Spin-charge gauge approach to metal-insulator crossover and transport properties in High-Tc_c cuprates

The spin-charge gauge approach to consider the metal-insulator crossover (MIC) and other anomalous transport properties in High-T$_c$ cuprates is briefly reviewed. A U(1) field gauging the global charge symmetry and an SU(2) field gauging the global spin-rotational symmetry are introduced to study the two-dimensional $t-J$ model in the limit $t\gg J$. The MIC as a clue to the understanding of the ``pseudogap'' (PG) phase, is attributed to the competition between the short-range antiferromagnetic order and dissipative motion of charge carriers coupled to the slave-particle gauge field. The composite particle formed by binding the charge carrier (holon) and spin excitation (spinon) via the slave particle gauge field exhibits a number of peculiar properties, and the calculated results are in good agreement with experimental data for both PG and ``strange metal'' phases. Connections to other gauge field approaches in studying the strong correlation problem are also briefly outlined.Comment: 32 pages, to appear in the special issue on "Correlated Electrons" of J. Phys.: Condens. Mat

Plastic energies in layered superconductors

We estimate the energy cost associated with two pancake vortices colliding in a layered superconductor. It is argued that this energy sets the plastics energy scale and is the analogue of the crossing energy for vortices in the continuum case. The starting point of the calculation is the Lawrence-Doniach version of the Ginzburg-Landau free energy for type-II superconductors. The magnetic fields considered are along the c-direction and assumed to be sufficiently high that the lowest Landau level approximation is valid. For Bi-2212, where it is know that layering is very important, the results are radically different from what would have been obtained using a three-dimensional anisotropic continuum model. We then use the plastic energy for Bi-2212 to successfully explain recent results from Hellerqvist {\em et al.}\ on its longitudinal resistance.Comment: 5 Pages Revtex, 4 uuencoded postscript figure

Weak point disorder in strongly fluctuating flux-line liquids

We consider the effect of weak uncorrelated quenched disorder (point defects) on a strongly fluctuating flux-line liquid. We use a hydrodynamic model which is based on mapping the flux-line system onto a quantum liquid of relativistic charged bosons in 2+1 dimensions [P. Benetatos and M. C. Marchetti, Phys. Rev. B 64, 054518, (2001)]. In this model, flux lines are allowed to be arbitrarily curved and can even form closed loops. Point defects can be scalar or polar. In the latter case, the direction of their dipole moments can be random or correlated. Within the Gaussian approximation of our hydrodynamic model, we calculate disorder-induced corrections to the correlation functions of the flux-line fields and the elastic moduli of the flux-line liquid. We find that scalar disorder enhances loop nucleation, and polar (magnetic) defects decrease the tilt modulus.Comment: 15 pages, submitted to Pramana-Journal of Physics for the special volume on Vortex State Studie

Phase Transitions in a Model Anisotropic High Tc Superconductor

We carry out simulations of the anisotropic uniformly frustrated 3D XY model, as a model for vortex line fluctuations in high Tc superconductors. We compute the phase diagram as a function of temperature and anisotropy, for a fixed applied magnetic field. We find that superconducting coherence parallel to the field persists into the vortex line liquid state, and that this transition lies well below the "mean-field" cross-over from the vortex line liquid to the normal state.Comment: 23 pages + 19 ps figure

Helicity Modulus and Fluctuating Type II Superconductors: Elastic Approximation and Numerical Simulations

We develop the helicity modulus as a criterion for superconducting order in the mixed phase of a fluctuating type II superconductor. We show that there is a duality relation between this helicity modulus and the superfluid density of a system of analog 2D bosons. We show that the vortex line lattice exhibits a perfect Meissner effect with respect to a shearing perturbation of the applied magnetic field, and this becomes our creterion for "longitudinal superconductivity" parallel to the applied field. We present arguments based on the 2D boson analogy, as well as the results of numerical simulations, that suggest that longitudinal superconductivity can persist into the vortex line liquid state for systems of finite thickness, comparable to those commonly found in experiments.Comment: 63 pages, 22 postscript figure

Field-driven topological glass transition in a model flux line lattice

We show that the flux line lattice in a model layered HTSC becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We confirm through a computer simulation that this indeed may lead to a phase transition from crystalline order at low fields to a topologically disordered phase at higher fields. We propose that this mechanism provides a model of the low temperature field--driven disordering transition observed in neutron diffraction experiments on ${\rm Bi_2Sr_2CaCu_2O_8\, }$ single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from [email protected]

Energy cost associated with vortex crossing in superconductors

Starting from the Ginzburg-Landau free energy of a type II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest Landau level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasi-periodic boundary conditions. We find that the answers are very similar suggesting that the energy is localised to the crossing point. The crossing energy is found to be field and temperature dependent -- with a value at the experimentally measured melting line of $U_\times \simeq 7.5 k T_m \simeq 1.16/c_L^2$, where $c_L$ is the Lindemann melting criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar {{\em et al.}\ }.Comment: 15 pages, RevTex v3.0, followed by 5 postscript figure

U(1)xSU(2) Chern--Simons gauge theory of underdoped cuprate superconductors

The Chern-Simons bosonization with U(1)xSU(2) gauge field is applied to 2-D t-J model in the limit t >> J, to study the normal state properties of underdoped cuprate superconductors. We prove the existence of an upper bound on the partition function for holons in a spinon background, and we find the optimal spinon configuration saturating the upper bound on average--a coexisting flux phase and s+id-like RVB state. After neglecting the feedback of holon fluctuations on the U(1) field B and spinon fluctuations on the SU(2) field V, the holon field is a fermion and the spinon field is a hard--core boson. We show that the B field produces a \pi flux phase for holons, converting them into Dirac--like fermions, while the V field, taking into account the feedback of holons produces a gap for spinons vanishing in zero doping limit. The nonlinear sigma-model with a mass term describes the crossover from short-ranged antiferromagnetic (AF) state in doped samples to long range AF order in reference compounds. Moreover, we derive a low--energy effective action in terms of spinons, holons and a self-generated U(1) gauge field. The gauge fluctuations are not confining due to coupling to holons, but yield an attractive interaction between spinons and holons leading to a bound state with electron quantum numbers. The renormalisation effects due to gauge fluctuations give rise to non--Fermi liquid behaviour for the composite electron.This formalism provides a new interpretation of the spin gap in underdoped superconductors (due to short-ranged AF order) and predicts the minimal gap for the physical electron is proportional to the square root of the doping concentration.Comment: 31 pages, REVTEX, to be published in Phys. Rev.

Muon-Spin Rotation Spectra in the Mixed Phase of High-T_c Superconductors : Thermal Fluctuations and Disorder Effects

We study muon-spin rotation (muSR) spectra in the mixed phase of highly anisotropic layered superconductors, specifically Bi_2+xSr_2-xCaCu_2O_8+delta (BSCCO), by modeling the fluid and solid phases of pancake vortices using liquid-state and density functional methods. The role of thermal fluctuations in causing motional narrowing of muSR lineshapes is quantified in terms of a first-principles theory of the flux-lattice melting transition. The effects of random point pinning are investigated using a replica treatment of liquid state correlations and a replicated density functional theory. Our results indicate that motional narrowing in the pure system, although substantial, cannot account for the remarkably small linewidths obtained experimentally at relatively high fields and low temperatures. We find that satisfactory agreement with the muSR data for BSCCO in this regime can be obtained through the ansatz that this ``phase'' is characterized by frozen short-range positional correlations reflecting the structure of the liquid just above the melting transition. This proposal is consistent with recent suggestions of a ``pinned liquid'' or ``glassy'' state of pancake vortices in the presence of pinning disorder. Our results for the high-temperature liquid phase indicate that measurable linewidths may be obtained in this phase as a consequence of density inhomogeneities induced by the pinning disorder. The results presented here comprise a unified, first-principles theoretical treatment of muSR spectra in highly anisotropic layered superconductors in terms of a controlled set of approximations.Comment: 50 pages Latex file, including 10 postscript figure