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Beyond Zero Resistance – Phenomenology of Superconductivity

Beyond Zero Resistance – Phenomenology of Superconductivity. Nicholas P. Breznay SASS Seminar – Happy 50 th ! SLAC April 29, 2009. Preview. Motivation / Paradigm Shift Normal State behavior Hallmarks of Superconductivity Zero resistance Perfect diamagnetism Magnetic flux quantization

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Beyond Zero Resistance – Phenomenology of Superconductivity

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  1. Beyond Zero Resistance – Phenomenology of Superconductivity Nicholas P. Breznay SASS Seminar – Happy 50th! SLAC April 29, 2009

  2. Preview Motivation / Paradigm Shift Normal State behavior Hallmarks of Superconductivity Zero resistance Perfect diamagnetism Magnetic flux quantization Phenomenology of SC London Theory, Ginzburg-Landau Theory Length scales: l and x Type I and II SC’s

  3. Physics of Metals - Introduction Atoms form a periodic lattice Know (!) electronic states key for the behavior we are interested in Solve the Schro … … in a periodic potential K is a Bravais lattice vector Wikipedia

  4. Physics of Metals – Bloch’s Theorem Bloch’s theorem tells us that eigenstates have the form … … where u(r) is a function with the periodicity of the lattice … Free particle Schro Wikipedia

  5. Physics of Metals – Drude Model Model for electrons in a metal Noninteracting, inertial gas Scattering time t Apply Fermi-Dirac statistics damping term http://www.doitpoms.ac.uk/tlplib/semiconductors/images/fermiDirac.jpg

  6. Physics of Metals – Magnetic Response Magnetism in media Larmor/Landau diamagnetism Weak anti-// response Pauli paramagnetism Moderate // response Typical c values – cCu~ -1 x 10-5 cAl~ +2 x 10-5  minimal response to B fields mr ~ 1  B = m0H in SI linear response familiarly

  7. Physics of Metals – Drude Model Comments Wrong! Lattice, e-e, e-p, defects, t ~ 10-14 seconds  MFP ~ 1 nm Useful! DC, AC electrical conductivity Thermal transport Lorenz number k/sT Heat capacity of solids Lattice Electronic contribution Wikipedia

  8. Preview Motivation / Paradigm Shift Normal State behavior Hallmarks of Superconductivity Zero resistance Perfect diamagnetism Magnetic flux quantization Phenomenology of SC London Theory, Ginzburg-Landau Theory Length scales: l and x Type I and II SC’s

  9. Hallmark 1 – Zero Resistance Metallic R vs T e-p scattering (lattice interactions) at high temperature Impurities at low temperatures R Lattice (phonon) interactions Electrical resistance Impure metal Residual Resistance (impurities) R0 Pure metal TD/3 Temperature

  10. Hallmark 1 – Zero Resistance Superconducting R vs T R Superconductor R0 Tc Temperature “Transition temperature”

  11. Hallmark 1 – Zero Resistance Hard to measure “zero” directly Can try to look at an effect of the zero resistance Current flowing in a SC ring Not thought experiment – standard configuration for high-field laboratory magnets (10-20T) Nonzero resistance  changing current  changing magnetic field One such measurement  Magnetic (dipole) field I Circulating supercurrent Superconductor From Ustinov “Superconductivity” Lectures (WS 2008-2009)

  12. Hallmark 1 – Zero Resistance Notes R = 0 only for DC AC response arises from kinetic inductance of superconducting electrons Changing current  electric field Model: perfect resistor (normal electrons), inductor (SC electrons) in parallel Magnitude of “kinetic inductance”:  At 1 kHz, http://www.apph.tohoku.ac.jp/low-temp-lab/photo/FUJYO1.png

  13. Hallmark 2 – Conductors in a Magnetic Field Normal metal Apply field Field off

  14. Hallmark 2 – Conductors in a Magnetic Field Normal metal Perfect (metallic) conductor Superconductor Apply field Apply field Apply field Cool Cool Field off

  15. Hallmark 2 – Meissner-Oschenfeld Effect B = 0  perfect diamagnetism: cM = -1 Field expulsion unexpected; not discovered for 20 years. Superconductor Apply field Cool B/m0 -M H H Hc Hc

  16. Hallmark 3 – Flux Quantization Earth’s magnetic field ~ 500 mG, so in 1 cm2 of BEarth there are ~ 2 million f0’s. first appearance of h in our description; quantum phenomenon Total flux (field*area) is integer multiple of f0

  17. Hallmark 3 – Flux Quantization Apply uniform field Measure flux

  18. Aside – Cooper Pairing In the presence of a weak attractive interaction, the filled Fermi sphere is unstable to the formation of bound pairs electrons Can excite two electrons de above Ef, obtain bound-state energy < 2Ef due to attraction New minimum-energy state allows attractive interaction (e-p scattering) by smearing the FS The physics of superconductors Shmidt, Müller, Ustinov

  19. Preview Motivation / Paradigm Shift Normal State behavior Hallmarks of Superconductivity Zero resistance Perfect diamagnetism Magnetic flux quantization Phenomenology of SC London Theory, Ginzburg-Landau Theory Length scales: l and x Type I and II SC’s

  20. SC Parameter Review Magnetic field  energy density Extract free energy difference between normal and SC states with Hc Know magnetic response important; use R = 0 + Maxwell’s equations … ? g(H) gnormal state gsc state H Hc

  21. London Theory – 1 Newton’s law (inertial response) for applied electric field Supercurrent density is Faraday’s law We know B = 0 inside superconductors Fritz & Heinz London, (1935)

  22. London Theory – 2 London Equations Ampere’s law =0; Gauss’s law for electrostatics

  23. Magnetic Penetration Depth - l Screening not immediate; characteristic decay length Typical l ~ 50 nm m,e fixed – l uniquely specifies the superconducting electron density ns SC B(z) B0 Sometimes called the “superfluid density” z l

  24. Ginzburg-Landau Theory - 1 First consider zero magnetic field Order parameter y Associate with cooper pair density: Expand f in powers of |y|2  To make sense, b > 0, a = a(T) Free energy of superconducting state Free energy of normal state Free energy of SC state ~ # of cooper pairs Need y > -Infinity; B > 0

  25. Ginzburg-Landau Theory - 2 • For a < 0, solve for minimum in fs-fn … http://commons.wikimedia.org/wiki/File:Pseudofunci%C3%B3n_de_onda_(teor%C3%ADa_Ginzburg-Landau).png

  26. Ginzburg-Landau Theory - 3 • Know that fn-fs is the condensation energy:

  27. Ginzburg-Landau Theory - 4 Momentum term in H: Now – include magnetic field Classically, know that to include magnetic fields …

  28. Ginzburg-Landau Theory - 5 Free Energy Density

  29. Ginzburg-Landau Theory - 6 Take y real, normalize Define Linearize in y

  30. Superconducting coherence length - x Characteristic length scale for SC wavefunction variation Vacuum SC y(x) Superconductor x x

  31. London Theory magnetic penetration depth l Ginzburg-Landau Theory coherence length x l + x two kinds of superconductors! Pause

  32. Surface Energy and “Type II” H(x) H(x) y(x) y(x) x l l x x x

  33. Surface Energy: x > l H(x) y(x) SC x l energy penalty for excluding B gmagnetic(x) gsc(x) energy gain for being in SC state

  34. Surface Energy: x > l H(x) y(x) SC x l energy penalty for excluding B gmagnetic(x) gsc(x) energy gain for being in SC state gnet(x) net energy penalty at a surface / interface

  35. Surface Energy: x < l H(x) y(x) SC l x energy penalty for excluding B gmagnetic(x) gsc(x) energy gain for being in SC state gnet(x) net energy gain at a surface / interface

  36. Type I Type II predicted in 1950s by Abrikosov • elemental superconductors

  37. Type II Superconductors (x < l) Normal state cores Superconducting region H http://www.nd.edu/~vortex/research.html

  38. London Theory magnetic penetration depth l Ginzburg-Landau Theory coherence length x l + x two kinds of superconductors The End

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