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Superconductivity Basics
Evolution of Understanding Phenomenology & Theory Predictions Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Literatures Introduction to Superconductivity Michael Tinkham, McGraw-Hill, Inc. Fundamentals of the Theory of Metals A. A. Abrikosov, North-Holland, 1988 Shuichi Noguchi 6-th ILC School, November 2011
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Evolution of Understanding
Phenomena Parameter Phenomenology Theory Zero DC Resistance Tc Onnes 1911 Phase Transition Hc, T Dependence Specific Heat Meissner Effect B = 0 Below Hc Meissner,Ochsenfeld 1933 Two Fluid Model Gorter, Casimir 1934 λ Penetration Depth London 1935 Impurity Effect ξ Pippard, Coherence Length Modification of London 1953 Δ Energy Gap Order Parameter Ginzburug-Landau 1950 κ Boundary Energy Type I, First Order Transition Intermediate State Fluxoid TypeII, Second Order Transition Mixed State Hc1 Abrikosov 1957 Hc2 Hc3 Electron-Phonon Isotope Effect Frolich 1950 BCS 1957 Vogoliubov GL Equation from BCS Theory Gorkov 1959 Strong Coupling Makmilan RF Surface Resistance Mattis Bardeen, Miller Josephson Effect Josephson Josephson 1962 High Tc Material Bednorz,Muller 1986 Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Observation Zero Resistance Jump of Specific Heat Meissner Effect Critical Magnetic Field Shuichi Noguchi 6-th ILC School, November 2011
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Observed Phase Transition
Hc Electron Specific Heat Normal State H0 Hc(T) = H0 {1-t2} t = T/Tc B = 0 Meissner State gT Tc T Tc T Shuichi Noguchi 6-th ILC School, November 2011
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Phase Transition of Superconductor
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6-th ILC School, November 2011
Thermodynamics n–th Order Phase Transition (n-1)-th Order Derivatives are continuous n-th Order Derivatives are not continuous Shuichi Noguchi 6-th ILC School, November 2011
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Phase Transition (Type-I)
Free Energy First Order Hc(T) Ｔ Tc Shuichi Noguchi 6-th ILC School, November 2011
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Something happen in the Electron System Super Electron
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Two Fluid Model by Gorter & Casimir
Specific Heat n = nn + nS Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Specific Heat Home Work Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Specific Heat Thermal Conductivity Shuichi Noguchi 6-th ILC School, November 2011
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Two Fluid Model by London
n = ns + nn Super Electron = Zero Resistance Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Ampere London Meissner State Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Static Field Shuichi Noguchi 6-th ILC School, November 2011
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Maxwell + London Equation
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Surface Impedance ; London
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Surface Impedance Normal
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6-th ILC School, November 2011
Surface Resistance Rs BCS Shuichi Noguchi 6-th ILC School, November 2011
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Impurity Effect ; Pippard
Shuichi Noguchi 6-th ILC School, November 2011
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Pippard modified London Eq.
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Success of Two Fluid Model
Specific Heat Meissner Effect T Dependence of Hc Ｔ Dependence of λ Impurity Effect What is the superelectron ? Shuichi Noguchi 6-th ILC School, November 2011
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Ginzburg – Landau Phenomenology
Not Uniform Not Independent on Near Tc Approximation ; << 1 No Dynamics Higher order terms are neglected. Shuichi Noguchi 6-th ILC School, November 2011
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Gintzburg – Landau Equation
Stable State is Free Energy Minimum Shuichi Noguchi 6-th ILC School, November 2011
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Outputs from GL Equation , Step I
> Tc = Tc G < Tc Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Step II Shuichi Noguchi 6-th ILC School, November 2011
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Step III , Coherence Length
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6-th ILC School, November 2011
Coherence Length Shuichi Noguchi 6-th ILC School, November 2011
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Appearance of Superconductivity
Eigen Value Shuichi Noguchi 6-th ILC School, November 2011
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Appearance of Superconductivity
Minimum Eigen Value Bulk Different Boundary Condition Shuichi Noguchi 6-th ILC School, November 2011
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Magnetic Behavior of Superconductor
H<<HC H~HC Fluxoid Normal State (Hc) Type-I Intermediate State Type-II Mixed State Shuichi Noguchi 6-th ILC School, November 2011
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Intermediate State (Type-I)
ｄ S S S S S S D How Normal Region are Divided ? Landau (1937) Shuichi Noguchi 6-th ILC School, November 2011
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Boundary Energy (One dimensional)
ξ λ x From Step III Normal Super Shuichi Noguchi 6-th ILC School, November 2011
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Boundary Energy Results
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Ａｂｒｉｋｏｓｏｖ Boundary Energy of Fluxoid
Cylindrical Coordinate, Bulk 2m0Hc1 ξ λ B r Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Fluxoid Energy κ>>1 Shuichi Noguchi 6-th ILC School, November 2011
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Lower Critical Magnetic Field at Surface
Surface Barrier / Superheating Model Effect of Mirror Image of Fluxoid
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Phase Diagram of Type II Superconductor
Bulk Parallel to Surface HC3 HC2 Normal State Mixed State HC HC HC1 HS Meisnner State T T Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Fluxoid Trapping Pinning Effect even at H << HC Residual Magnetic Field T Tc Fluxoid Trapping Residual Resistance Cavity Wall Shuichi Noguchi 6-th ILC School, November 2011
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Critical RF Magnetic Field HCRF
????? Fluxoid HRF HCRF Cavity Wall Shuichi Noguchi 6-th ILC School, November 2011
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Ｇｏｒｋｏｖ showed using BCS Theory
T ~ TC Shuichi Noguchi 6-th ILC School, November 2011
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Typical Superconductor
Nb Pb Nb3Sn Critical Temperature TC （Ｋ） 9.25 7.2 18.3 Energy Gap 2Δ(0)/kBTc 3.5 3.6 4.5 Penetration Depth λ（０） （ｎｍ） 32 28 170 Coherence Length ξ（０） （ｎｍ） 39 110 3 Ginzburg-Landau Parameter κ（０） 0.82 0.25 56 Thermo dynamical Critical Magnetic Field μ０ＨＣ （Ｔ） 0.2 0.08 0.53 μ０ＨＣ１ （Ｔ） 0.18 0.01 μ０ＨＣ２ （Ｔ） 0.4 29 Fluxoid Φ0 2.068 x Wb Boltzman Constant kＢ 1.38 x JK-1 = x 10-5 eV K-1 Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Theory BCS Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Flohrich Isotope Effect Not a Coulomb Interaction k - q k’+ q k’+ q k - q Phonon q + - q V k k’ k k’ Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Fermi Distribution PF,εＦ Spin up Spin down N(e) T=0 Fermi Sphere T ε εＦ Shuichi Noguchi 6-th ILC School, November 2011
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Cooper Pair Interaction
How the Fermi Sphere is changed by Phonon Interaction ? Probability Amplitude Occupied vk vk’ Empty uk uk’ vk2 + uk2 = vk’2 + uk’2 = 1 Shuichi Noguchi 6-th ILC School, November 2011
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Total Energy of the System
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6-th ILC School, November 2011
vk2 uk2 Normal 2Δｋ Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
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Prediction of BCS Theory
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6-th ILC School, November 2011
Near Tc Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
Ｔ～０ Shuichi Noguchi 6-th ILC School, November 2011
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6-th ILC School, November 2011
RF Surface Resistance Shuichi Noguchi 6-th ILC School, November 2011
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BCS Surface Resistance
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6-th ILC School, November 2011
Shuichi Noguchi 6-th ILC School, November 2011
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