SoSe 23: Superconductivity and Higgs Spectroscopy
Dirk Manske
Kommentar
Table of Contents
1 Green’s function and Observables
T=0, spectral representation, sum rules
Matsubara Green functions
Connection to observables
Feynman diagrams
2 Meanfield theory of superconductivity, BCS Theory
Hartree-Fock
Gorkov equations
Singlet order parameters
Pairing interaction
Self-consistency
Critical temperature
Current carrying state
Abrikosov vortex lattice
Higher angular momentum pairing
3 Functional methods
Green’s function from the path integral
Grassmann numbers
Coherent state path integral
Gaussian integration
Coherent state path integral
Superconductivity from the path integral
Hubbard Stratonovich transformation
Saddle point equation
4 Collective modes
Higgs and Leggett mode from the path integral
Anderson-Higgs mechanism
Symmetry action in Landau Ginzburg theories
Anderson’s theorem: impurity scattering
5 Higgs spectroscopy: experimental and theoretical methods
General response formalism from effective action
Linear response
Linear coupling to Leggett mode
Fluctuation dissipation theorem
Gauge invariance
Nonlinear response
Kernel method of quasi-equilibrium
Sum-Frequency Generation (SFG), Difference-Frequency-Generation (DFG)
Excitation schemes for collective modes: Quench, drive (THG)
Polarization dependence
Raman spectroscopy
A manuscript of the lecture will be delivered.
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