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Introduction to Conventional Superconductivity: Theoretical Background and Physical Properties

Explore the classical and quantum theories of superconductivity, including the BCS theory, London theory, and Ginzburg-Landau theory. Learn about the historical development, thermodynamics, and electrodynamics of superconductors, as well as the Ising superconductivity and Majorana Fermion in 2D materials. Understand the origin of superconductive carriers, critical temperature, and superconductive gaps. Delve into the principles of Cooper pairs, singlet pairing, and triplet cooper pairs in different superconducting systems.

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Introduction to Conventional Superconductivity: Theoretical Background and Physical Properties

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  1. Introduction toConventionalSuperconductivity Ziling Li 2018.07.02

  2. Conventional Superconductivity • Background • Classical theory: London theory & Ginzburg-Landau theory • Quantum theory: BCS theory • 2D superconductivity

  3. Conventional Superconductivity • Background • Classical theory: London theory & Ginzburg-Landau theory • Quantum theory: BCS theory • 2D superconductivity Historical story of superconductivity; basic physical properties of superconductors.

  4. Conductivity of metal at low temperature? Before 1911 Scientific American. March, 1997

  5. Physical properties of superconductors Zero resistance Meissner effect Critical field/current Persistent current

  6. Superconducting elements

  7. Conventional Superconductivity • Background • Classical theory: London theory & Ginzburg-Landau theory • Quantum theory: BCS theory • 2D superconductivity Thermodynamics and electrodynamics of superconductors.

  8. Thermodynamics of superconductor • Gibbs free energy For constant and , Gibbs free energy per unit volume When , Meissner effect: Gorter-Casimir formula:

  9. Thermodynamics of superconductor • Entropy latent heat: when , , . • Specific heat when , From Experiment: Electrons open a gap

  10. Two-fluid model • ; : normal electrons, : superconductive electrons. • Only normal electrons make contribution to resistance and entropy. • Order parameter: ; , . • Two fluids are independent and completely penetration.

  11. London theory At Steady condition ，. London equations + Maxwell equations + Continuity equation where , penetration depth Zero resistance Meissner effect Current distribution

  12. Ginzburg-Landau theory Order parameter: pseudo wave function: , Free energy density: Landau 2nd PT: Inhomogeneous material: External field: Gibbs free energy density: Gibbs free energy:

  13. Ginzburg-Landau theory Variation at 1st G-L equation: 1st Boundary condition:

  14. Ginzburg-Landau theory Variation at 2nd G-L equation: 2nd Boundary condition:

  15. Ginzburg-Landau theory 1st G-L equation: at zero field Let , where at zero field Let , coherent length 2nd G-L equation: Let , penetration depth =

  16. Type-I and Type-II superconductors Ginzburg-Landau parameter: , positive interface energy. Type-I SC , negative interface energy. Type-II SC Magnetic flux vortex

  17. Type-I and Type-II superconductors

  18. Conventional Superconductivity • Background • Classical theory: London theory & Ginzburg-Landau theory • Quantum theory: BCS theory • 2D superconductivity Origin of superconductive carrier; superconductive gap; critical temperature.

  19. Cooper pair Singlet pairing, creator and annihilator , Ground state wave function Hamiltonian Total Energy Minimal energy condition , Electron-phonon interaction

  20. Superconductive gap Break cooper pair need energy Single particle excitation: Density of state: ()

  21. Critical temperature K BCS theory: Similarly, , , : Isotope effect Doping : change Au, Ag, Cu : very weak

  22. Conventional Superconductivity • Background • Classical theory: London theory & Ginzburg-Landau theory • Quantum theory: BCS theory • 2D superconductivity Ising superconductivity; Zeeman-type SOC; Majorana Fermion.

  23. 2D Ising superconductivity • 2D TMDCs Ising superconductivity ( example: ) Hamiltonian near and valley: (for /valley) - T for Lu,J.M. et al. Science350, 1353–1357 (2015).

  24. Large in-plane upper critical magnetic field Saito,Y. et al. Nat. Phys.12, 144–149 (2016). Lu,J.M. et al. Science350, 1353–1357 (2015).

  25. Large in-plane upper critical magnetic field From 2D G-L equation: Nature Reviews Materials2,16094 (2016)

  26. Topological Superconductivity • Majorana Fermion and zero-energy mode • Majorana zero-energy mode in topological superconductivity

  27. Majorana Fermion • Majorana Fermion: Single-bound state Hamiltonian: Minus energy solution: , Let , , , .

  28. Majorana Fermion in topological SC Cooper pair Triplet cooper pair: p-wave superconductor Or singlet cooper pair: s-wave superconductor + topological insulator

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