Coulomb repulsion andTcin BCS theory of superconductivity

2005 ◽  
Vol 71 (13) ◽  
Author(s):  
X. H. Zheng ◽  
D. G. Walmsley
Keyword(s):  
Coulomb Repulsion ◽  
Bcs Theory ◽  
Theory Of Superconductivity

N-quantum approach to the BCS theory of superconductivity

1994 ◽  
Vol 72 (9-10) ◽  
pp. 574-577 ◽  
Author(s):  
O. W. Greenberg
Keyword(s):  
Field Theory ◽  
Finite Temperature ◽  
Bcs Theory ◽  
Zero Temperature ◽  
General Applicability ◽  
Finite Temperature Field Theory ◽  
Gap Equation ◽  
Quantum Approach ◽  
Quantized Field ◽  
Theory Of Superconductivity

A method of general applicability to the solution of second-quantized field theories at finite temperature is illustrated using the BCS (Bardeen–Cooper–Schrieffer) model of superconductivity. Finite-temperature field theory is treated using the thermo field-theory formalism of Umezawa and collaborators. The solution of the field theory uses an expansion in thermal modes analogous to the Haag expansion in asymptotic fields used in the N-quantum approximation at zero temperature. The lowest approximation gives the usual gap equation.

Zero-temperature equation-of-motion of electron pair in the BCS theory of superconductivity

1996 ◽  
Vol 74 (6) ◽  
pp. 1106-1115
Author(s):  
Akitomo Tachibana
Keyword(s):  
Hilbert Space ◽  
Density Functional ◽  
Electron Pair ◽  
Equation Of Motion ◽  
Real Space ◽  
Bcs Theory ◽  
Zero Temperature ◽  
Functional Theory ◽  
Theory Of Superconductivity ◽  
Pair Function

By projecting the BCS ground state of superconducting electron condensate on the N-electron Hilbert space, a real-space equation-of-motion is obtained for the electron pair function [Formula: see text] at absolute zero temperature (T = 0):[Formula: see text]where ρN−2 denotes electron density of the (N – 2)-electron condensate given as[Formula: see text]Since the exchange-correlation potential is given as an explicit functional of electron density, this equation represents the fundamental working equation for the new density functional theory of superconductivity. The 2nd-order density matrix ΓN(1, 2|1′, 2′) projected on the N-electron Hilbert space satisfies[Formula: see text]so that asymptotically[Formula: see text]where [Formula: see text] denotes the center-of-mass coordinate of electrons e1and e2; this is considered the ODLRO (off-diagonal long-range order) at T = 0 projected on the N-electron Hilbert space. A new attractive potential analysis for the two-electron scattering problem (A. Tachibana, Bull. Chem. Soc. Jpn. 66, 3319 (1993); Int. J. Quantum Chem. 49, 625 (1994)) is straightforwardly applicable to the present equation-of-motion, and we can also plug in the vibronic interaction for the enhancement of the attractive force. Our approach is purely mathematical and basic, restricted merely at T = 0, but proves to serve as a real-space analysis of the pair function itself. Key words: equation-of-motion of electron pair, BCS theory, superconductivity, electron pair function, density functional theory.

scholarly journals Unusual symmetries of the order parameter in cuprates

2020 ◽  
Vol 2 (4) ◽  
pp. 207-212
Author(s):  
Tran Van Luong ◽  
Nguyen Thi Ngoc Nu
Keyword(s):  
High Temperature ◽  
Order Parameter ◽  
Cuprate Superconductors ◽  
High Temperature Superconductivity ◽  
Spin Fluctuation ◽  
High Temperature Superconductors ◽  
Coulomb Repulsion ◽  
Bcs Theory ◽  
S Wave ◽  
Wave Symmetry

The BCS superconducting theory, introduced by J. Bardeen, L. Cooper and R. Schriffer in 1957, succeeded in describing and satis-factorily explaining the nature of superconductivity for low-temperature superconductors. However, the BCS theory cannot explain the properties of high-temperature superconductors, discovered by J. G. Bednorz and K. A. Müller in 1986. Although scientists have found a lot of new superconductors and their transition temperatures are constantly increasing, most high-temperature superconductors are found by experiment and so far no theory can fully explain their properties. Many previous studies have suggested that the order parameter in high-temperature copper-based superconductors (cuprate superconductors - cuprates) is in the form of d-wave symmetry, but recent results show that the order parameter has an extended s-wave symmetry (extended s wave). Studying the symmetric forms of order parameters in cuprate can contribute to understanding the nature of high-temperature superconductivity. In this article, the authors present an overview of the development of high-temperature supercon-ductors over the past 30 years and explains unusual symmetries of the order parameter in copper-based superconductors. The com-petition of three coupling mechanisms of electrons in cuprates (the mechanism of coupling through coulomb repulsion, electron-phonon mechanism and spin-fluctuation mechanism) affects the unusual symmetry of the order parameter. The solution of the self-consistency equation in simple cases has been found and the ability to move the phase within the superconducting state has been shown.

Reminiscences of early days in solid state physics

1980 ◽  
Vol 371 (1744) ◽  
pp. 77-83 ◽  
Keyword(s):  
State Physics ◽  
Solid State ◽  
Nobel Prize ◽  
Bcs Theory ◽  
Solid State Physics ◽  
University Of Illinois ◽  
Theory Of Superconductivity

Bardeen, John. Born Wisconsin 1908. Educated Universities of Wisconsin and Princeton. Research in many aspects of solid state science. Nobel Prize for physics (shared) 1956 for research leading to the invention of the ; Nobel Prize for physics ( shared) 1972 for the ‘ BCS ’ theory of superconductivity associated with his name. Professor, University of Illinois, since 1951.

EXACTLY SOLVABLE PAIRING HAMILTONIANS

2007 ◽  
Vol 16 (02) ◽  
pp. 210-221 ◽  
Author(s):  
J. DUKELSKY ◽  
B. ERREA ◽  
S. LERMA H. ◽  
S. PITTEL
Keyword(s):  
Exact Solution ◽  
Bcs Theory ◽  
Exactly Solvable ◽  
Theory Of Superconductivity ◽  
Solvable Pairing

We review the development of the microscopic BCS theory of superconductivity and the exact solution of the pairing Hamiltonian given by Richardson in 1963. We then introduce the generalized Richardson-Gaudin exactly-solvable pairing models for SU(2) (pairing between like particles), SO(5) ( T =1 pairing) and SO(8) ( T =0,1 pairing) algebras.

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