Modern Aspects of Superconductivity: Theory of Superconductivity

Contents
Preface
1. Theory of Superconductivity
	1.1. Introduction
	1.2. Spinors
		1.2.1. Spinor
		1.2.2. Noether theorem and Nambu–Goldstone theorem
	1.3. Propagator
		1.3.1. Hamiltonian
	1.4. Non-interacting
	1.5. Interacting
		1.5.1. Unrestricted HF
		1.5.2. Gap equation for superconductivity
	1.6. Illustrative Example, Critical Temperature
		1.6.1. Bond alternation
		1.6.2. Deformation energy
		1.6.3. Polyacene, gap equation, critical temperature
		1.6.4. Conclusion
	1.7. Linear Response Magnetic Resonance in Normal and Superconducting Species: Spin-Lattice Relaxation Time
		1.7.1. Introduction
		1.7.2. T1 in NMR
		1.7.3. Theory with Green’s function
		1.7.4. Non-interacting
		1.7.5. Interacting; normal
	1.8. Interacting; Superconductor
		1.8.1. The extended Nambu spinor
		1.8.2. Green’s function
		1.8.3. Spin dynamics
		1.8.4. Conclusion
	1.9. Ginzburg–Landau Theory from BCS Hamiltonian
		1.9.1. BCS theory
		1.9.2. Hubbard–Stratonovitch transformation
		1.9.3. Fourier transform
		1.9.4. Nambu spinor
		1.9.5. Critical temperature
		1.9.6. Temperature dependence of ϕ
		1.9.7. Dynamics of the boson field, symmetry breaking
		1.9.8. Instability
		1.9.9. Supersymmetry
		1.9.10. Toward the Ginzburg–Landau equation
		1.9.11. Discussion
2. Physics of High-Tc Superconductors
	2.1. Introduction
	2.2. History of the Development of Superconductivity
	2.3. Structural Properties of High-Temperature Superconductors
		2.3.1. Phase diagram of cuprate superconductors
			2.3.1.1. Antiferromagnetism of HTSC
	2.4. Mechanisms of Pairing of High-Temperature Superconductors
		2.4.1. Specific mechanisms of pairing in superconductivity
		2.4.2. Magnetic mechanism of pairing
		2.4.3. Exciton mechanisms of pairing
		2.4.4. The anharmonic model and superconductivity
		2.4.5. Van Hove singularities (vHs)
		2.4.6. Plasmon mechanism of pairing
		2.4.7. Bipolaronic mechanism of superconductivity
	2.5. The Symmetry of Pairing in Cuprate Superconductors
		2.5.1. Superconductor’s order parameter
		2.5.2. Classification of the superconductor’s order parameter by the representations of symmetry groups
	2.6. Experimental Studies of a Symmetry of the Superconducting Order Parameter
		2.6.1. Measurements of the Josephson tunnel current
		2.6.2. Measurements of the quantization of a flow by the technique of three-crystal unit
	2.7. Thermodynamics of the d-Pairing in Cuprate Superconductors
		2.7.1. Introduction
		2.7.2. Antiferromagnetic spin fluctuations in high-temperature superconductors
		2.7.3. Continual model of antiferromagnetic spin fluctuations
		2.7.4. Equation for superconducting gap
		2.7.5. Thermodynamic potential of antiferromagnetic spin fluctuations
		2.7.6. Heat capacity of the d-pairing
		2.7.7. Heat capacity jump in superconductors
	2.8. Summary
3. Iron Superconductors
	3.1. Introduction
	3.2. Structural Properties of Iron Superconductors
	3.3. Compounds of the Type ReFeAsO
	3.4. Compounds of the Type AFe2As2 (A = Ba, Sr, Ca)
	3.5. Compounds of the Type AFeAs (A = Li)
	3.6. Compounds of the Type FeSe and FeTe (iron selenide and iron telluride)
		3.6.1. FeSe films
	3.7. Superconductivity
	3.8. Electronic Structure
		3.8.1. Multiorbital and multizone cases
	3.9. Minimum Model
	3.10. Experimental Study of the Fermi Surface
	3.11. Antiferromagnetism
	3.12. Phase Diagrams
	3.13. Mechanisms and Types of Pairing
		3.13.1. Multizone superconductivity
		3.13.2. Electron–phonon mechanism
		3.13.3. Spin-fluctuation mechanism of pairing
		3.13.4. Symmetry of pairing
		3.13.5. Multiorbital model
	3.14. Properties of a Superconductor with s±-Symmetry of Parameters of Order
	3.15. t–J1–J2 Model
		3.15.1. Superconductivity with different parameters of order
	3.16. Conclusion
4. Multiband Superconductivity
	4.1. Introduction
	4.2. Multiband Hamiltonian
		4.2.1. Hamiltonian
		4.2.2. Two-particle Green’s function
		4.2.3. Traditional superconductivity
		4.2.4. Copper oxides
		4.2.5. Cooperative mechanism
		4.2.6. Room-temperature superconductors
	4.3. Two-gap Superconductivity in MgB2
		4.3.1. The physical properties of MgB2
			4.3.1.1. Mg1−xAlxB2
		4.3.2. Theoretical model
		4.3.3. Superconductivity in MgB2
	4.4. Theoretical Studies of Multiband Effects in Superconductivity by Using the Renormalization Group Approach
		4.4.1. Theoretical model
		4.4.2. Renormalization group approach
		4.4.3. Vertex correction and response function for Cooper pairs
		4.4.4. Renormalization equation
		4.4.5. Phase diagrams
	4.5. Room Superconductors
		4.5.1. On the superconductivity of hydrogen sulfide
		4.5.2. Formalism for standard superconductors
			4.5.2.1. Microscopic theory of superconductivity: BCS theory
		4.5.3. Éliashberg theory
			4.5.3.1. Theory of superconductivity by Éliashberg–McMillan
5. Nanoscale Superconductivity
	5.1. Introduction
	5.2. Nanosize Two-gap Superconductivity
		5.2.1. Hamiltonian for nanosize grains
		5.2.2. Path integral approach
		5.2.3. Condensation energy
		5.2.4. Critical level spacing
		5.2.5. Parity gap
	5.3. Exact Solution of Two-band Superconductivity in Ultrasmall Grains
		5.3.1. Exact solution for two-band superconductivity
		5.3.2. Hamiltonian
		5.3.3. Exact solution
		5.3.4. Preprocessing for numerical calculations
		5.3.5. Results and discussion
		5.3.6. Pair energy level
		5.3.7. Condensation energy
		5.3.8. Parity gap
	5.4. Kondo Effect Coupled to Superconductivity
		5.4.1. Kondo regime coupled to superconductivity
		5.4.2. Model
		5.4.3. Mean-field approximation
		5.4.4. Critical level spacing in the Kondo effect
		5.4.5. Kondo effect coupled to the superconductivity
		5.4.6. Exact solution for the Kondo regime
	5.5. Interaction of Nanoscale Ferromagnetic Granules in London Superconductors
		5.5.1. Magnetic field of ferromagnetic inclusions in a London superconductor
		5.5.2. Magnetic field of ferromagnetic quantum dots in a superconducting nanocomposite material
		5.5.3. Interaction energy of quantum dots in a superconducting nanocomposite material
		5.5.4. Spin orientation phase transitions in a nanocomposite material with arrays of ferromagnetic quantum dots
	5.6. Spin-orientation Phase Transitions in a Two-dimensional Lattice of Ferromagnetic Granules in a London-type Superconductor
	5.7. Energy Spectrum and Wave Function of Electrons in Hybrid Superconducting Nanowires
		5.7.1. Methodology
		5.7.2. Calculation of the spectrum
	5.8. Quantum Computer on Superconducting Qubits
		5.8.1. Principle of quantum computers
		5.8.2. Superconducting qubits
		5.8.3. The Josephson effect
			5.8.3.1. Current passing through two series-connected Josephson junctions
			5.8.3.2. SQUIDS
			5.8.3.3. Flux qubit
			5.8.3.4. Charge qubit
			5.8.3.5. Phase qubit
		5.8.4. Quantum computer
			5.8.4.1. D-wave quantum computer
			5.8.4.2. Quantum advantage of Google
		5.8.5. Topological quantum computers
			5.8.5.1. Majorana fermion
			5.8.5.2. Kitaev’s superconducting chain
Summary and Conclusions
Appendix A
	A.1. Two-particle Green Function for Multiband Superconductors
Appendix B
	B.1. A Solution Method for the Ferromagnetic Granules in the London Superconductors
Bibliography
Index