru fourth order for the Hubbard model. The self energy is quite accurately reproduced by the theory, but the vertex functions are not. Anomalous behavior occurs near half filling because the iterated perturbation theory is not a conserving approximation. (REPLACED WITH UUENCODED FIGURES AT THE END. THE TEXT IS UNCHANGED)Comment: 27 pages, RevTex (figures appended at end

Superconductivity in the Two-Band Hubbard Model in Infinite Dimensions

We study a two-band Hubbard model in the limit of infinite dimensions, using a combination of analytical methods and Monte-Carlo techniques. The normal state is found to display various metal to insulators transitions as a function of doping and interaction strength. We derive self-consistent equations for the local Green's functions in the presence of superconducting long-range order, and extend previous algorithms to this case. We present direct numerical evidence that in a specific range of parameter space, the normal state is unstable against a superconducting state characterized by a strongly frequency dependent order-parameter.Comment: 12 pages (14 figures not included, available upon request), Latex, LPTENS Preprint 93/1

Electronic Structure of Paramagnetic V_2O_3: Strongly Correlated Metallic and Mott Insulating Phase

LDA+DMFT, the computation scheme merging the local density approximation and the dynamical mean-field theory, is employed to calculate spectra both below and above the Fermi energy and spin and orbital occupations in the correlated paramagnetic metallic and Mott insulating phase of V_2O_3. The self-consistent DMFT equations are solved by quantum Monte Carlo simulations. Room temperature calculations provide direct comparison with experiment. They show a significant increase of the quasiparticle height in comparison with the results at 1160 K. We also obtain new insights into the nature of the Mott-Hubbard transition in V_2O_3. Namely, it is found to be strikingly different from that in the one-band Hubbard model due to the orbital degrees of freedom. Furthermore we resolve the puzzle of the unexpectedly small Mott gap in Cr-doped V_2O_3.Comment: 14 pages, 22 figure