Superconductivity Basics Evolution of Understanding Phenomenology & Theory Predictions Shuichi Noguchi 6-th ILC School, November 2011
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
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
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
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
Phase Transition of Superconductor Shuichi Noguchi 6-th ILC School, November 2011
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
Phase Transition (Type-I) Free Energy First Order Hc(T) Ｔ Tc Shuichi Noguchi 6-th ILC School, November 2011
Something happen in the Electron System Super Electron Shuichi Noguchi 6-th ILC School, November 2011
Two Fluid Model by Gorter & Casimir Specific Heat n = nn + nS Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Specific Heat Home Work Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Specific Heat Thermal Conductivity Shuichi Noguchi 6-th ILC School, November 2011
Two Fluid Model by London n = ns + nn Super Electron = Zero Resistance Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Ampere London Meissner State Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Static Field Shuichi Noguchi 6-th ILC School, November 2011
Maxwell + London Equation Shuichi Noguchi 6-th ILC School, November 2011
Surface Impedance ; London Shuichi Noguchi 6-th ILC School, November 2011
Surface Impedance Normal Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Surface Resistance Rs BCS Shuichi Noguchi 6-th ILC School, November 2011
Impurity Effect ; Pippard Shuichi Noguchi 6-th ILC School, November 2011
Pippard modified London Eq. Shuichi Noguchi 6-th ILC School, November 2011
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
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
Gintzburg – Landau Equation Stable State is Free Energy Minimum Shuichi Noguchi 6-th ILC School, November 2011
Outputs from GL Equation , Step I > Tc = Tc G < Tc Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Step II Shuichi Noguchi 6-th ILC School, November 2011
Step III , Coherence Length Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Coherence Length Shuichi Noguchi 6-th ILC School, November 2011
Appearance of Superconductivity Eigen Value Shuichi Noguchi 6-th ILC School, November 2011
Appearance of Superconductivity Minimum Eigen Value Bulk Different Boundary Condition Shuichi Noguchi 6-th ILC School, November 2011
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
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
Boundary Energy (One dimensional) ξ λ x From Step III Normal Super Shuichi Noguchi 6-th ILC School, November 2011
Boundary Energy Results Shuichi Noguchi 6-th ILC School, November 2011
Ａｂｒｉｋｏｓｏｖ Boundary Energy of Fluxoid Cylindrical Coordinate, Bulk 2m0Hc1 ξ λ B r Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Fluxoid Energy κ>>1 Shuichi Noguchi 6-th ILC School, November 2011
Lower Critical Magnetic Field at Surface Surface Barrier / Superheating Model Effect of Mirror Image of Fluxoid
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
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
Critical RF Magnetic Field HCRF ????? Fluxoid HRF HCRF Cavity Wall Shuichi Noguchi 6-th ILC School, November 2011
Ｇｏｒｋｏｖ showed using BCS Theory T ~ TC Shuichi Noguchi 6-th ILC School, November 2011
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 10-15 Wb Boltzman Constant kＢ 1.38 x 10-23 JK-1 = 8.617 x 10-5 eV K-1 Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Theory BCS Shuichi Noguchi 6-th ILC School, November 2011
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
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
Cooper Pair Interaction How the Fermi Sphere is changed by Phonon Interaction ? Probability Amplitude Occupied vk vk’ Empty uk uk’ vk2 + uk2 = 1 vk’2 + uk’2 = 1 Shuichi Noguchi 6-th ILC School, November 2011
Total Energy of the System Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 vk2 uk2 Normal 2Δｋ Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Shuichi Noguchi 6-th ILC School, November 2011
Prediction of BCS Theory Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Near Tc Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Ｔ～０ Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 RF Surface Resistance Shuichi Noguchi 6-th ILC School, November 2011
BCS Surface Resistance Shuichi Noguchi 6-th ILC School, November 2011
6-th ILC School, November 2011 Shuichi Noguchi 6-th ILC School, November 2011