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Introduction to Conventional Superconductivity

Introduction to Conventional Superconductivity. Ziling Li 2018.07.02. Conventional Superconductivity. Background Classical theory: London theory & Ginzburg-Landau theory Quantum theory: BCS theory 2D superconductivity. Conventional Superconductivity. Background

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Introduction to Conventional Superconductivity

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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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