Statistical Mechanics of Superconductivity

1. Front Matter

   Pages i-xi

   PDF

2. Review of Thermodynamics

   • Takafumi Kita

   Pages 1-12

3. Basics of Equilibrium Statistical Mechanics

   • Takafumi Kita

   Pages 13-23

4. Quantum Mechanics of Identical Particles

   • Takafumi Kita

   Pages 25-41

5. Statistical Mechanics of Ideal Gases

   • Takafumi Kita

   Pages 43-60

6. Density Matrices and Two-Particle Correlations

   • Takafumi Kita

   Pages 61-71

7. Hartree–Fock Equations and Landau’s Fermi-Liquid Theory

   • Takafumi Kita

   Pages 73-89

8. Attractive Interaction and Bound States

   • Takafumi Kita

   Pages 91-99

9. Mean-Field Equations of Superconductivity

   • Takafumi Kita

   Pages 101-123

10. BCS Theory

    • Takafumi Kita

    Pages 125-141

11. Superfluidity, Meissner Effect, and Flux Quantization

    • Takafumi Kita

    Pages 143-157

12. Responses to External Perturbations

    • Takafumi Kita

    Pages 159-174

13. Tunneling, Density of States, and Josephson Effect

    • Takafumi Kita

    Pages 175-187

14. P-Wave Superfluidity

    • Takafumi Kita

    Pages 189-200

15. Gor’kov, Eilenberger, and Ginzburg–Landau Equations

    • Takafumi Kita

    Pages 201-227

16. Abrikosov’s Flux-Line Lattice

    • Takafumi Kita

    Pages 229-246

17. Surfaces and Vortex Cores

    • Takafumi Kita

    Pages 247-263

18. Solutions to Problems

    • Takafumi Kita

    Pages 265-286

19. Back Matter

    Pages 287-289

    PDF

This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch–De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematicalclarity based on a coherent state in terms of the Cooper-pair creation operator, a quasiparticle field for describing the excitation and the variational principle in statistical mechanics. They have the advantage that the phase coherence due to the Cooper-pair condensation can be clearly seen making the superfluidity comprehensible naturally. Subsequently, they are applied to homogeneous cases to describe the BCS theory for classic s-wave superconductors and its extension to the p-wave superfluidity of ³He. Later, the mean-field equations are simplified to the Eilenberger and Ginzburg–Landau equations so as to describe inhomogeneous superconductivity such as Abrikosov’s flux-line lattice concisely and transparently. Chapters provide the latest studies on the quasiclassical theory of superconductivity and a discovery of p-wave superfluidity in liquid ³He. The book serves as a standard reference for advanced courses of statistical mechanics withexercises along with detailed answers.

• Abrikosov’s Flux-line Lattice
• Bogoliubov-de Gennes Equations
• Coherence of the Cooper-pair Condensation
• Cooper-pair Condensation and BCS Theory
• Eilenberger Equations
• Ginzburg-Landau Theory
• Landau Theory of Fermi Liquids
• Origin of Superfluidity
• Second Quantization
• Spin-statistics Theorem

“This book has a unique approach to formulating mean field theory of superconductivity especially in a way most useful for studying inhomogeneous and/or unconventional superconductors. Building up from the fundamental laws of thermodynamics and the basic techniques of statistical mechanics such that it is readable for students, it develops the Bogoliubov-de Gennes formalism of superconductivity. The book culminates in derivation of the quasiclassical theory of superconductivity and its application to description of vortex states. While it is informative and useful for researchers in the field, it is an excellent textbook – either as the main text or for supplementary reading – for a variety of graduate courses ranging from a standard class on statistical mechanics or condensed matter physics to more specialised classes such as one on superconductivity.” (Professor K.Tanaka, Department of Physics & Engineering Physics, University of Saskatchewan)

• Department of Physics, Hokkaido University, Sapporo, Japan

  Takafumi Kita

Takafumi Kita is an associate professor at Department of Physics, Hokkaido University, Japan. He obtained a PhD from Department of Applied Physics, the University of Tokyo in 1988. He held positions at Institute of Solid State Physics, the University of Tokyo (1988-1993, research associate), at Department of Physics and Astronomy, University of Illinois at Urbana-Champaign (1991-1993, visiting scientist), and joined Hokkaido University subsequently. He spent a year in Germany (2000-2001) at University of Karlsruhe and at University of Bayreuth (half a year per each) as an overseas research fellow. He has been teaching quantum mechanics, thermodynamics, statistical mechanics, mathematical methods in physics, field theory in statistical mechanics, etc., over 20 years.

Policies and ethics