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Novel Phases of Planar Fermionic Systems

We discuss a {\em family} of planar (two-dimensional) systems with the following phase strucure: a Fermi liquid, which goes by a second order transition (with non classical exponent even in mean-field) to an intermediate, inhomogeneous state (with nonstandard ordering momentum) , which in turn goes by a first order transition to a state with canonical order parameter. We analyze two examples: (i) a superconductor in a parallel magnetic field (which was discussed independently by Bulaevskii)for which the inhomogeneous state is obtained for $1.86 T_c \stackrel{\sim}{<} B \stackrel{\sim}{<} 1.86 \sqrt{2} T_c$ where $T_c$ is the critical temperature (in Kelvin) of the superconductor without a field and $B$ is measured in Tesla, and (ii) spinless (or, as is explained, spin polarized) fermions near half-filling where a similar, sizeable window (which grows in size with anisotropy) exists for the intermediate CDW phase at an ordering momentum different from $(π, π)$. We discuss the experimental conditions for realizing and observing these phases and the Renormalization Group approach to the transitions.

cond-mat↗

On the Decoupling of Layered Superconducting Films in Parallel Magnetic Field

The issue of the decoupling of extreme type-II superconducting thin films ($λ_L\rightarrow\infty$) with weakly Josephson-coupled layers in magnetic field parallel to the layers is considered via the corresponding frustrated $XY$ model used to describe the mixed phase in the critical regime. For the general case of arbitrary field orientations such that the perpendicular magnetic field component is larger than the decoupling cross-over scale characteristic of layered superconductors, we obtain independent parallel and perpendicular vortex lattices. Specializing to the double-layer case, we compute the parallel lower-critical field with entropic effects included, and find that it vanishes exponentially as temperature approaches the layer decoupling transition in zero-field. The parallel reversible magnetization is also calculated in this case, where we find that it shows a cross-over phenomenon as a function of parallel field in the intermediate regime of the mixed phase in lieu of a true layer-decoupling transition. It is argued that such is the case for any finite number of layers, since the isolated double layer represents the weakest link.

cond-mat↗

Strong coupling theory of the interlayer tunneling model for high temperature superconductors

The interlayer pair tunneling model of Anderson et al. is generalized to include the strong coupling effects associated with in-plane interactions. The equations for the superconducting transition temperature T_{c} are solved numerically for several models of electron-optical phonon coupling. The nonmagnetic in-plane impurity scattering suppresses T_{c} in all cases considered, and it is possible to obtain a fair agreement with experiments for a reasonable choice of parameters. For the anisotropic electron-phonon coupling proposed by Song and Annett we find that the interlayer pair tunneling can stabilize the d_{x^2-y^2}-wave superconducting state with a high T_{c}. Moreover, in this case there is a possibility of an impurity induced crossover from the d$_{x^2-y^2}$-wave state stabilized by the interlayer tunneling to the s-wave state at a low impurity concentration. We also calculate the isotope effect associated with the in-plane oxygen optic mode and its dependence on the strength of the interlayer pair tunneling. Small positive values of the isotope exponent are obtained for strengths of pair tunneling that give high transition temperatures.

supr-con↗

Superconductivity in an exactly solvable Hubbard model with bond-charge interaction

The Hubbard model with an additional bond-charge interaction $X$ is solved exactly in one dimension for the case $t=X$ where $t$ is the hopping amplitude. In this case the number of doubly occupied sites is conserved. In the sector with no double occupations the model reduces to the $U=\infty$ Hubbard model. In arbitrary dimensions the qualitative form of the phase diagram is obtained. It is shown that for moderate Hubbard interactions $U$ the model has superconducting ground states.

cond-mat↗

Density of states of a layered S/N d-wave superconductor

We calculate the density of states of a layered superconductor in which there are two layers per unit cell. One of the layers contains a d-wave pairing interaction while the other is a normal metal. The goal of this article is to understand how the d-wave behaviour of the system is modified by the coupling between the layer-types. This coupling takes the form of coherent, single particle tunneling along the c-axis. We find that there are two physically different limits of behaviour, which depend on the relative locations of the Fermi surfaces of the two layer-types. We also discuss the interference between the interlayer coupling and pairing interaction and we find that this interference leads to features in the density of states.

supr-con↗

INTERLAYER COUPLING AND THE METAL-INSULATOR TRANSITION IN Pr-SUBSTITUTED Bi(2)Sr(2)CaCu(2)O(8+y)

Substitution of rare-earth ions for Ca in Bi2Sr2CaCu2O8+y is known to cause a metal-insulator transition. Using resonant photoemission we study how this chemical substitution affects the electronic structure of the material. For the partial Cu-density of states at E_F and in the region of the valence band we observe no significant difference between a pure superconducting sample and an insulating sample with 60% Pr for Ca. This suggests that the states responsible for superconductivity are predomi- nately O-states. The partial Pr-4f density of states was extracted utilizing the Super- Koster-Kronig Pr 4d-4f resonance. It consists of a single peak at 1.36eV binding energy. The peak shows a strongly assymetric Doniach-Sunjic line- shape indicating the presence of a continuum of electronic states with sharp cut off at E_F even in this insulating sample. This finding excludes a bandgap in the insulating sample and supports the existance of a mobility gap caused by spatial localization of the carriers. The presence of such carriers at the Pr-site, between the CuO_2 planes shows that the electronic structure is not purely 2-dimensional but that there is a finite interlayer coupling. The resonance enhancement of the photoemission cross section, at the Pr-4d threshold, was studied for the Pr-4f and for Cu-states. Both the Pr-4f and the Cu-states show a Fano-like resonance. This resonance of Cu-states with Pr-states is another indication of coupling between the the Pr-states and those in the CuO_2 plane. Because of the statistical distribution of the Pr-ions this coupling leads to a non-periodic potential for the states in the CuO_2 plane which can lead to localization and thus to the observed metal-insulator transition.

cond-mat↗

Linear Response of Thin Superconductors in Perpendicular Magnetic Fields: An Asymptotic Analysis

The linear response of a thin superconducting strip subjected to an applied perpendicular time-dependent magnetic field is treated analytically using the method of matched asymptotic expansions. The calculation of the induced current density is divided into two parts: an ``outer'' problem, in the middle of the strip, which can be solved using conformal mapping; and an ``inner'' problem near each of the two edges, which can be solved using the Wiener-Hopf method. The inner and outer solutions are matched together to produce a solution which is uniformly valid across the entire strip, in the limit that the effective screening length $λ_{\rm eff}$ is small compared to the strip width $2a$. From the current density it is shown that the perpendicular component of the magnetic field inside the strip has a weak logarithmic singularity at the edges of the strip. The linear Ohmic response, which would be realized in a type-II superconductor in the flux-flow regime, is calculated for both a sudden jump in the magnetic field and for an ac magnetic field. After a jump in the field the current propagates in from the edges at a constant velocity $v=0.772 D/d$ (with $D$ the diffusion constant and $d$ the film thickness), rather than diffusively, as it would for a thick sample. The ac current density and the high frequency ac magnetization are also calculated. The long time relaxation of the current density after a jump in the field is found to decay exponentially with a time constant $τ_{0} = 0.255 ad/D$. The method is extended to treat the response of thin superconducting disks, and thin strips with an applied current. There is generally excellent agreement between the results of the asymptotic analysis and the recent numerical calculations by E. H. Brandt [Phys. Rev. B {\bf 49}, 9024; {\bf 50}, 4034 (1994)].

cond-mat↗

Spin pseudo-gap and interplane coupling in Y_2Ba_4Cu_7O_{15}: a ^{63}Cu nuclear spin-spin relaxation study

We report measurements of the Gaussian contribution, T_{2G}, to the plane ^{63}Cu nuclear spin--spin relaxation time in the YBa_2Cu_3O_7 and YBa_2Cu_4O_8 blocks of normal and superconducting Y_2Ba_4Cu_7O_{15}. The data confirm our previous results that adjacent CuO_2 planes have different doping levels and that these planes are strongly coupled. -- The static spin susceptibility at the anti-ferromagnetic wave vector exhibits a Curie--Weiss like temperature dependence in the normal state. -- The Y_2Ba_4Cu_7O_{15} data are incompatible with a phase diagram based on a single CuO_2 plane theory and suggest that the appearance of a spin gap implies interplane coupling. Additional data for YBa_2Cu_4O_8 and YBa_2Cu_3O_{6.982} are in accord with the single plane theory. -- The temperature dependence of T_{2G,ind} below T_c excludes isotropic s-wave superconductivity in all three compounds.

supr-con↗

The Nonlinear Meissner Effect in Unconventional Superconductors

We examine the long-wavelength current response in anisotropic superconductors and show how the field-dependence of the Meissner penetration length can be used to detect the structure of the order parameter. Nodes in the excitation gap lead to a nonlinear current-velocity constitutive equation at low temperatures which is distinct for each symmetry class of the order parameter. The effective Meissner penetration length is linear in $H$ and exhibits a characteristic anisotropy for fields in the $ab$-plane that is determined by the positions of the nodes in momentum space. The nonlinear current-velocity relation also leads to an intrinsic magnetic torque for in-plane fields that are not parallel to a nodal or antinodal direction. The torque scales as $H^3$ for $T\rightarrow 0$ and has a characteristic angular dependence. We analyze the effects of thermal excitations, impurity scattering and geometry on the current response of a $d_{x^2-y^2}$ superconductor, and discuss our results in light of recent measurements of the low-temperature penetration length and in-plane magnetization of single-crystals of $YBa_2Cu_3O_{7-δ}$ and $LuBa_2Cu_3O_{7-δ}$.

cond-mat↗

Onset of Vortices in Thin Superconducting Strips and Wires

Spontaneous nucleation and the consequent penetration of vortices into thin superconducting films and wires, subjected to a magnetic field, can be considered as a nonlinear stage of primary instability of the current-carrying superconducting state. The development of the instability leads to the formation of a chain of vortices in strips and helicoidal vortex lines in wires. The boundary of instability was obtained analytically. The nonlinear stage was investigated by simulations of the time-dependent generalized Ginzburg-Landau equation.

supr-con↗

Universality Classes, Statistical Exclusion Principle and Properties of Interacting Fermions

We point to the possibility of existence of the statistical-spin-liquid state as the state which differs from either Fermi or Luttinger liquid states. In the statistical spin liquid the double occupancies are excluded from the physical space. Each of the above three cases (Fermi, Luttinger and spin liquids) represents an universality class for the interacting many-particle fermion systems. The properties of the spin liquid such as the chemical potential, the entropy, and the magnetization curve, as well as the quasiparticle structure are briefly discussed.

cond-mat↗

Spin Dynamics of La_2CuO_4 and the Two-Dimensional Heisenberg Model

The spin-lattice relaxation rate $1/T_1$ and the spin echo decay rate $1/T_{2G}$ for the 2D Heisenberg model are calculated using quantum Monte Carlo and maximum entropy analytic continuation. The results are compared to recent experiments on La$_2$CuO$_4$, as well as predictions based on the non-linear $σ$-model.

supr-con↗

Superconducting, magnetic, and charge correlations in the doped two-chain Hubbard model

Superconducting, magnetic, and charge correlation functions and dynamic spin correlation functions of the doped two-chain Hubbard model is studied with the projector Quantum Monte carlo method and Lanczos recursion method. Of the three correlation functions, the interchain singlet superconducting correlation function is the most long range. Our data is not consistent with the Luther-Emery picture.

supr-con↗

Microscopic Derivation of Magnetic Flux Density Profiles, Magnetization Hysteresis Loops, and Critical Currents in Strongly Pinned Superconductors

We present a microscopic derivation, without electrodynamical assumptions, of $B(x,y,H(t))$, $M(H(t))$, and $J_c(H(t))$, in agreement with experiments on strongly pinned superconductors, for a range of values of the density and strength of the pinning sites. We numerically solve the overdamped equations of motion % dynamics of these flux-gradient-driven vortices which can be temporarily trapped at pinning centers. The field is increased (decreased) by the addition (removal) of flux lines at the sample boundary, and complete hysteresis loops can be achieved by using flux lines with opposite orientation. The pinning force per unit volume we obtain for strongly-pinned vortices, $J_c B \sim n_p f_p^{1.6}$, interpolates between the following two extreme situations: very strongly-pinned independent vortices, where $J_c B \sim n_p f_p$, and the 2D Larkin-Ovchinikov collective-pinning theory for weakly-pinned straight vortices, where $J_c B \sim n_p f_p^{2}$. Here, $n_p$ and $f_p$ are the density and maximum force of the pinning sites.

cond-mat.mtrl-sci↗

Two-hole bound states in modified t-J model

We consider modified $t-J$ model with minimum of single-hole dispersion at the points $(0,\pm π)$, $(\pm π,0)$. It is shown that two holes on antiferromagnetic background produce a bound state which properties strongly differs from the states known in the unmodified $t-J$ model. The bound state is d-wave, it has four nodes on the face of the magnetic Brillouin zone. However, in the coordinate representation it looks like as usual s-wave.

supr-con↗

Superconductivity in the two dimensional Hubbard Model.

Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (pi,0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. Singlet d_{x^2-y^2}-wave pairing is strongly favoured and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest neighbour antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favouring superconductivity. However the mechanism for superconductivity is a local one, in contrast to spin fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature T_c is in the range 10-100K. The optimum doping delta_c lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and (2*Delta_{max})/(kT_c) ~ 4.

cond-mat↗

Odd Parity and Line Nodes in Heavy Fermion Superconductors

Group theory arguments have demonstrated that a general odd parity order parameter cannot have line nodes in the presence of spin-orbit coupling. In this paper, it is shown that these arguments do not hold on the $k_z = π/c$ zone face of a hexagonal close packed lattice. In particular, three of the six odd parity representations vanish identically on this face. This has potential relevance to the heavy fermion superconductor $UPt_3$.

cond-mat↗

Polarization Selection Rules and Superconducting Gap Anisotropy in $Bi_2Sr_2CaCu_2O_8$

We discuss polarization selection rules for angle-resolved photoemission spectroscopy in Bi2212. Using these we show that the ``hump'' in the superconducting gap observed in the $X$ quadrant in our earlier work is not on the main $CuO_2$ band, but rather on an umklapp band arising from the structural superlattice. The intrinsic gap is most likely quite small over a range of $\pm 10^\circ$ about the diagonal directions.

cond-mat↗