Theory Of High-temperature Superconductors Research Articles

Cuprate High Temperature Superconductors and the Vision for Room Temperature Superconductivity

Superconducting transition temperatures of 164 K in cuprate high temperature superconductors (HTS) and recently 200 K in H3S under high pressure encourage us to believe that room temperature superconductivity (RTS) might be possible. In considering paths to RTS, we contrast conventional (BCS) SC, such as probably manifested by H3S, with the unconventional superconductivity (SC) in the cuprate HTS family. Turning to SC models, we show that in the presence of one or more van Hove singularities (vHs) near the Fermi level, SC mediated by classical phonons ([Formula: see text]phonon frequency) can occur. The phonon frequency in the standard [Formula: see text] formula is replaced by an electronic cutoff, enabling a much higher [Formula: see text] independent of phonon frequency. The resulting [Formula: see text] and isotope shift plot versus doping strongly resembles that seen experimentally in HTS. A more detailed theory of HTS, which involves mediation by classical phonons, satisfactorily reproduces the chief anomalous features characteristic of these materials. We propose that, while a path to RTS through an H3S-like scenario via strongly-coupled ultra-high frequency phonons is attractive, features perhaps unavailable at ordinary pressures, a route involving SC mediated by classical phonons which can be low frequency may be found.

A novel percolation theory for high temperature superconductors

We present a percolation theory for the high-Tc oxides pseudogap and Tc dependence on the hole level. The doping dependent inhomogeneous charge structure is modeled by a distribution which may represent the stripe morphology and yield a spatial distribution of local Tc(r). The temperature onset of spatial dependent superconducting gap is identified with the vanishing of the pseudogap temperature T*. The transition to a superconducting state corresponds to the percolation threshold among regions of different Tc. As a paradigm we use a Hubbard Hamiltonian with a mean field approximation to yield a doping and temperature dependent superconducting d-wave gap. We show here that this new approach reproduces the phase diagram, explains and gives new insights on several experimental features of high-Tc oxides.

A new approach to transport theory of high Tc bismuth-based ceramic superconductors

A new transport theory for high temperature superconductors is propos#ed and supported with extensive calculations. The Cooper-pairs while remaining on a pseudo Fermi surface behave like weak Fermions. When the Cooper-pairs become free they behave as spinless bosons. The polarons and bipolarons are highly localized quantum states with virtually no gap existing in between them and are considered as bosons with nondegenerate spining. The binding energies of Cooper-pairs both in a weak Fermion system and for a spinless boson are calculated. A kind of a semimetallic softening transition is responsible for high temperature superconductivity and is temperature independent. There is no electron–phonon coupling for high temperature superconductors. High temperature ceramic superconductors before the onset of superconductivity are found to be Mott–Hubbard dielectric insulating materials.

SUSCEPTIBILITY AND VERTEX CORRECTIONS FOR A SQUARE FERMI SURFACE

We investigate the response of an electron system which exhibits ideal nesting features. Using the standard Matsubara formalism we derive analytic expressions for the imaginary and real parts of the bare particle–hole susceptibility. The imaginary part has sharp peaks whose maxima at the nesting momenta approximately scale with (ω/T). The peak lineshapes resemble neutron scattering data on chromium and some copper oxide superconductors. The real part of the bare susceptibility at the nesting vectors diverges logarithmically at low temperatures. Analytic formulas for the first vertex correction to the susceptibility are derived for a Hubbard interaction and its momentum and temperature variations are calculated numerically. This term detracts substantially from the ordinary RPA terms for intermediate values of the Coulomb repulsion. Exact cancellation of a certain class of diagrams at half filling is shown to result from particle–hole symmetry. We discuss the consequences of these results for spin fluctuation theories of high temperature superconductors and spin density wave instabilities.

Intrinsic resistivity and the SO(5) theory of high-temperature superconductors

The topological structure of the order parameter in Zhang's SO(5) theory of superconductivity allows for an unusual type of dissipation mechanism via which current-carrying states can decay. The resistivity due to this mechanism, which involves orientation rather than amplitude order-parameter fluctuations, is calculated for the case of a thin superconducting wire. The approach is a suitably modified version of that pioneered by Langer and Ambegaokar for conventional superconductors.

The Neutron Peak in the Interlayer Tunneling Model of High Temperature Superconductors

Recent neutron scattering experiments in YBCO exhibit an unusual magnetic peak that appears only below the superconducting transition temperature. The experimental observations are explained within the context of the interlayer tunneling theory of high temperature superconductors.

Phenomenological models for the gap anisotropy of Bi2Sr2CaCu2O8 as measured by angle-resolved photoemission spectroscopy.

Recently, high resolution angle-resolved photoemission spectroscopy has been used to determine the detailed momentum dependence of the superconducting gap in the high temperature superconductor Bi-2212. In this paper, we first describe tight binding fits to the normal state dispersion and superlattice modulation effects. We then discuss various theoretical models in light of the gap measurements. We find that the simplest model which fits the data is the anisotropic s-wave gap $\cos(k_x)\cos(k_y)$, which within a one-band BCS frame- work suggests the importance of next near neighbor Cu-Cu interactions. Various alternative interpretations of the observed gap are also discussed, along with the implications for microscopic theories of high temperature superconductors.

The bipolaron theory of high-temperature superconductors and its relation to the properties of superfluid4He

Abstract Starting from the model of spin-dielectric polarons proposed by the author and others, it is suggested that all the carriers (oxygen 2p holes) form bipolarons, and that they are responsible for the current above and below T c. A comparison is made with superfluid 4He in which only 10% of the helium atoms are believed to condense into the zero-momentum state. A similar assumption for the superconductors can account for the small values of the change of entropy through the transition. The model breaks down for concentrations (x) of carriers so great that Tc decreases with x, for which overlap between the polarons may lead to BCS behaviour with breakup of the bosons above Tc , but not necessarily phonon-induced pairing. It is suggested also that the model is compatible with observations of a Fermi surface.

Derivation of Models for the Interacting Electrons in Cu-O Superconductors

Key questions for theory of high temperature superconductors involve the nature of the electronic system: the minimum essential Hamiltonian and the low energy states of such Hamiltonians. To attempt to answer these questions we are carrying out studies using constrained density functional (CDF) methods to identify the relevant electronic states and realistic values of the parameters, combined with exact calculations on the reduced model Hamiltonians. The CDF calculations lead to a 3-band Hubbard model for Cu-O planes with parameters in general agreement with high energy spectroscopies and low energy magnetic excitations. We describe a modified Lanczos method to carry out large many-body calculations and give a representative result, where we find the spectra are described by the 1-band Hubbard model in regimes which imply spin interactions beyond the usual Heisenberg form.

Valence bond ground states in a frustrated two-dimensional spin-1/2 Heisenberg antiferromagnet

We study a class of two-dimensional spin-1/2 Heisenberg antiferromagnets, introduced by Klein [1], in which the nearest-neighbor term is supplemented by next-nearest-neighbor pair and four-body interactions, producing additional frustration. For certain lattices, including e.g. the hexagonal lattice, we prove that any finite subset which admits a dimer covering has a ground state space spanned by valence bond states, each of which consists only of nearest-neighbor (dimer) singlet pairs. We also establish linear independence of these valence bond states. The possible relevance to resonating-valence-bond theories of high-temperature superconductors is briefly discussed. In particular, our results apply both to regular subsets of the lattice and to subsets with static holes.

A Ginzburg-Landau theory for a multi-layer high Tc superconductor

A Ginzburg-Landau theory for high temperature superconductors having the oxygen deficient perovskite structure is developed. It is assumed that there are two different types of superconducting layers and that there exist two order parameters, one for each layer. Mathematical criteria for the enhancement of the critical temperatures are derived.