Theory Of Cuprate Superconductivity Research Articles

Glimpses of Greatness

P W Anderson was a theoretical physicist. He won the Nobel Prize in 1977. He catalysed Nobel Prizes for several others. His career spanned 72 years of relentless research, filled with path-breaking contributions. He focussed on ‘here and now’ phenomena of inanimate materials and built theoretical quantum models of lasting value. He communed with nature by contemplation and study of experimental results. As a founding father, he set agenda for the field of condensed matter physics, for half a century. It is a growing fertile field now, with a web of connection to different corners of science, technology, and sometimes beyond. As a person, Anderson was remarkable. He was my long time collaborator since 1984. I had a wonderful opportunity to join hands with him when he initiated the resonating valence bond (RVB) theory of high-temperature superconductivity in cuprates in early 1987.

Theory of High-Temperature Superconductivity in Cuprates

We propose a microscopic theory of superconductivity for systems with strong electron correlations such as cuprates in the framework of the extended Hubbard model where the intersite Coulomb repulsion and electron-phonon interaction (EPI) are taken into account. The Dyson equation for the normal and pair Green functions for the Hubbard operators (HOs) is derived. Due to the unconventional commutation relations for the HOs, a specific kinematical interaction of electrons with spin and charge fluctuations with a large coupling constant of the order of the kinetic energy of electrons W emerges that results in the d-wave pairing with high- Tc. Superconductivity can be suppressed only for a large intersite Coulomb repulsion \(V \gtrsim W\). Isotope effect on Tc caused by electron-phonon interaction is weak at optimal doping and increases at low doping. The kinematical interaction is absent in the spin-fermion models and is lost in the slave-boson (-fermion) models treated in the mean-field approximation.

Theory of High Temperature Superconductivity in Cuprates and Other Doped Polar Insulators

In the last two decades, there have been tremendous attempts to build an adequate theory of high-temperature superconductivity. Most studies used some model Hamiltonians with input parameters not directly related to the material. The dielectric response function of electrons in strongly correlated high-temperature superconductors is a priori unknown. Hence, one has to start with the generic Hamiltonian including unscreened Coulomb and Frohlich electron–phonon interactions operating on the same scale since any ad-hoc assumption on their range and relative magnitude might fail. Using such a generic Hamiltonian, the analytical theory of high-temperature superconductivity in doped polar insulators predicting the critical temperature in excess of a hundred Kelvin without any adjustable parameters has been built. The many-particle electron system is described by an analytically solvable polaronic t–Jp Hamiltonian with reduced hopping integral, t, allowed double on-site occupancy, large phonon-induced antiferromagnetic exchange, Jp>t, and a high-temperature superconducting state of small superlight bipolarons protected from clustering. Here, major steps of the theory are outlined suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron–electron correlations with a significant finite-range (Frohlich) EPI, and that the theory is fully compatible with the key experiments.

Phenomenological Ginzburg-Landau-like theory for superconductivity in the cuprates

We propose a phenomenological Ginzburg-Landau-like theory of cuprate superconductivity. The free energy is expressed as a functional F of the spin-singlet pair amplitude psi_ij=psi_m=Delta_m exp(i phi_m); i and j are nearest-neighbor sites of the Cu lattice in which the superconductivity is believed to primarily reside and m labels the site at the center of the bond between i and j. The system is modeled as a weakly coupled stack of such planes. We hypothesize a simple form, F[Delta,phi]=sum_m (A Delta_m^2+ B Delta_m^4/2)+C sum_<mn> Delta_m Delta_n cos(phi_m-phi_n), for the functional. The coefficients A, B and C are determined from comparison with experiments. We work out a number of consequences of the proposed functional for specific choices of A, B and C as functions of hole density x and temperature T. There can be a rapid crossover of <Delta_m> from small to large values as A changes sign on lowering T and the crossover temperatures is identified with the observed pseudogap temperature. The superconducting phase-coherence transition occurs at a different temperature T_c, and describes superconductivity with d-wave symmetry for C>0. We calculate T_c(x) which has the observed parabolic shape, being strongly influenced by the coupling between Delta_m and phi_m present in F. The superfluid density, the local gap magnitude, the specific heat (with and without a magnetic field) and vortex properties are obtained using F. We compare our results successfully with experiments. We also obtain the electron spectral density as influenced by the coupling between the electrons and the pair correlation function calculated from F. Features such as temperature dependent Fermi arcs, antinodal pseudogap filling temperature, pseudogapped density of states in different momentum regions of the Fermi surface and `bending' of the energy gap versus momentum on the Fermi surface emerge from the theory.

A theory of superconductivity in cuprates

A theory of superconductivity in cuprates

Coexistence of bulk antiferromagnetic order and superconductivity in theQED3theory of copper oxides

Within the framework of the ${\mathrm{QED}}_{3}$ theory of cuprate superconductivity it is argued that bulk antiferromagnetic (AF) order can coexist with d-wave superconductivity in the underdoped region, in agreement with recent experiments. The AF order arises from the phase fluctuating d-wave superconductor via the mechanism of spontaneous chiral-symmetry breaking, provided that fluctuations are sufficiently strong. The phase diagram for this coexistence is mapped out by means of analytical and numerical solutions of the underlying Dyson-Schwinger equation in the large N limit.

Excitation spectrum of the homogeneous spin liquid

We discuss the excitation spectrum of a disordered, isotropic and translationally invariant spin state in the 2D Heisenberg antiferromagnet. The starting point is the nearest-neighbor RVB state which plays the role of the vacuum of the theory, in a similar sense as the Neel state is the vacuum for antiferromagnetic spin wave theory. We discuss the elementary excitations of this state and show that these are not Fermionic spin-1/2 `spinons' but spin-1 excited dimers which must be modeled by bond Bosons. We derive an effective Hamiltonian describing the excited dimers which is formally analogous to spin wave theory. Condensation of the bond-Bosons at zero temperature into the state with momentum (pi,pi) is shown to be equivalent to antiferromagnetic ordering. The latter is a key ingredient for a microscopic interpretation of Zhang's SO(5) theory of cuprate superconductivity

Spin-free quantum chemistry. XXVI. The Ising, small-bipolaron theory of cuprate superconductivity

The Ising, small-biopolaron (ISB) theory is a strong-coupling theory of cuprate superconductivity which is based in the negative-U, Hubbard Hamiltonian. Its ground state is composed of (small) biopolarons and (small-biopolaron) holes with a vibronically induced, biopolaron-hole exchange interaction, J{sub BH}, between them. The energy gap, {Delta}(0), is taken to be equal to the dissociation energy of a small biopolaran and which, since it is defined spectroscopically, is not an order parameter. The application of the Ising meanfield theory to the highly degenerate ground-state yields a second-order phase change with kT{sub c}/2=J{sub BH} and a real order parameter, {Omega}(T), which is valid over the entire temperature range from zero to T{sub c}. Near T{sub c}, the Ising free energy functional takes the same form as does the Landau. In the presence of an electromagnetic field, the Ising functional is a generalization of the Ginzburg-Landau functional which employs a complex order parameter and which is invariant under the electromagnetic gauge transformation. The breaking of the gauge invariance yields the London theory of superconductivity. 6 refs., 9 figs.