The theory of superconductivity

References

• Allen , W.D. , Dawton , R.H. , Bär , M. , Mendelssohn , K. and Olsen , J.L. 1950 a . Nature, Lond. , 166 : 1071 – 1071 . see Allen et al., 1950 b
   PubMedGoogle Scholar
• Allen , W.D. , Dawton , R.H. , Lock , J.M. , Pippard , A.B. and Shoenberg , D. 1950 b . Nature, Lond. , 166 : 1071 – 1071 . Isotope effect in tin
   PubMedGoogle Scholar
• Anderson , P.W. 1958 . Phys. Rev. , 110 : 827 – 827 . ‘Approximate gauge invariance’ and Meissner effect
   Web of Science ®Google Scholar
• Bardeen , J. 1937 . Phys. Rev. , 52 : 688 – 688 . Matrix elements of Bloch theory, taking umklappprozesse and Hartree self-consistent field of electrons into account; 1950, Ibid., 80, 567; Variational wave functions, leading to the same results as Fröhlich's perturbation theory; 1951, Rev. mod. Phys., 23, 261; Review of the theory of superconductivity, including Bloch-Nordsiek transformation; proves equivalence of Bardeen's variational wave function method with Fröhlich's perturbation theory; 1956, Hand. Phys. Encycl. Phys., 15 (Berlin: Springer), p. 274. Extensive review of theory and phenomenological theory of superconductivity, including a discussion of the energy gap model
   Google Scholar
• Bardeen , J. , Cooper , L.N. and Schrieffer , J.R. 1957 . Phys. Rev. , 106 : 162 – 162 . 108, 1175; Theory of superconductivity—variational trial wave functions with pair correlations using simplified Hamiltonian
   Web of Science ®Google Scholar
• Bardeen , J. 1958 . Phys. Rev. , 1 : 399 – 399 . The two-fluid model
   Google Scholar
• Bardeen , J. , Rickayzen , G. and Tewordt , L. 1959 . (to be published): Theory of the thermal conductivity of superconductors
   Google Scholar
• Bardeen , J. and Pines , D. 1955 . Phys. Rev. , 99 : 1140 – 1140 . Theory of electronphonon interaction, taking account of Coulomb interactions by the plasma theory of Bohm and Pines
   Web of Science ®Google Scholar
• Bernardes , N. 1957 . Phys. Rev. , 107 : 354 – 354 . Specific heat of an energy gap model
   Google Scholar
• Biondi , M.A. , Forrester , A.T. , Garfunkel , M.P. and Satterthwaite , C.B. 1958 . Rev. mod. Phys. , 30 : 1109 – 1109 . Review of experimental work on energy gap in superconductors
   Google Scholar
• Biondi , M.A. , Garfunkel , M.P. and McCoubrey , A.O. 1958 a . Phys. Rev. , 108 : 495 – 495 . see Biondi et al., 1958 b
   Google Scholar
• Biondi , M.A. , Forrester , A.T. and Garfunkel , M.P. 1958 b . Phys. Rev. , 108 : 497 – 497 . Microwave absorption experiments (in aluminium and tin respectively) giving evidence for an energy gap Γ (T), in good agreement with the Bardeen-Cooper-Schrieffer theory
   Google Scholar
• Bloch , F. 1928 . Z. Phys. , 52 : 555 – 555 . Theory of metallic conduction
   Google Scholar
• Bogoliubov , N.N. 1947 . J. Phys., Moscow , 11 : 23 – 23 . The quasi-particle transformation for Bosons; 1958 a, Zh. eksp. teor. Fiz., 34, 58 (translated in Sov. Phys. jetp, 7, 41), Nuovo Cim., 7, 794; The quasi-particle transformation for Fermions-derivation of the ground state and excitation spectrum of superconductors, from Fröhlich's Hamiltonian; 1958 b, Zh. eksp. teor, Fiz., 34, 73 (translated in Sov. Phys. jetp, 7, 51); Quasi-particle theory of superconductivity, with the simplified Hamiltonian of Bardeen, Cooper and Schrieffer
   Google Scholar
• Bogoliubov , N.N. , Tolmachev , V.V. and Shirkov , D.V. 1958 a . Novii Metod v Teorii Sverkhprovodimosti , Moscow : Akad. Nauk SSSR . (to be published in English translation in Fortschr. Phys.); A very full account of the quasi-particle method, with discussion of renormalization and of Coulomb interaction
   Google Scholar
• Bogoliubov , N.N. , Zubarev , D.N. and Tserkovnikov , Yu.A. 1958 b . Dokl. Akad. Nauk SSSR , 117 : 788 – 788 . (translated in Sov. Phys. Dokl., 2, 535): The superconducting phase transition, calculated with the quasi-particle transformation and statistical perturbation theory
   Google Scholar
• Bohm , D. and Pines , D. 1953 . Phys. Rev. , 92 : 609 – 609 . Theory of a quantum-mechanical plasma
   Web of Science ®Google Scholar
• Buckingham , M.J. 1951 . Nature, Lond. , 168 : 281 – 281 . see Buckingham and Schafroth, 1954: 1957, Nuovo Cim., 5, 1763; Proves that the Meissner effect does not follow uniquely from the energy gap model; Bardeen's assumptions concerning transition matrix elements are not consistent
   Web of Science ®Google Scholar
• Buckingham , M.J. and Schafroth , M.R. 1954 . Proc. phys. Soc. A , 67 : 828 – 828 . Perturbation calculation of the effect of the electron-phonon interaction on the specific heat of normal metals
   Google Scholar
• Casimir , H.B.G. 1953 . Physica , 19 : 764 – 764 . Remarks in the discussion on Fröhlich's paper (p. 755)
   Google Scholar
• Chester , G.V. and Houghton , A. 1959 . Use of Born-Oppenheimer approximation for calculation of the electron-phonon interaction; confirms the results of Nakajima and of Bardeen and Pines in the press
   Google Scholar
• Chester , P.F. and Jones , G.O. 1953 . Phil. Mag. , 44 : 1281 – 1281 . Pressure dependence of the superconducting transition
   Google Scholar
• Cooper , L.N. 1956 . Phys. Rev. , 104 : 1189 – 1189 . Demonstrates the possible formation of bound electron pairs under the Fröhlich interaction
   Web of Science ®Google Scholar
• Corak , W.S. , Goodman , B.B. , Satterthwaite , C.B. and Wexler , A. 1954 . Phys. Rev. , 96 : 1442 – 1442 . 1956, Ibid., 102, 656; Measurements of specific heat of vanadium; results show exponential dependence on T -1 at low temperatures
   Web of Science ®Google Scholar
• Corak , W.S. and Satterthwaite , C.B. 1956 . Phys. Rev. , 102 : 662 – 662 . Measurement of the specific heat of tin
   Web of Science ®Google Scholar
• Ehrenfest P. Proc. Kon. Acad. Wet. Amsterdam 1933 36 153 153 (Science Section) Classification of phase transitions
   Google Scholar
• Forrester , A.T. 1958 . Phys. Rev. , 110 : 776 – 776 . Shows that the results of Glover and Tinkham cannot settle the question of an energy gap
   Google Scholar
• Fröhlich , H. 1936 . Elektrontheorie der Metalle , Berlin : Springer . Contains the Bloch theory; 1950, Phys. Rev., 79, 845; The Bloch interaction as the mechanism of superconductivity—perturbative calculation; 1952, Proc. roy. Soc. A, 215, 291; Field-theoretical formulation of Bloch theory; renormalization of coupling constant and sound velocity; 1953, Physica, 19, 755; Qualitative discussion on theory of super-conductivity; difficulties in perturbation theory; 1954, Proc. roy. Soc. A, 223, 296; The one-dimensional model with very strong coupling
   Google Scholar
• Fröhlich , H. , Pelzer , H. and Zienau , S. 1950 . Phil. Mag. , 41 : 221 – 221 . Theory of an electron in an ionic lattice (‘polaron’)
   Google Scholar
• Galkin , A.A. , Kan , Ya.S. and Lazarev , B.G. 1957 . Zh. eksp. teor. Fiz. , 32 : 1582 – 1582 . (translated in Sov. Phys. jetp, 5, 1292); Observed occasional downward jumps in a persistent current, at temperatures near T 0; interpreted as showing a fluctuation of some kind in which R ∼ 10−11 ohm (Rn ∼ 10−7 ohm)
   Google Scholar
• Geilikman , B.T. 1958 . Zh. eksp. teor. Fiz. , 34 : 1042 – 1042 . (translated in Sov. Phys. jetp, 7, 721; Theory of the thermal conductivity of superconductors
   Google Scholar
• Gell-Mann , M. and Brueckner , K.A. 1957 . Phys. Rev. , 106 : 364 – 364 . Rigorous theory of Coulomb correlations in a dense electron gas
   Web of Science ®Google Scholar
• Ginsburg , V.L. 1946 . Zh. eksp. teor. Fiz. , 14 : 134 – 134 . The energy gap model for superconductors; 1953, Fortschr. Phys., 1, 101; Review of the theory, including discussion of the spectrum of elementary excitations
   Google Scholar
• Ginsburg , V.L. and Landau , L.D. 1950 . Zh. eksp. teor. Fiz. , 20 : 1064 – 1064 . Phenomenological theory of superconductors
   Google Scholar
• Glover , R.E. and Tinkham , M. 1956 . Phys. Rev. , 104 : 844 – 844 . 1957, Ibid., 108, 243; Infra-red and microwave absorption in superconducting films; the results are consistent with an energy gap
   Google Scholar
• Goodman , B.B. 1953 . Proc. phys. Soc. A , 66 : 217 – 217 . Thermal conductivity measurements on tin, supporting the idea of an energy gap and its variation with temperature; 1958, C. R. Acad. Sci., Paris, 246, 3031; Table of Γ/κT 0 for superconductors
   Google Scholar
• Gorkov , L.P. 1958 . Zh. eksp. teor. Fiz. , 34 : 735 – 735 . (translated in Sov. Phys. jetp, 7, 505); Calculation of the energy gap and excitation spectrum by use of Green's functions
   Google Scholar
• Gorter , C.J. and Casimir , H.G.B. 1934 . Phys. Z. , 35 : 963 – 963 . Two-fluid model of superconductivity
   Google Scholar
• Hebel , L.C. and Slichter , C.P. 1957 . Phys. Rev. , 107 : 901 – 901 . Measured the nuclear spin-lattice relaxation time in aluminium; the results agree well with the Bardeen-Cooper-Schrieffer energy gap provided the matrix elements for electron spin reversal are assumed roughly the same in normal and superconducting states
   Web of Science ®Google Scholar
• Heine , V. and Pippard , A.B. 1958 . Phil. Mag. , 3 : 1046 – 1046 . Interpretation of the experimental Knight shift in superconductors
   Google Scholar
• Huang , K. 1951 . Proc. phys. Soc. A , 64 : 867 – 867 . Electrons follow lattice displacements adiabatically; resolves Wentzel's lattice instability paradox
   Google Scholar
• Kan , L.S. , Sudovstov , A.I. and Lasarev , B.G. 1948 . Zh. eksp. teor. Fiz. , 18 : 825 – 825 . Effect of pressure on superconducting transition
   Google Scholar
• Knight , W.D. 1949 . Phys. Rev. , 76 : 1259 – 1259 . Shift in nuclear magnetic resonance frequency in solids
   Web of Science ®Google Scholar
• Knight , W.D. , Androes , G.M. and Hammond , R.H. 1956 . Phys. Rev. , 104 : 852 – 852 . Measurement of the Knight shift in colloidal mercury (Δω/ω=0.5%)
   Google Scholar
• Koppe , H. 1947 . Ann. Phys., Lpz. , 1 : 405 – 405 . 1950, Ergebn. Exakt. Naturw., 23, 283; A two-fluid model with an energy gap
   Web of Science ®Google Scholar
• Koppe , H. and Mühlschlegel , B. 1958 . Z. Phys. , 151 : 613 – 613 . Derives Bardeen-Cooper-Schrieffer wave function by canonical transformation
   Google Scholar
• Kuper , C.G. 1955 . Proc. roy. Soc. A , 227 : 214 – 214 . The thermal properties of Fröhlich's one-dimensional model of a superconductor; 1958, Physica, 24, 304; Variational calculation using the wave function of Bardeen, Cooper and Schrieffer with Fröhlich's renormalized Hamiltonian
   Google Scholar
• Kvasnikov , I.A. 1958 . Dokl. Akad. Nauk SSSR , 119 : 475 – 475 . 675, The thermodynamics of superconductors
   Google Scholar
• Landau , L.D. 1941 . J. Phys., Moscow , 5 : 71 – 71 . 1947, Ibid., 11, 91; Theory of superfluidity of liquid helium
   Google Scholar
• Laredo , S.J. 1955 . Proc. roy. Soc. A , 229 : 473 – 473 . Measurements of the thermal conductivity of tin
   Google Scholar
• Laue , M. von . 1952 . Theory of Superconductivity , New York : Academic Press . Full account and generalization of London's phenomenological theory
   Google Scholar
• Lock , J.M. , Pippard , A.B. and Shoenberg , D. 1951 . Proc. Camb. Phil. Soc. , 47 : 811 – 811 . Isotope effect in tin
   Google Scholar
• London , F. 1950 . Superfluids, Vol. I: Macroscopic Theory of Superconductivity , New York : Wiley .
   Google Scholar
• London , F. and London , H. 1935 . Physica , 2 : 341 – 341 . Phenomenological theory of superconductors
   Google Scholar
• Lüthi , B. and Rohrer , H. 1958 . Helv. phys. acta , 31 : 294 – 294 . Tabulation of the volume dependence of the coupling constant F, from the experimental data on the pressure effect and T 0
   Google Scholar
• Lynton , E.A. , Serin , B. and Zucker , M. 1957 . J. Phys. Chem. Solids , 3 : 165 – 165 . Measurements of transition temperature and specific heat of tin
   Google Scholar
• Maxwell , E. 1950 . Phys. Rev. , 78 : 477 – 477 . Isotope effect in mercury
   Web of Science ®Google Scholar
• Meissner , W. and Ochsenfeld , R. 1933 . Naturwissenschaften , 21 : 787 – 787 . Discovery of the totally diamagnetic property of superconductors
   Web of Science ®Google Scholar
• Mikura , Z. 1957 . J. phys. Soc. Japan , 12 : 587 – 587 . Artificial spin-dependent electron-electron interaction, yielding Meissner effect
   Google Scholar
• Montgomery , H. 1957 . Proc. roy. Soc. A , 244 : 85 – 85 . Thermal conductivity of lead, 1–4°K
   Google Scholar
• Morse , R.W. and Bohm , H.V. 1957 . Phys. Rev. , 108 : 1094 – 1094 . Ultrasonic attenuation measurements, giving evidence for an energy gap in good agreement with Bardeen-Cooper-Schrieffer theory
   Web of Science ®Google Scholar
• Muench , N.H. 1955 . Phys. Rev. , 99 : 1814 – 1814 . Pressure dependence of the superconducting transition
   Google Scholar
• Nakajima , S. 1953 . Busseiron Kenkyu , 65 : 116 – 116 . Proc. Int. Conf. Theor. Phys., Kyoto and Tokyo, p. 916; The electron-phonon interaction, with Coulomb correlations taken into account; 1955, Advanc. Phys., 4, 363: Statistical mechanical perturbation theory
   Google Scholar
• Onnes , H. Kamerlingh . 1911 . Commun. phys. Lab. Univ. Leiden , : 119 b – 119 b . 120 b, 122 b, Discovery of superconductivity
   Google Scholar
• Peierls , R.E. 1930 . Ann. Phys. , 4 : 121 – 121 . Energy spectrum of electron in sinusoidal potential; 1932, Ibid., 12, 154; Umklappprozesse; 1955, Quantum theory of solids (Oxford: University Press)
   Google Scholar
• Pines , D. 1953 . Phys. Rev. , 92 : 626 – 626 . Plasma theory of Coulomb correlations in metals; 1958, Ibid., 109, 280; Variation of T 0 for different superconductors, used as test for the Bardeen-Cooper-Schrieffer criterion for superconductivity
   Web of Science ®Google Scholar
• Pines , D. and Schrieffer , J.R. 1958 . Nuovo Cim. , 10 : 496 – 496 . Discussion of gauge invariance and Meissner effect
   Google Scholar
• Pines , D. and Schrieffer , J.R. 1958 . Phys. Rev. , 1 : 407 – 407 . Criticizes Wentzel's derivation of the Meissner effect
   Google Scholar
• Pippard , A.B. 1953 . Proc. roy. Soc. A , 216 : 547 – 547 . Non-local phenomenological theory
   Google Scholar
• Reif , F. 1957 . Phys. Rev. , 106 : 208 – 208 . Measurements of the Knight shift in colloidal superconducting mercury (Δω/ω≃1.6%; Δω/ω≃2.5/% for normal state)
   Web of Science ®Google Scholar
• Reynolds , C.A. , Serin , B. and Nesbitt , L.B. 1951 . Phys. Rev. , 84 : 691 – 691 . see Reynolds et al., 1950
   Web of Science ®Google Scholar
• Reynolds , C.A. , Serin , B. , Weight , W.H. and Nesbitt , L.B. 1950 . Phys. Rev. , 78 : 487 – 487 . Isotope effect in mercury
   Web of Science ®Google Scholar
• Richards , P.L. and Tinkham , M. 1958 . Phys. Rev. Letters , 1 : 318 – 318 . Infra-red absorption measurements
   Google Scholar
• Rickayzen , G. 1958 . Phys. Rev. , 111 : 817 – 817 . Attempts a gauge-invariant derivation of the Meissner effect
   Google Scholar
• Sawada , K. 1957 . Phys. Rev. , 106 : 372 – 372 . Theory of Coulomb correlations in the limit of high density
   Web of Science ®Google Scholar
• Schafroth , M.R. 1951 . Helv. phys. acta , 24 : 645 – 645 . London's equations in Fourier space; statistical mechanical perturbation theory; 1955, Phys. Rev., 100, 463; Superconductivity of a charged ideal Bose gas; 1958, Ibid., 111, 72; Shows the need for a rigorously gauge-invariant theory of the Meissner effect
   Google Scholar
• Schafroth , M.R. and Blatt , J.M. 1955 . Phys. Rev. , 100 : 1221 – 1221 . 1956, Nuovo Cim., 4, 786; Phenomenological theory, with a finite correlation length
   Google Scholar
• Schafroth , M.R. , Butler , S.T. and Blatt , J.M. 1957 . Helv. phys. acta , 30 : 93 – 93 . Quasi-chemical equilibrium model for superconductivity
   Google Scholar
• Serin B. Hand, Phys./Encycl. Phys. 1956 15 210 210 (Berlin: Springer) Extensive review of experiments on superconductivity
   Google Scholar
• Shoenberg , D. 1952 . Superconductivity , 2nd ed , Cambridge : University Press . A very full account of the experimental knowledge about superconductivity; 1953, Suppl. Nuovo Cimento., 10, 459; Review of Russian work
   Google Scholar
• Seitz , F. 1940 . The modern theory of solids , New York : McGraw-Hill . Contains Bardeen's derivation of the Bloch matrix elements
   Google Scholar
• Sommerfeld A. Bethe H.A. Handb. Phys. 1933 24 2 333 333 2 e Aufl (Berlin: Springer) Electron theory of metals, including a full account of the Bloch theory of conduction
   Google Scholar
• Tolmachev , V.V. and Tyablikov , S.V. 1958 . Zh. eksp. teor. Fiz. , 34 : 66 – 66 . (translated in Sov. Phys. JETP 7, 46); Use of the quasi-particle transformation with the renormalized Hamiltonian
   Google Scholar
• Tyablikov , S.V. and Tolmachev , V.V. 1958 . Zh. eksp. teor. Fiz. , 34 : 1254 – 1254 . (translated in Sov. Phys. jetp, 7, 867); The condition for lattice stability under the electron-phonon interaction
   Google Scholar
• Valatin , J.G. 1958 . Novo Cimento , 7 : 843 – 843 . Quasi-particle notation for Bardeen-Cooper-Schrieffer theory
   Google Scholar
• Wada , Y. , Takano , F. and Fukuda , N. 1958 . Prog. theor. Phys. , 19 : 5 – 5 . Exact solution of the Bardeen-Cooper-Schrieffer model with strong coupling
   Google Scholar
• Weiss , P. 1907 . J. Phys. , 6 : 661 – 661 . Theory of ferromagnetism
   Google Scholar
• Wentzel , G. 1951 . Phys. Rev. , 83 : 168 – 168 . Lattice instability if Fröhlich's interaction constant is too large; 1958, Ibid., 111, 1488; Derives a Meissner effect by a perturbative expansion in the magnetic field and a Bogoliubov quasi-particle transformation
   Google Scholar
• Wilson , A.H. 1953 . Theory of metals , 2nd ed , Cambridge : University Press . Contains a very full account of the Bloch theory
   Google Scholar
• Zavaritskií , N.V. 1957 . Zh. eksp. teor. Fiz. , 33 : 1085 – 1085 . (translated in Sov. Phys. jetp, 6, 837); Measurement of thermal conductivity and specific heat of tin to 0.18°K
   Google Scholar