TTC Workshop, Fermilab, November 15, 2017 Nonequilibrium Superconductvity in Inhomogeneous Materials James A. Sauls & Wave Ngampruetikorn Center for Applied Physics & Superconducting Technologies Northwestern University & Fermilab Electrodynamics of Superconductors Inhomogeneous Surface Structures Vortex Nucleation, Dynamics & Instabilities NSF-PHY 01734332 James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Electrodynamics of Superconductor-Vacuum Interfaces Vacuum Nb ◮ Program: “Real Materials” Calculations of the Current Response & Local EM Fields near ↔ R J ( q , ω ) = − 1 q � ( q , ω ; � A ) · � A ( q , ω ) K Superconducting-Vacuum Interfaces c James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Electrodynamics of Superconductor-Vacuum Interfaces Vacuum Nb ◮ Program: “Real Materials” Calculations of the Current Response & Local EM Fields near ↔ R J ( q , ω ) = − 1 q � ( q , ω ; � A ) · � A ( q , ω ) K Superconducting-Vacuum Interfaces c ◮ Material Inputs to Nonequilibrium SC Theory ◮ Fermi Surfaces - DFT dHvA, dI / dV & APRPES ◮ Pairing/Decoherence via Electron-Phonon Coupling James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Electrodynamics of Superconductor-Vacuum Interfaces Vacuum Nb ◮ Program: “Real Materials” Calculations of the Current Response & Local EM Fields near ↔ R J ( q , ω ) = − 1 q � ( q , ω ; � A ) · � A ( q , ω ) K Superconducting-Vacuum Interfaces c ◮ Material Inputs to Nonequilibrium SC Theory ◮ Fermi Surfaces - DFT dHvA, dI / dV & APRPES ◮ Pairing/Decoherence via Electron-Phonon Coupling ◮ Impurity & Structural Disorder James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Electrodynamics of Superconductor-Vacuum Interfaces Vacuum Nb ◮ Program: “Real Materials” Calculations of the Current Response & Local EM Fields near ↔ R J ( q , ω ) = − 1 q � ( q , ω ; � A ) · � A ( q , ω ) K Superconducting-Vacuum Interfaces c ◮ Material Inputs to Nonequilibrium SC Theory ◮ Fermi Surfaces - DFT dHvA, dI / dV & APRPES ◮ Pairing/Decoherence via Electron-Phonon Coupling ◮ Impurity & Structural Disorder Surface Scattering: S surf ( p , p ′ ) ◮ surface structure factor ◮ mesoscopic roughnes � backscattering � Andreev scattering � sub-gap dissipation James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Electrodynamics of Superconductor-Vacuum Interfaces Vacuum Nb ◮ Program: “Real Materials” Calculations of the Current Response & Local EM Fields near ↔ R J ( q , ω ) = − 1 q � ( q , ω ; � A ) · � A ( q , ω ) K Superconducting-Vacuum Interfaces c ◮ Material Inputs to Nonequilibrium SC Theory ◮ Theoretical & Analytical Tools ◮ Fermi Surfaces - DFT dHvA, dI / dV & APRPES QFT ` a la Matsubara, Abrikosov, Gorkov ◮ Pairing/Decoherence via Electron-Phonon Coupling Eilenberger, Larkin & Ovchinnikov ◮ Impurity & Structural Disorder Migdal-Eliashberg: electron-phonon Surface Scattering: S surf ( p , p ′ ) Asymptotic Expansions: k B T c / E f , ¯ h / τ E f , ¯ h / p f ξ , ¯ h ω / E f ... ◮ surface structure factor ◮ mesoscopic roughnes � backscattering � Andreev scattering Symmetry, Selection Rules & Scattering Theory � sub-gap dissipation James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Electrodynamics of Superconductor-Vacuum Interfaces Vacuum Nb ◮ Program: “Real Materials” Calculations of the Current Response & Local EM Fields near ↔ R J ( q , ω ) = − 1 q � ( q , ω ; � A ) · � A ( q , ω ) K Superconducting-Vacuum Interfaces c ◮ Material Inputs to Nonequilibrium SC Theory ◮ Theoretical & Analytical Tools ◮ Fermi Surfaces - DFT dHvA, dI / dV & APRPES QFT ` a la Matsubara, Abrikosov, Gorkov ◮ Pairing/Decoherence via Electron-Phonon Coupling Eilenberger, Larkin & Ovchinnikov ◮ Impurity & Structural Disorder Migdal-Eliashberg: electron-phonon Surface Scattering: S surf ( p , p ′ ) Asymptotic Expansions: k B T c / E f , ¯ h / τ E f , ¯ h / p f ξ , ¯ h ω / E f ... ◮ surface structure factor ◮ mesoscopic roughnes � backscattering � Andreev scattering Symmetry, Selection Rules & Scattering Theory � sub-gap dissipation ◮ Developing Methods & Numerical Codes to Compute the Nonlinear A.C. Surface Impedance James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Electrodynamics of Superconductor-Vacuum Interfaces Vacuum Nb ◮ Program: “Real Materials” Calculations of the Current Response & Local EM Fields near ↔ R J ( q , ω ) = − 1 q � ( q , ω ; � A ) · � A ( q , ω ) K Superconducting-Vacuum Interfaces c ◮ Material Inputs to Nonequilibrium SC Theory ◮ Theoretical & Analytical Tools ◮ Fermi Surfaces - DFT dHvA, dI / dV & APRPES QFT ` a la Matsubara, Abrikosov, Gorkov ◮ Pairing/Decoherence via Electron-Phonon Coupling Eilenberger, Larkin & Ovchinnikov ◮ Impurity & Structural Disorder Migdal-Eliashberg: electron-phonon Surface Scattering: S surf ( p , p ′ ) Asymptotic Expansions: k B T c / E f , ¯ h / τ E f , ¯ h / p f ξ , ¯ h ω / E f ... ◮ surface structure factor ◮ mesoscopic roughnes � backscattering � Andreev scattering Symmetry, Selection Rules & Scattering Theory � sub-gap dissipation ◮ Developing Methods & Numerical Codes to Compute the Nonlinear A.C. Surface Impedance ◮ Nonequilibrium Quasiparticle, Cooper Pair & Vortex Dynamics D. Rainer & J. A. Sauls, Strong-Coupling Theory of Superconductivity, World Scientific (1995) James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
S1S2heVeh Sub-Gap Dissipation in Weak Links under a.c. Excitation 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sub-Gap Dissipation Multiple Andreev Reflection � dissipation Impurity & Branch Conversion Scattering � Non-equilibrium QP distribution T. Klapwijkz, G. Blonder and M. Tinkham, Physica BC 109, 1657 (1982). E. Zhao and JAS, Nonequilibrium Josephson Weak-Links, PRB 78, 174511 (2008). James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
Vortex Structure, Nucleation and Dynamics in Superconductors Program: Computational Theory for Vortex Structure, Spectroscopy, & Non-Equilibrium Vortex Nucleation, Dissipation & Instabilities � ∇ ϑ · d � = m × 2 π h Ψ ( R , t ) = | Ψ ( R , t ) | e i ϑ ( R , t ) v f R = h ( m, n ) � C d R · ∇ ϑ ( R , t ) = m C 2 π ◮ Vortex Structures & Dynamics ◮ Nucleation, Pinning & Catastrophes Core Structure in Strong-Coupling SCs Phase Fluctuations at Surfaces Field & Current Distributions Surface Nucleation Barriers NMR & SANS - Spectrosocpy Disorder Fluctuations & Pinning Electrodynamics of Vortex States Critical Currents & Critical States ◮ Robert Regan & JAS, Northwestern & CAPST James A. Sauls & Wave Ngampruetikorn Nonequilibrium Superconductvity in Inhomogeneous Materials
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