Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Investigations towards an understanding of superconductivity

Robert Mccredie May

Published Jan 1, 1959• 0 citations
OpenAlex

Abstract

The work embodied in this thesis falls into three distinct parts :- the magnetic behaviour of a charged 2-dimensional Bose gas; the Meissner-Ochsenfeld effect in the Bogoljubov theory; and a study of pair correlations in the quasi-chemical equilibrium approach to superconductivity.

Related papers

Electron Pairs in the Theory of Superconductivity

John M. Blatt

The detailed mathematical correspondence between the Bogoliubov theory and the quasi-chemical equilibrium theory is established by means of identities. The Bogoliubov-BCS Ansatz is a special case of the quasi-chemical equilibrium Ansatz, corresponding to prefect Bose-Einstein condensation of the electron pairs.

Progress of Theoretical Physics•Mar 1, 1960•47 citations

BCS Theory of Superconductivity

A. S. Alexandrov, Nevill Mott

The crucial demonstration that superfluidity was linked to Bose particles and Bose-Einstein condensation came after the discovery of He3 in 1949, which failed to show the characteristic A transition within a reasonable wide temperature interval around the critical temperature for the onset of superfluidity in He4. The idea of the bosonization of electrons due to their pairing, introduced by Ogg (1946) became very attractive as an explanation for superconductivity after Schafroth (1955) showed that a gas of charged bosons with charge 2e would indeed show a Meissner effect, which is one of the most crucial features of superconductors (see Chapter 1). However this phenomenological Bose-gas picture was condemned and later on practically forgotten because it was unable to account quantitatively for the critical parameters of the classical (low-temperature) superconductors. Using for Tc the Bose-Einstein condensation temperature Eq.(l.S) one obtains the utterly meaningless result Tc = lOOOO.R&s; with the atomic density of electron pairs ~ 1022cm~3 and with the effective mass m** = 2me. The failure of the Schafroth picture stems from a very large size £ of pairs in classical superconductors, which can be estimated from the uncertainty principle: The uncertainty of the momentum 8p is estimated from the uncertainty of the kinetic energy 8E ~ vpSp, which should be of the order of Tc, the only characteristic energy of the superconducting state. Therefore and turns out to be more than one micron for simple metals with Tc ~ IK and the Fermi velocity VF — I0scm/s. That means that pairs in classical superconductors overlap strongly and the Shafroth model of real space pairs is wrong. The finally successful theory for classical superconductors was formulated by Bardeen, Cooper and Schrieffer (1957). In this chapter we present the main points of the BCS theory, using the Bogoliubov transformation (1947,1958) for the weak-coupling regime and the Green&s;s function technique for the intermediate coupling in Chapter 3. More details will be found in the excellent books by Schrieffer(1965), De Gennes (1989) and Abrikosov, Gor&s;kov and Dzyaloshinskii (1963).

WORLD SCIENTIFIC eBooks•Nov 24, 1994•0 citations

Superconductivity and superfluidity

敏彦 恒藤, 幹夫 中原

1. Superconductivity and superfluidity 2. Mean field theory of pair condensation 3. BCS theory 4. Superconductivity due to electron-phonon interaction 5. Ginzburg-Landau theory 6. Superfluid 3He 7. Unconventional superconducting materials Appendix 1. Bose-Einstein condensation in polarized alkaline atoms Appendix 2. Recent developments in research of high temperature superconductors.

Cambridge University Press eBooks•Jan 1, 1998•1 citation

Superconductivity of a Charged Ideal 2-Dimensional Bose Gas

Robert Mccredie May

It is well-known that the 2-dimensional Bose gas does not condense, and that no transition occurs in its thermodynamic behavior. Despite this, we find that in a magnetic field a 2-dimensional gas of charged, ideal bosons has a nearly sharp transition temperature, below which it displays an "imperfect" Meissner-Ochsenfeld effect, practically indistinguishable from the perfect London one. This fact is relevant to the application of the Bose gas model of superconductivity to thin films.The main interest of the model is, however, that it exhibits an (essentially perfect) Meissner-Ochsenfeld effect without any irregularity in ${C}_{V}(T)$.

Physical Review•Jul 15, 1959•45 citations

Superconductivity in a quasi-two-dimensional bose gas: High Tc from boson pair condensation

M. J. Rice, Y.R. Wang

Physica C Superconductivity•Jun 1, 1988•0 citations

Superconductivity of a Charged Ideal Bose Gas

M. R. Schafroth

It is shown that an ideal gas of charged bosons exhibits the essential equilibrium features of a superconductor. The onset of Bose-Einstein condensation marks the transition temperature ${T}_{c}$. Below ${T}_{c}$ a Meissner-Ochsenfeld effect is exhibited which is described in a very good approximation by London's equation.The singular nature of the condensed ideal Bose gas exhibits itself in a space dependence of the London constant $\ensuremath{\lambda}$, determined by the boundary conditions on the wave function. It is shown that the electrostatic repulsion between the bosons compensates this effect and leads to a spatially constant $\ensuremath{\lambda}$, independently of the boundary conditions.The critical field ${H}_{c}(T)$ is determined and found to be related to the penetration depth $d(T)$ by ${H}_{c}=\frac{\ensuremath{\hbar}c}{2e{d}^{2}}$ ($e$ being the boson charge).The $B(H)$ law is different from the one usually assumed for actual superconductors. Corresponding changes occur in the thermodynamical relation.A comparison with superconducting metals is made. The main conclusion is that if superconductivity in metals is due to the concurrence of bosons, then the number of these bosons must be strongly temperaturedependent below ${T}_{c}$.

Physical Review•Oct 15, 1955•366 citations
The crucial demonstration that superfluidity was linked to Bose particles and Bose-Einstein condensation came after the discovery of He3 in 1949, which failed to show the characteristic A transition within a reasonable wide temperature interval around the critical temperature for the onset of superfluidity in He4. The idea of the bosonization of electrons due to their pairing, introduced by Ogg (1946) became very attractive as an explanation for superconductivity after Schafroth (1955) showed that a gas of charged bosons with charge 2e would indeed show a Meissner effect, which is one of the most crucial features of superconductors (see Chapter 1). However this phenomenological Bose-gas picture was condemned and later on practically forgotten because it was unable to account quantitatively for the critical parameters of the classical (low-temperature) superconductors. Using for Tc the Bose-Einstein condensation temperature Eq.(l.S) one obtains the utterly meaningless result Tc = lOOOO.R&s; with the atomic density of electron pairs ~ 1022cm~3 and with the effective mass m** = 2me. The failure of the Schafroth picture stems from a very large size £ of pairs in classical superconductors, which can be estimated from the uncertainty principle: The uncertainty of the momentum 8p is estimated from the uncertainty of the kinetic energy 8E ~ vpSp, which should be of the order of Tc, the only characteristic energy of the superconducting state. Therefore and turns out to be more than one micron for simple metals with Tc ~ IK and the Fermi velocity VF — I0scm/s. That means that pairs in classical superconductors overlap strongly and the Shafroth model of real space pairs is wrong. The finally successful theory for classical superconductors was formulated by Bardeen, Cooper and Schrieffer (1957). In this chapter we present the main points of the BCS theory, using the Bogoliubov transformation (1947,1958) for the weak-coupling regime and the Green&s;s function technique for the intermediate coupling in Chapter 3. More details will be found in the excellent books by Schrieffer(1965), De Gennes (1989) and Abrikosov, Gor&s;kov and Dzyaloshinskii (1963).
It is well-known that the 2-dimensional Bose gas does not condense, and that no transition occurs in its thermodynamic behavior. Despite this, we find that in a magnetic field a 2-dimensional gas of charged, ideal bosons has a nearly sharp transition temperature, below which it displays an "imperfect" Meissner-Ochsenfeld effect, practically indistinguishable from the perfect London one. This fact is relevant to the application of the Bose gas model of superconductivity to thin films.The main interest of the model is, however, that it exhibits an (essentially perfect) Meissner-Ochsenfeld effect without any irregularity in CV(T){C}_{V}(T)CV​(T).
It is shown that an ideal gas of charged bosons exhibits the essential equilibrium features of a superconductor. The onset of Bose-Einstein condensation marks the transition temperature Tc{T}_{c}Tc​. Below Tc{T}_{c}Tc​ a Meissner-Ochsenfeld effect is exhibited which is described in a very good approximation by London's equation.The singular nature of the condensed ideal Bose gas exhibits itself in a space dependence of the London constant $\ensuremath{\lambda}$, determined by the boundary conditions on the wave function. It is shown that the electrostatic repulsion between the bosons compensates this effect and leads to a spatially constant $\ensuremath{\lambda}$, independently of the boundary conditions.The critical field Hc(T){H}_{c}(T)Hc​(T) is determined and found to be related to the penetration depth d(T)d(T)d(T) by ${H}_{c}=\frac{\ensuremath{\hbar}c}{2e{d}^{2}}$ (eee being the boson charge).The B(H)B(H)B(H) law is different from the one usually assumed for actual superconductors. Corresponding changes occur in the thermodynamical relation.A comparison with superconducting metals is made. The main conclusion is that if superconductivity in metals is due to the concurrence of bosons, then the number of these bosons must be strongly temperaturedependent below Tc{T}_{c}Tc​.