Session K39: Focus Session: Superconductivity: Theory and Computation II

Kondo Physics and Strongly Correlated Superconductivity in Model Fullerene Conductors

The effects of electronic correlations on superconductivity are investigated by means of Dynamical Mean Field Theory (DMFT) in a model for alkali doped fullerenes. It is shown that the proximity to a Mott transition actually amplifies the $s$-wave phonon-mediated pairing mechanism built into the model. It leads to a superconduting pocket adjacent the Mott insulator with a superconducting gap which is huge in comparison with the corresponding BCS value.The physical properties of this strongly correlated superconductor are compatible with the experimental data available on fullerenes. Yet, contradicting the common belief for fullerenes, superconductivity in this model is not of the BCS-type nor is the normal state a conventional Fermi-liquid. We find on the contrary several aspects which rather resemble those of cuprate superconductors, such as an increase of Drude weight accompaning the onset of superconductivity. We identify the origin of these anomalies to the unconventional properties displayed by the Anderson impurity model for a C$_{60}^{n-}$ molecule onto which the lattice model maps within DMFT. We also argue that this behavior should be common to other models that contain pairing mechanisms able to survive inside the Mott insulator, which translate within DMFT into impurity models where Kondo screening competes against an internal mechanism that tends to freeze the impurity in a low-spin state.   

Renormalization Group approach to anisotropic-pairing superconductivity

The Renormalization Group (RG) approach to interacting fermions [R. Shankar, \emph{Rev. Mod. Phys.} \textbf{66} 129 (1994)] has been extended to the case where both electron-electron and electron-phonon interactions are present [S.-W. Tsai \emph{et al}, \emph{Phys. Rev. B} \textbf{72} 054531 (2005)]; [S.-W. Tsai \emph{et al}, cond- mat/0505426] . There Eliashberg's equations are derived for the case of a two dimensional Hubbard model with a circular Fermi surface (FS) in the presence of isotropic Einstein phonons. However, there are materials where the isotropic electron-phonon coupling is not a good approximation. In this work we study the problem of superconductivity mediated by anisotropic electron-phonon couplings, and derive a generalization of the Eliashberg's equations for this case. We solve, for the case of a circular FS, the flow equations for the interaction vertices in the particle-particle channel up to one loop, taking into account the retardation effects due to the presence of phonons. Retardation effects lead to important corrections to the imaginary part of the self-energy. For a generic anisotropic electron- phonon coupling these corrections are momentum dependent and the RG flow equations for superconducting couplings with different symmetries become coupled. We find an instability of the Fermi liquid state towards superconductivity for various momentum-dependent el-ph couplings, with competition between superconducting channels with different symmetries of the order parameter.   

Correlations in Dynamic Hubbard Model: A DMRG Study

The Dynamic Hubbard model has been introduced to study how holes behave in the Hubbard Model with dynamic degrees of freedom modelled by pseudo-spins. It has previously been analyzed using exact diagonalization on small clusters. However the lattice sizes used are not sufficiently large to understand the behaviour of the system in the thermodynamic limit. We present our analysis using the density-matrix-renormalization- group (DMRG) to understand the behaviour of two holes for different system sizes. We observed a decrease in kinetic energy, and an increase in the effective nearest neighbor attraction, even for moderate on-site repulsion, which indicates pairing of the holes through effective nearest neighbor attraction.   

Dynamical Mean-Field calculation of kinetic energy for the one-band doped Hubbard Model

We present a Dynamical Mean-Field calculation of the interaction, doping and temperature dependence of the kinetic energy for the one-band doped Hubbard model. We combine Quantum Monte-Carlo and an improved finite temperature Exact Diagonalization method to obtain results over a wide range of temperatures. The overlapping temperature region for the two methods enables an improved error estimation. The results are compared to recent experimental data.   

Fermi surface splittings in multilayered high-$T_{\rm c}$ cuprates with charge imbalance

Cuprate superconductors have layered structure of CuO$_2$ planes, which makes conducting blocks separated by an charge- reservoir block. Multilayered high-$T_{\rm c}$ cuprates, e.g., Ba$_2$Ca$_3$Cu$_4$O$_8$(O$_{1-y}$F$_y$)$_2$ and HgBa$_2$Ca$_4 $Cu$_5$O$_y$, have two kinds of CuO$_2$ planes in a unit cell; the outer-pyramidal-coordinated-planes (OP's) and the inner- square-coordinated-planes (IP's). The carrier density in the OP is generally different from that in the IP. We call such an inhomogeneous charge-distribution $\lq$charge imbalance'. We study doping dependence of interlayer hoppings, $t_{\perp}$, in such a charge-imbalance system in the Gutzwiller approximation. When the double occupancy is forbidden in the CuO$_2$ plane, an effective amplitude of $t_{\perp}$ is shown to be proportional to the square root of the product of doping rates in adjacent two planes. Therefore, the charge imbalance in more than three-layered cuprates results in two different values of $t^{\rm eff}_{\perp} $, i.e., $t^{\rm eff}_{\perp1}\propto t_{\perp}\sqrt{\delta_{\rm IP} \delta_{\rm IP}}$ between IP's, and $t^{\rm eff}_{\perp2}\propto t_{\perp}\sqrt{\delta_{\rm IP} \delta_{\rm OP}}$ between IP and OP, where $\delta_{\rm IP}$ ($\delta_{\rm OP}$) is the doping rates in IP (OP). Fermi surfaces are calculated in the four-layered $t$-$t'$- $t''$-$J$ model by the mean-field theory. The order parameters, the renormalization factor of $t_{\perp}$, and the site- potential making the charge imbalance between IP and OP are self-consistently determined for several doping rates. We show the interlayer splitting of the Fermi surfaces, which may be observed in the angle resolved photoemission spectroscopy measurement. *cond-mat/0511249.   

Effective theory of underdoped cuprates and the puzzle of superfluid density

I will discuss the recently proposed low-energy description of fluctuating d-wave superconductors (I. F. Herbut, PRL 94, 237001 (2005)), and its implications for the evolution of the superfluid density with doping and temperature. Recent experiments find that while the T=0 superfluid density becomes reduced by more than two orders of magnitude by going from optimal to extremely underdoped regime in single crystals of YBCO, the slope of the temperature dependence stays roughly the same. This apparent violation of the Ioffe-Larkin rule, argued otherwise rather generally to hold in the underdoped regime, is explained as being due to the particular form of the bosonic (fluctuation) term, which resembles the condensate of the weakly interacting layered Bose gas. This suggests that, its linear appearance notwithstanding, the reduction of the superfluid density with temperature in extremely underdoped cuprates may be due to phase fluctuations over most of the temperature range. Further experimental tests of this idea will be proposed.   

Magnetic Origin of the Tetragonal-Orthorhombic Phase Transition in the Cuprates

It is shown that a quasi two dimensional (layered) Heisenberg antiferromagnet with fully frustrated interplane couplings generically exhibits two thermal phase transitions with lowering temperature -- an upper transition (``order from disorder without order'') in which the lattice point-group symmetry is spontaneously broken, and a lower Ne{e}l transition at which spin-rotational symmetry is broken. We therefore suggest that it may primarily be the magnetic interactions between planes, rather than strains associated with a mismatch of ionic radii, that are responsible for the tetragonal to orthorhombic (T-O) structural phase transition seen in many of the cuprates.   

A 4D-XY model of the superfluid density of strongly underdoped cuprate superconductors

A new phenomenology is proposed for the superfluid density of strongly underdoped cuprate superconductors based on data for ultra-clean single crystals of YBCO. The data feature a puzzling departure from Uemura scaling and a decline of the slope as the $T_c = 0$ quantum critical point is approached. We argue that the proximity of a Mott insulator drives quantum fluctuations of the superconducting phase which are described by a (3+1)-dimensional XY model. The subsequent renormalization of the superfluid density is computed using variational methods and then studied systematically as a function of c-axis anisotropy, interaction strength, and doping. We find that non-critical phase fluctuations explain key features of the new cuprate phenomenology, which is expected to fail in the true critical regime.   

Microscopic Spectral Model of High Temperature Superconductors

The self-organized dopant percolative filamentary model [1], entirely orbital in character (no spins), explains the evolution with doping of Fermi arcs observed by ARPES, including the abrupt transitions in quasiparticle strength observed near optimal doping in cuprate high temperature superconductors [2]. Similarly abrupt transitions are also observed [3] in time-resolved picosecond relaxation spectroscopy at 1.5 eV, and these are explained as well, using no new assumptions and no adjustable parameters. The anomalous ``precursive'' temperature-dependent strains observed by EXAFS [4] are associated with relaxation of filamentary ends. \newline \newline [1] J. C. Phillips, Phys. Rev. Lett. 88, 216401 (2002). \newline [2] T. Yoshida, X. J. Zhou, T. Sasagawa et al., Phys. Rev. Lett. 91, 027001 (2003). \newline [3] N. Gedik, M. Langer, J. Orenstein et al., Phys. Rev. Lett. 95, 117005 (2005). \newline [4] N. L. Saini and H. Oyanagi, Phys. C 412, 152 (2004).   

Pairing in Marignal Fremi Liquid and Luttinger Liquid in Terms of the Bethe-Salpeter Equation

The pairing between two fermions in the fermionic systems with the smeared Fermi distribution is considered in terms of the Bethe-Slapeter equation. The examples of the systems with the smeared Fermi distribution are the marginal Fermi liquid and the Luttinger liquid where the quasiparticle pole is absent in the Green's function. Although the pairing between two fermions in the systems with the smeared Fermi distribution is, in general, absent, the pairing similar to the Cooper's pairing can occur and the conditions for such pairing to exist are discussed.   

High-T$_c$ superconductivity does not originate in cuprate-planes.

CuO$_2$ planes are not needed for high-T$_c$ superconductivity, as demonstrated by Sr$_2$YRuO$_6$ and Ba$_2$YRuO$_6$, weakly doped on Ru sites with Cu, with onset T$_c$'s of 49K and 93K, but no cuprate-planes. Gd$_{2-z}$Ce$_z$Sr$_2$Cu$_2$RuO$_{10}$ and GdSr$_2$Cu$_2$RuO$_8$ do not superconduct in their cuprate- planes, which are magnetic, but in their SrO layers (with onset T$_c\approx$45K). High-temperature superconductivity resides in SrO, BaO, or interstitial oxygen regions, not in cuprate-planes. In YBa$_2$Cu$_3$O$_7$, Harshman {\it et al.} [1], using muon spectroscopy, found $s$-wave character, not $d$-wave character (to better than one percent) which measures the {\it superconducting} layers. This contradicts scanning tunneling microscopy and photoemission, which claim $d$-wave behavior after measuring {\it near-surface} layers (which often do not superconduct). High-temperature superconductivity originates in the BaO, SrO, or interstitial oxygen regions, not in the cuprate planes. [1] D. R. Harshman, {\it et al.}, Phys. Rev. {\bf B 69,} 174505 (2004).   

Feasibility of Superconductivity in Semiconductor Superlattices

The possibility of designing a semiconducting superlattice of alternating electron and hole layers that exhibits high temperature superconductivity is studied by numerical simulation of modulation-doped GaAs/Al$_{x}$Ga$_{1-x}$As superlattices. The feasibility of superconductivity is based on observations of high-temperature superconductors by Harshman and Mills$^{1}$, who concluded that the mechanism for Cooper pairing is a Coulomb interaction that is optimum when the mean distance between charge carriers within the layers equals the distance between the layers. Superlattice design considers optimum layer spacings, doping concentrations, and alloy concentration, x. The program employed in the superlattice simulations is a one-dimensional Schr\"{o}dinger-Poisson solver developed by Snider$^{2}$. \newline \newline 1. D. R. Harshman and A. P. Mills, \textit{Concerning the nature of high-Tc superconductivity}, Phys. Rev. B 45, 707 (1992). \newline 2. G. Snider, \textit{1D Poisson/Schr\"{o}dinger User's Manual: A Band Diagram Calculator}, (http://www.nd.edu/$\sim $gsnider, Univ. Notre Dame, Notre Dame, Indiana).   

Unconventional Pairing in 2D lattice with an ``Inherent Gap''

We investigate superconducting pairing in 2D lattice with an ``inherent gap''. In this calculation, we take this gap to be a constant, and thus similar to that in semiconductors. We consider different pairing symmetries, namely, s-wave, extended-s-wave, p-wave and d-wave. We calculate superconducting gap parameters, critical temperatures, chemical potential, etc in terms of interaction strength and filling factor. There is a sharp transition fom the ``inherent gapped state'' to a superconducting state for half filling f=1/2, corresponding to the undoped case. For finite doping, the transition becomes a smooth crossover. We also explore other features, such as the effect of phase fluctuations and the resulting Kosterlitz-Thouless transition; tunneling density of states, etc.