ISSN:
1572-9605
Keywords:
Theory
;
superconductivity
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
,
Physics
Notes:
Abstract Based on a generalized BCS Hamiltonian in which the interaction strengths (V 11,V 22,V 12) among and between “electron” (1) and “hole” (2) Cooper pairs are differentiated, the thermodynamic properties of a type-I superconductor below the critical temperatureT c are investigated. An expression for the ground-state energy,W-W 0, relative to the unperturbed Bloch system is obtained:W-W 0=−1/4[N 1(0)Δ 1 2 +N 2(0)Δ 2 2 ], whereN j(0) represent the electron and hole densities of states at the Fermi energy εF, and Δj are the solutions of the simultaneous equations, $$\Delta _j = \tfrac{1}{2}V_{j1} N_1 (0)\Delta _1 {\text{ sinh}}^{ - {\text{1}}} (\hbar \omega _D /\Delta _1 ) + \tfrac{1}{2}V_{j2} N_2 (0)\Delta 2_2 {\text{ sinh}}^{ - {\text{1}}} (\hbar \omega _D /\Delta _2 )$$ with ωD denoting the Debye frequency. The usual BCS formulas are obtained in the limits: (all)V jl=V0,N 1(0) =N 2(0). Any excitations generated through the BCS interaction Hamiltonian containingV jl must involve Cooper pairs of antiparallel spins and nearly opposite momenta. The nonzero momentum orexcited Cooper pairs belowT c are shown to have an excitation energy band minimum lower than the quasi-electrons, which were regarded as the elementary excitations in the original BCS theory. The energy gapε g(T) defined relative to excited and zero-momentum Cooper pairs (whenV jl〉0) decreases fromε g(0) to 0 as the temperatureT is raised from 0 toT c. If “electrons” only are available as in a monovalent metal like sodium (V 12=0), the energy constant Δ1 is finite but the energy gap vanishes identically for allT. In agreement with the BCS theory, the present theory predicts that a pure nonmagnetic metal in any dimensions should have a Cooper-pair ground state whose energy is lower than that of the Bloch ground state. Additionally it predicts that a monovalent metal should remain normal down to 0K, and that there should be no strictly one-dimensional superconductor.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00618000
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