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TIME DEPENDENCE OF THE ORDER PARAMETER OF A SUPERCONDUCTOR NEAR THE TRANSITION TEMPERATURE.

T. Tsuneto, Elihu Abrahams

Published Nov 23, 1964• 0 citations
OpenAlex

Abstract

An equation is derived that describes how interelectronic interactions determine the time variation of one specific order parameter in a pure superconductor. The equation is derived from the equations of motion obeyed by the (non-equilibrium) one particle Green's function in the presence of time dependent fields and interactions. These are related to the findings of L. P. Gor'kov (Sov. Phys. JETP, 7:505 (1958), 9:1364 (1962), and 10:998 (1960).

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Journal of the Physical Society of Japan•Sep 12, 2017•8 citations
An equation is derived that describes how interelectronic interactions determine the time variation of one specific order parameter in a pure superconductor. The equation is derived from the equations of motion obeyed by the (non-equilibrium) one particle Green's function in the presence of time dependent fields and interactions. These are related to the findings of L. P. Gor'kov (Sov. Phys. JETP, 7:505 (1958), 9:1364 (1962), and 10:998 (1960).
This chapter considers the analog of the time-dependent Hartree–Fock (mean-field) decoupling treated in Part I and extends it to the broken-symmetry phase for superfluid fermions. Two coupled equations for the “normal” and “anomalous” time-dependent single-particle Green’s functions are obtained, which extend to nonequilibrium situations the equations originally obtained at equilibrium by Gor’kov, soon after the BCS original article on the theory of superconductivity. Accordingly, the time-dependent gap (order) parameter is also introduced.
The study of quantum phase transitions provides a new route to ¯nd and understand unconventional phases in Condensed Matter Physics. The past decades have seen a sub- stantial rejuvenation of interest in this area of study, driven by experiments on the cuprate superconductors, heavy fermions' materials, organic conductors and related compounds. Nevertheless, the transitions involving superconducting phases are not as well explored theoretically as transitions involving magnetic phases. Thus, the study of superconduct- ing systems with treatments beyond mean ¯eld theories seems to be necessary to verify the behavior of °uctuations in the normal phase near the transition to the superconductor state. We propose a generalization of the equation of motion method for equilibrium Green's functions to handle systems with time-dependent perturbations. This generalization is based on the properties of Green's functions and in the adiabatic application of the disturbance. We study a two band s-wave superconductor with hybridization, based on an attractive Hubbard model. We consider the system under the action of a fictitious field, time and wave vector dependent, which couples to the superconducting order parameter. We calculate the zero order propagators in the field, using the conventional equation of motion method, and the first order ones, using the generalized equation of motion. The response to the field is given by a generalized susceptibility, which in the one-band case reduces to the one obtained by Thouless. We associate the emergence of superconductivity with the divergence of the static part of the generalized susceptibility. The advantage of this method is its simplicity, because we only deal with single-particle propagators. We analyze this superconducting susceptibility, which allows us to find a critical hybridization above which there is no superconducting phase, determine the critical and the crossover lines and determine the dynamical critical exponent z for this system. Therefore we can predict the behavior of some quantities measured experimentally at low temperatures close to the superconducting quantum critical point.
We present the current-density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current-density, and electron density are chosen as basic variables that uniquely determine the equilibrium properties of the system. In order to construct this theory, the development of the approximate form of the exchange-correlation (xc) energy functional is indispensable as well as the derivation of the effective single-particle equation which makes it possible to reproduce the equilibrium densities mentioned above. The rigorous expression of the xc-energy functional is derived using the technique of the coupling-constant integration. Furthermore, the approximate form of the xc energy functional is proposed such that the energy gap resulting from the effective single-particle equation is consistent with the attractive interaction energy of the system.
Equations of motion are derived for the normal and anomalous single-electron density matrices of a Fermi liquid using a time-dependent finite-temperature generalized coherent-state variational ansatz for the many-body density matrix. Self-consistent equations for the order parameter $\ensuremath{\Delta}$ allow us to investigate the interplay of the Coulomb repulsion and pairing attraction in homogeneous and inhomogeneous Fermi liquids with spontaneously broken symmetry such as high-temperature superconductors. The temperature of the Kosterlitz-Thouless transition to the two-dimensional superfluidity is calculated.
We present the current–density functional theory for the superconductor immersed in the magnetic field. The order parameter of the superconducting state, transverse component of the paramagnetic current–density, and electron density are chosen as basic variables that uniquely determine the equilibrium properties of the system. In order to construct this theory, the development of the approximate form of the exchange–correlation (xc) energy functional is indispensable as well as the derivation of the effective single-particle equation which makes it possible to reproduce the equilibrium densities mentioned above. The rigorous expression of the xc-energy functional is derived using the technique of the coupling-constant integration. Furthermore, the approximate form of the xc energy functional is proposed such that the energy gap resulting from the effective single-particle equation is consistent with the attractive interaction energy of the system.