There are two main theories in superconductivity: Ginzburg-Landau Theory. Outline of the Lecture. Ginzburg-Landau theory
|
|
- Buddy Sutton
- 6 years ago
- Views:
Transcription
1 Ginzburg-Landau Theory There are two main theories in superconductivity: i Microscopic theory describes why materials are superconducting Prof. Damian Hampshire Durham University ii Ginzburg-Landau Theory describes the properties of superconductors in magnetic fields Cambridge Winter School January 7 1 Ginzburg-Landau theory This is a phenomenological theory, unlike the microscopic BCS theory. Based on a so-called phenomenological order parameter. Not strictly an ab initio theory, but essential for problems concerning superconductors in magnetic fields. G-L was the first theory to explain the difference between Type I and Type II superconductivity, and enable the calculation of two critical fields H c1 and H c. Outline of the Lecture Ginzburg-Landau theory The two G-L equations The basic phenomenology Type I and Type II superconductors Time dependent G-L theory Ginzburg-Landau and Pinning Conclusions 3 4
2 Ginzburg-Landau Theory Ginzburg and Landau (G-L postulated a Helmholtz energy density for superconductors of the form: The two Ginzburg-Landau Equations Functional differentiation w.r.t. ψ and A gives the two G-L equations (coupled partial differential equations: f = αψ + βψ + (-i - e A ψ + Hd B m G-L I 1 m (- i ea Ψ + αψ + β Ψ Ψ = where α and β are constants and ψ is the wavefunction. α is of the form α (T-T C which changes sign at T C G-L II J = i e * * 4e ( A m Ψ Ψ Ψ Ψ m Ψ 5 6 London Theory Type I superconductors The London brothers - E = μλ t B = μλ where * m λl = * μ n e L J s B = λ L J s s Substituting the second London equation into one of Maxwell s equations we get the Meissner state: 1 L B 7 Magnetisation of superconductors M -H c H H c1 H c H c Type I Type II H T H c Mixed H c H c1 Meissner Normal The magnetisation (M of a type I and type II superconductor, with the same H c as a function of applied magnetic field (H o. Inset: The phase diagrams of type I and type II superconductors. 8 T c
3 The structure of the fluxon The Mixed state μ H c1 B z (r J θ B z ψ ψ(r J θ (r ξ λ The order parameter, magnetic field (B and supercurrent density (J C as a function of distance (r from the centre of an isolated vortex (κ 8. The order parameter squared is proportional to the density of superelectrons. r 9 λ: depth of the current flow d: fluxon fluxon spacing If B increases, d decreases. 1 The Mixed State in NbSe The Mixed State in Nb (a (b The hexagonal Abrikosov lattice: (a contour diagram of the order parameter from Kleiner et al.; the lines also represent contours of B and streamlines of J. (b Scanning-tunnellingmicroscope image of the flux lattice in NbSe (1 T, 1.8 K from Hess et al. the vortex spacing is ~479Å. 11 Vortex lattice in niobium the triangular layout can clearly be seen. (The normal regions are preferentially dark because of the ferromagnetic powder. 1
4 Flux Quantisation By considering the persistent current as a wave, phase coherence demands (n: integer - leads to flux quantisation. k: momentum of the superelectrons. 13 G-L Theory Type I and Type II superconductors Ginzburg-Landau theory predicts that a superconductor should have two characteristic lengths: Coherence length Penetration depth The Ginzburg-Landau parameter ξ = λ = m e 4e m e α β μ α λ κ = ξ This ratio, κ, distinguishes Type-I superconductors, for which κ 1/, from Type-II superconductors which have higher κ values. 14 Thermodynamic Critical Field, H C In Type I superconductors H C is the critical field at which superconductivity is destroyed ψ drops abruptly to zero in a first-order phase transition. At the thermodynamic critical field H C, the Gibbs free energies for superconducting and normal phases are equal. For the superconducting phase B =, and for the normal phase ψ = H c = α μβ Lower and upper critical fields HC Hc1 ln κ κ H c μ = α μβ φ H c = πξ H κh κ H c C C
5 Flux entering a superconductor Time evolution of order parameter Time evolution of order parameter This simulation is simply applying an instantaneous fields of.5h c Time evolution of order parameter Time evolution of order parameter 19
6 Time evolution of order parameter Time evolution of order parameter 1 Flux nucleation and entry into a superconductor Contour plot of a superconductor bounded by an insulating outer surface. The applied magnetic field was increased to above the initial vortex penetration field (i.e. to Hp +.1Hc 3 Other Ginzburg-Landau predictions The magnetization of in the mixed state near B c is given by: μ c M = ( B B ( κ 1 β A β A = ψ 4 ( ψ Surface barriers C3 C Depairing current density: B = 1.69B J D Hc Hc = = κξ κξ 4
7 Critical Current Density (H c /κ ξ Critical Current Density (H c /κ ξ Josephson diffraction Junction Thickness.5ξ 3x Applied Field (H c Junction Thickness 4.5ξ x1-3 1x Applied Field (H c Critical Current Density (H c /κ ξ Critical Current Density (H c /κ ξ Junction Thickness 1.5ξ 4x Applied Field (H c Junction Thickness 9.5ξ 3x1-4 x1-4 1x Applied Field (H c J c computed for an ρ N = 1ρ S junction in a 3ξwide κ = 5 superconductor. 5 Ginzburg-Landau predictions - restricted dimensionality behaviour Behaviour of thin films - A thin film has a much higher critical field (if the field lines are parallel to the film, than a bulk superconductor. This is predicted by Ginzburg- Landau theory. Anisotropic Ginzburg-Landau theory - It is possible to extend Ginzburg-Landau theory to anisotropic systems (eg high-t c superconductors. This shows that H c is isotropic, but H c is not. Lawrence-Doniach theory - D version of GL theory. Predicts that H c is higher for layered superconductors, and that at low T s, fluxons are locked parallel to planes (a kind of transverse Meissner effect 6 Flux Pinning using G-L theory Model Pinning at surfaces 5 (Dew-Hughes 1974 Pinning at surfaces 7 (Dew-Hughes 1987 Force F p =J C.B per unit volume B 1 c = b ( 1 b 4μκD π 3Bc = b( 1 b 16μκD Reversible Magnetic Properties of Perfect Superconductors Flux shear past point pinning sites 3 (Kramer, Labusch 31 C 66 Flux shear past point pinning sites 3 (Kramer, Brandt 33 C 66 Maximum shear strength of lattice 7 (Dew-Hughes 1987 Flux shear along grain boundaries in D 15 (Pruymboom 1988 Collective pinning model 34 (Larkin-Ovchinnikov = B c π 1 b μκ φ ( 1 a d ( 1 b Bc π 1.9b b 1 = exp b ( 1 b μκ φ 3 ( 1 a κb d Bc b 1 = exp ( 1.9 ( 1 b b b 8πμ κ ( D a 3κ b 5 3 Bc π b ( 1 b μκ φ nf = 16aC C 4 p p Below Hc, Type I superconductors are in the Meissner state: current flows in a thin layer around the edge of the superconductor, and there is no magnetic flux in the bulk of the superconductor. (Hc : Thermodynamic Critical Field. In Type II superconductors, between the lower critical field (Hc1, and the upper critical field (Hc, magnetic flux penetrates into the sample, giving a mixed state. 8
8 Reversible Magnetization Loop The reversible response of a superconductor Magnetizaion M (H c ( ΗC H -. M =, (κ 1 β μ H SC C A μ H C1 Applied field H (H c 1ξ 8ξ, κ = 5 M vs. H for a Superconductor Coated With a Normal Metal, κ = 5 Magnetizaion M (H c H =.5 H c Applied field H (H c ξ 8ξ, κ = 5 The material is in the Meissner state Magnetization Loop Magnetization Loop Magnetizaion M (H c Applied field H (H c ξ 8ξ, κ = 5 Magnetizaion M (H c Applied field H (H c ξ 8ξ, κ = 5 H =.1 H c The material is in the Meissner state H =.15 H c The material is in the mixed state 31 3
9 Magnetization Loop Magnetization Loop...1 Applied field H (H c.1 Applied field H (H c Magnetizaion M (H c ξ 8ξ, κ = 5 Magnetizaion M (H c ξ 8ξ, κ = H =.4 H c H =.7 H c Note the nucleation of fluxons at the superconductor-normal boundary In the reversible region, one can determine κ Magnetization Loop Magnetization Loop...1 Applied field H (H c.1 Applied field H (H c Magnetizaion M (H c ξ 8ξ, κ = 5 Magnetizaion M (H c ξ 8ξ, κ = H =.9 H c H = 1. H c The core of the fluxons overlap and the average value of the order parameter drops Eventually the superconductivity is destroyed 35 36
10 Magnetization Loop Magnetization Loop...1 Applied field H (H c.1 Applied field H (H c Magnetizaion M (H c ξ 8ξ, κ = 5 Magnetizaion M (H c ξ 8ξ, κ = H =.5 H c H =. H c Note the Abrikosov fluxline-lattice with hexagonal symmetry A few fluxons remain as the inter-fluxon repulsion is lower than the surface pinning Time-dependent Ginzburg-Landau equations e 1 eϕ Δ 1 Δ+ A Δ+ + i Δ = ξ D t 1 T T c i J e 1 * A = Re e ϕ Δ A Δ σ + eμλ i t These equations were postulated by Schmid (1966, and then derived using microscopic theory in the gapless case by Gor kov and Eliashberg ( Uncertainty/Complexity in G-L theory Thermodynamics is seductive but very complex. There are number of different approaches to deriving the G-L equations (DeGennes, Campbell, Clem, Pippard, Jackson and Landau and Lifshitz There is confusion in the literature about the length scales on which G-L applies TDGL for real systems has only been possible in the last 3-5 years 4
11 Model for a polycrystalline superconductor A collection of truncated octahedra Avoids the problematic straight channels of a simple cubic system. The Bean critical state model is used to obtain J c. A symmetrical straightline Bean profile is fitted to the calculated B-field data The E-field is calculated from the ramp rate by Maxwell s equations. Obtaining bulk J c Local Field (B c DIffused region Down ramp at.3h c Up ramp at.98h c region over which J is calculated DIffused region y-coordinate (ξ 41 4 Branching test runs up, fast 1.45 Layout of granular system Current Density (1 3 H c /κ ξ Applied Field Main-line Data Branch Data E max = H c ρ S /κ ξ Diffusive resistivity 31ρ S Applied Field (H c y b a x Superconductor Weak superconductor Normal metal Edges matched by periodic boundary conditions Time (t 43 Show the -field movie! 44
12 Flux motion in low fields (.43 HC along grain boundaries b a Time dependant Ginzburg-Landau theory provides the framework for understanding flux pinning ^-3 1^ ^-5 1^ ^ (a Order parameter 45 Order Parameter at.43 Bc -5 5 (b Normal current 46 Normal Current at.43 Hc The motion of flux through the system takes place predominantly along the grain boundaries. 47 The normal current movie shows that dissipation above Jc occurs principally in the grain boundaries. 48
13 Flux motion in high fields into the interior of grain boundaries Order Parameter at.94 Hc b a ^-3-1^ ^ ^ ^ (a Order parameter -5 5 (b Normal current 49 Normal Current at.94 Hc 5 Conclusion Ginzburg-Landau theory is a triumph of physical intuition. It is the central theory for understanding the properties of superconductors in magnetic fields Bibliography/electronic version of the talk will be available at:
The Ginzburg-Landau Theory
The Ginzburg-Landau Theory A normal metal s electrical conductivity can be pictured with an electron gas with some scattering off phonons, the quanta of lattice vibrations Thermal energy is also carried
More informationTheory of Nonequilibrium Superconductivity *
Theory of Nonequilibrium Superconductivity * NIKOLAI B.KOPNIN Low Temperature Laboratory, Helsinki University of Technology, Finland and L.D. Landau Institute for Theoretical Physics, Moscow, Russia CLARENDON
More information14.4. the Ginzburg Landau theory. Phys520.nb Experimental evidence of the BCS theory III: isotope effect
Phys520.nb 119 This is indeed what one observes experimentally for convectional superconductors. 14.3.7. Experimental evidence of the BCS theory III: isotope effect Because the attraction is mediated by
More informationBaruch Rosenstein Nat. Chiao Tung University
Dissipationless current carrying states in type II superconductors in magnetic field Baruch Rosenstein Nat. Chiao Tung University D. P. Li Peking University, Beijing, China B. Shapiro Bar Ilan University,
More informationTDGL Simulation on Dynamics of Helical Vortices in Thin Superconducting Wires in the Force-Free Configuration
5th International Workshop on Numerical Modelling of High-Temperature Superconductors, 6/15-17/2016, Bologna, Italy TDGL Simulation on Dynamics of Helical Vortices in Thin Superconducting Wires in the
More informationSuperconductivity and the BCS theory
Superconductivity and the BCS theory PHY 313 - Statistical Mechanics Syed Ali Raza Roll no: 2012-10-0124 LUMS School of Science and Engineering Monday, December, 15, 2010 1 Introduction In this report
More informationVortices in superconductors& low temperature STM
Vortices in superconductors& low temperature STM José Gabriel Rodrigo Low Temperature Laboratory Universidad Autónoma de Madrid, Spain (LBT-UAM) Cryocourse, 2011 Outline -Vortices in superconductors -Vortices
More informationDurham E-Theses. Studies of coated and polycrystalline superconductors using the time dependant Ginzburg-Landau equations. Carty, George James
Durham E-Theses Studies of coated and polycrystalline superconductors using the time dependant Ginzburg-Landau equations Carty, George James How to cite: Carty, George James (2006) Studies of coated and
More informationSuperconductivity. S2634: Physique de la matière condensée & nano-objets. Miguel Anía Asenjo Alexandre Le Boité Christine Lingblom
Superconductivity S2634: Physique de la matière condensée & nano-objets Miguel Anía Asenjo Alexandre Le Boité Christine Lingblom 1 What is superconductivity? 2 Superconductivity Superconductivity generally
More informationLecture 10: Supercurrent Equation
Lecture 10: Supercurrent Equation Outline 1. Macroscopic Quantum Model 2. Supercurrent Equation and the London Equations 3. Fluxoid Quantization 4. The Normal State 5. Quantized Vortices October 13, 2005
More informationModeling of Magnetisation and Intrinsic Properties of Ideal Type-II Superconductor in External Magnetic Field
Modeling of Magnetisation and Intrinsic Properties of Ideal Type-II Superconductor in External Magnetic Field Oleg A. Chevtchenko *1, Johan J. Smit 1, D.J. de Vries 2, F.W.A. de Pont 2 1 Technical University
More informationIntroduction to Superconductivity. Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance
Introduction to Superconductivity Superconductivity was discovered in 1911 by Kamerlingh Onnes. Zero electrical resistance Meissner Effect Magnetic field expelled. Superconducting surface current ensures
More informationWHAT IS SUPERCONDUCTIVITY??
WHAT IS SUPERCONDUCTIVITY?? For some materials, the resistivity vanishes at some low temperature: they become superconducting. Superconductivity is the ability of certain materials to conduct electrical
More informationUNIVERSITÀ DEGLI STUDI DI GENOVA
UNIVERSITÀ DEGLI STUDI DI GENOVA Outline Story of superconductivity phenomenon going through the discovery of its main properties. Microscopic theory of superconductivity and main parameters which characterize
More informationVortex matter in nanostructured and hybrid superconductors
Vortex matter in nanostructured and hybrid superconductors François Peeters University of Antwerp In collaboration with: B. Baelus, M. Miloševic V.A. Schweigert (Russian Academy of Sciences, Novosibirsk)
More informationSHANGHAI JIAO TONG UNIVERSITY LECTURE
Lecture 4 SHANGHAI JIAO TONG UNIVERSITY LECTURE 4 017 Anthony J. Leggett Department of Physics University of Illinois at Urbana-Champaign, USA and Director, Center for Complex Physics Shanghai Jiao Tong
More informationsmaller mfp coh L type II
Type II superconductors Superconductivity: outline of 10.10 Superconductor in magnetic field Thin superconductor in magnetic field Interface energy Type II superconductors Mixed phase Abrikosov vortices
More informationNote that some of these solutions are only a rough list of suggestions for what a proper answer might include.
Suprajohtavuus/Superconductivity 763645S, Tentti/Examination 07.2.20 (Solutions) Note that some of these solutions are only a rough list of suggestions for what a proper answer might include.. Explain
More informationQuantum Theory of Matter
Quantum Theory of Matter Overview Lecture Derek Lee Imperial College London January 2007 Outline 1 Course content Introduction Superfluids Superconductors 2 Course Plan Resources Outline 1 Course content
More informationSuperconductivity and Superfluidity
Superconductivity and Superfluidity Contemporary physics, Spring 2015 Partially from: Kazimierz Conder Laboratory for Developments and Methods, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland Resistivity
More informationVortex lattice pinning in high-temperature superconductors.
Vortex lattice ning in high-temperature superconductors. Victor Vakaryuk. Abstract. Vortex matter in high temperature superconductors has many peculiar properties such as melting of the vortex lattice,
More informationFor a complex order parameter the Landau expansion of the free energy for small would be. hc A. (9)
Physics 17c: Statistical Mechanics Superconductivity: Ginzburg-Landau Theory Some of the key ideas for the Landau mean field description of phase transitions were developed in the context of superconductivity.
More informationSuperconductivity - Overview
Superconductivity - Overview Last week (20-21.11.2017) This week (27-28.11.2017) Classification of Superconductors - Theory Summary - Josephson Effect - Paraconductivity Reading tasks Kittel: Chapter:
More informationAbrikosov vortex lattice solution
Abrikosov vortex lattice solution A brief exploration O. Ogunnaike Final Presentation Ogunnaike Abrikosov vortex lattice solution Physics 295b 1 / 31 Table of Contents 1 Background 2 Quantization 3 Abrikosov
More informationChapter Phenomenological Models of Superconductivity
TT1-Chap2-1 Chapter 3 3. Phenomenological Models of Superconductivity 3.1 London Theory 3.1.1 The London Equations 3.2 Macroscopic Quantum Model of Superconductivity 3.2.1 Derivation of the London Equations
More informationSuperconducting Single Photon Detectors and Diamond Nanophotonics
Superconducting Single Photon Detectors and Diamond Nanophotonics John Y. Shin UCSC August 30, 2015 John Y. Shin (UCSC) SSPDs and Diamond Nanophotonics August 30, 2015 1 / 26 Stepping Back, Diamond and
More informationIntroduction Critical state models Pinning regimes Kinds of pinning sites HTS Results on YBCO Conclusions. Flux pinning.
Department of Physics and Astronomy 14.6.2011 Contents Introduction Critical state models Pinning regimes Kinds of pinning sites HTS Results on YBCO Type II superconductors and vortices Type I ξ < λ S/N
More informationarxiv:cond-mat/ v2 [cond-mat.supr-con] 29 Mar 2007
Critical fields for vortex expulsion from narrow superconducting strips P. Sánchez-Lotero and J. J. Palacios Departamento de Física Aplicada, Universidad de Alicante, San Vicente del Raspeig, Alicante
More informationGinzburg-Landau length scales
597 Lecture 6. Ginzburg-Landau length scales This lecture begins to apply the G-L free energy when the fields are varying in space, but static in time hence a mechanical equilibrium). Thus, we will be
More informationCritical fields and intermediate state
621 Lecture 6.3 Critical fields and intermediate state Magnetic fields exert pressure on a superconductor: expelling the flux from the sample makes it denser in the space outside, which costs magnetic
More informationLecture 4: London s Equations. Drude Model of Conductivity
Lecture 4: London s Equations Outline 1. Drude Model of Conductivity 2. Superelectron model of perfect conductivity First London Equation Perfect Conductor vs Perfect Conducting Regime 3. Superconductor:
More informationA variational approach to the macroscopic. Electrodynamics of hard superconductors
A variational approach to the macroscopic electrodynamics of hard superconductors Dept. of Mathematics, Univ. of Rome La Sapienza Torino, July 4, 2006, joint meeting U.M.I. S.M.F. Joint work with Annalisa
More informationSuperconductivity. Introduction. Final project. Statistical Mechanics Fall Mehr Un Nisa Shahid
1 Final project Statistical Mechanics Fall 2010 Mehr Un Nisa Shahid 12100120 Superconductivity Introduction Superconductivity refers to the phenomenon of near-zero electric resistance exhibited by conductors
More informationLecture 23 - Superconductivity II - Theory
D() Lecture 23: Superconductivity II Theory (Kittel Ch. 10) F mpty D() F mpty Physics 460 F 2000 Lect 23 1 Outline Superconductivity - Concepts and Theory Key points xclusion of magnetic fields can be
More informationQuantum Theory of Matter
Quantum Theory of Matter Revision Lecture Derek Lee Imperial College London May 2006 Outline 1 Exam and Revision 2 Quantum Theory of Matter Microscopic theory 3 Summary Outline 1 Exam and Revision 2 Quantum
More informationSuperconducting phase transition
University of Illinois, Urbana-Champaign Yulia Maximenko Superconducting phase transition Phys 569 ESM Term Essay December 15, 2011 Contents 1 Review 1 1.1 Ginzburg-Landau theory............................
More informationSuperconductivity. Alexey Ustinov Universität Karlsruhe WS Alexey Ustinov WS2008/2009 Superconductivity: Lecture 3 1
Superconductivity Alexey Ustinov Universität Karlsruhe WS 2008-2009 Alexey Ustinov WS2008/2009 Superconductivity: Lecture 3 1 Electrodynamics of superconductors Two-fluid model The First London Equation
More informationCONDENSED MATTER: towards Absolute Zero
CONDENSED MATTER: towards Absolute Zero The lowest temperatures reached for bulk matter between 1970-2000 AD. We have seen the voyages to inner & outer space in physics. There is also a voyage to the ultra-cold,
More informationQuantum Phase Slip Junctions
Quantum Phase Slip Junctions Joël Peguiron Insitute of Physics, University of Basel Monday Morning Meeting, 24 April 2006 1 Goal Monday Morning Meeting, 24 April 2006 2 Evidence for Thermodynamic Fluctuations
More informationScanning Tunnelling Microscopy Observations of Superconductivity
Department of physics Seminar I a Scanning Tunnelling Microscopy Observations of Superconductivity Author: Tim Verbovšek Mentor: dr. Rok Žitko Co-Mentor: dr. Erik Zupanič Ljubljana, February 013 Abstract
More informationVortex Liquid Crystals in Anisotropic Type II Superconductors
Vortex Liquid Crystals in Anisotropic Type II Superconductors E. W. Carlson A. H. Castro Netro D. K. Campbell Boston University cond-mat/0209175 Vortex B λ Ψ r ξ In the high temperature superconductors,
More informationCritical Magnetic Field Ratio of Anisotropic Magnetic Superconductors
Critical Magnetic Field Ratio of Anisotropic Magnetic Superconductors A.Changjan,,3 and P.Udomsamuthirun, Prasarnmitr Physics Research Unit,Department of Physics, Faculty of Science,Srinakharinwirot Uniersity
More informationChapter 1. Macroscopic Quantum Phenomena
Chapter 1 Macroscopic Quantum Phenomena Chap. 1-2 I. Foundations of the Josephson Effect 1. Macroscopic Quantum Phenomena 1.1 The Macroscopic Quantum Model of Superconductivity Macroscopic systems Quantum
More informationStrongly Correlated Systems:
M.N.Kiselev Strongly Correlated Systems: High Temperature Superconductors Heavy Fermion Compounds Organic materials 1 Strongly Correlated Systems: High Temperature Superconductors 2 Superconductivity:
More information1 Superfluidity and Bose Einstein Condensate
Physics 223b Lecture 4 Caltech, 04/11/18 1 Superfluidity and Bose Einstein Condensate 1.6 Superfluid phase: topological defect Besides such smooth gapless excitations, superfluid can also support a very
More informationAPS March Meeting Years of BCS Theory. A Family Tree. Ancestors BCS Descendants
APS March Meeting 2007 50 Years of BCS Theory A Family Tree Ancestors BCS Descendants D. Scalapino: Ancestors and BCS J. Rowell : A tunneling branch of the family G. Baym: From Atoms and Nuclei to the
More informationCharacterization Techniques. M. Eisterer Atominstitut, TU Wien Stadionallee 2, 1020 Vienna, Austria
Characterization Techniques M. Eisterer Atominstitut, TU Wien Stadionallee 2, 1020 Vienna, Austria EASIschool, September 7 th 2018 Outline Quantities of interest Intrinsic material parameters: T c, l,
More informationSuperconductivity and Quantum Coherence
Superconductivity and Quantum Coherence Lent Term 2008 Credits: Christoph Bergemann, David Khmelnitskii, John Waldram, 12 Lectures: Mon, Wed 10-11am Mott Seminar Room 3 Supervisions, each with one examples
More informationFrom Last Time. Partially full bands = metal Bands completely full or empty = insulator / seminconductor
From Last Time Solids are large numbers of atoms arranged in a regular crystal structure. Each atom has electron quantum states, but interactions shift the energies. End result is each type atomic electron
More informationVORTICES in SUPERFLUIDS & SUPERCONDUCTORS. CIFAR Q MATERIALS SUMMER SCHOOL (May 14-16, 2012) LECTURE 2 VORTICES
VORTICES in SUPERFLUIDS & SUPERCONDUCTORS CIFAR Q MATERIALS SUMMER SCHOOL (May 14-16, 2012) LECTURE 2 VORTICES Quantum Vortices in Superfluids Suppose we look at a vortex in a superfluid- ie., fluid circulating
More informationQuantum Statistical Derivation of a Ginzburg-Landau Equation
Journal of Modern Physics, 4, 5, 56-568 Published Online October 4 in SciRes. http://www.scirp.org/journal/jmp http://dx.doi.org/.46/jmp.4.5657 Quantum Statistical Derivation of a Ginzburg-Landau Euation
More informationScuola Dottorale di Ingegneria Sezione di Ingegneria dell Elettronica Biomedica, dell Elettromagnetismo e delle Telecomunicazioni
Scuola Dottorale di Ingegneria Sezione di Ingegneria dell Elettronica Biomedica, dell Elettromagnetismo e delle Telecomunicazioni XXV CICLO DEL CORSO DI DOTTORATO EXPERIMENTAL MICROWAVE PROPERTIES OF INNOVATIVE
More informationCritical state analysis in MgB 2 bulk by means of quantitative MO technique
Critical state analysis in MgB 2 bulk by means of quantitative MO technique L. Gozzelino, F. Laviano, D. Botta, A. Chiodoni, R. Gerbaldo, G. Ghigo and E. Mezzetti INFM - U.d.R Torino-Politecnico; INFN
More information10 Supercondcutor Experimental phenomena zero resistivity Meissner effect. Phys463.nb 101
Phys463.nb 101 10 Supercondcutor 10.1. Experimental phenomena 10.1.1. zero resistivity The resistivity of some metals drops down to zero when the temperature is reduced below some critical value T C. Such
More informationOn the Higgs mechanism in the theory of
On the Higgs mechanism in the theory of superconductivity* ty Dietrich Einzel Walther-Meißner-Institut für Tieftemperaturforschung Bayerische Akademie der Wissenschaften D-85748 Garching Outline Phenomenological
More informationUnit V Superconductivity Engineering Physics
1. Superconductivity ertain metals and alloys exhibit almost zero resistivity (i.e. infinite conductivity), when they are cooled to sufficiently low temperatures. This effect is called superconductivity.
More informationTheory of the lower critical magnetic field for a two-dimensional superconducting film in a non-uniform field
Theory of the lower critical magnetic field for a two-dimensional superconducting film in a non-uniform field Thomas R. Lemberger and John Draskovic Dept. of Physics The Ohio State University Columbus,
More informationGinzburg-Landau Theory of Phase Transitions
Subedi 1 Alaska Subedi Prof. Siopsis Physics 611 Dec 5, 008 Ginzburg-Landau Theory of Phase Transitions 1 Phase Transitions A phase transition is said to happen when a system changes its phase. The physical
More informationChapter 1. Macroscopic Quantum Phenomena
Chapter 1 Macroscopic Quantum Phenomena Chap. 1-2 I. Foundations of the Josephson Effect 1. Macroscopic Quantum Phenomena 1.1 The Macroscopic Quantum Model of Superconductivity quantum mechanics: - physical
More information6.763 Applied Superconductivity Lecture 1
6.763 Applied Superconductivity Lecture 1 Terry P. Orlando Dept. of Electrical Engineering MIT September 4, 2003 Outline What is a Superconductor? Discovery of Superconductivity Meissner Effect Type I
More informationSuperconducting films with antidot arrays Novel behavior of the critical current
EUROPHYSICS LETTERS 1 May 2006 Europhys. Lett., 74 (3), pp. 493 499 (2006) DOI: 10.1209/epl/i2006-10013-1 Superconducting films with antidot arrays Novel behavior of the critical current G. R. Berdiyorov,
More informationSECOND PUBLIC EXAMINATION. Honour School of Physics Part C: 4 Year Course. Honour School of Physics and Philosophy Part C C3: CONDENSED MATTER PHYSICS
2753 SECOND PUBLIC EXAMINATION Honour School of Physics Part C: 4 Year Course Honour School of Physics and Philosophy Part C C3: CONDENSED MATTER PHYSICS TRINITY TERM 2011 Wednesday, 22 June, 9.30 am 12.30
More informationarxiv: v2 [cond-mat.supr-con] 5 Apr 2017
Vortex Dynamics in Type II Superconductors Dachuan Lu (Kuang Yaming Honors School, Nanjing University) (Dated: April 6, 2017) Time dependent Ginzburg-Landau equation is solved for type II superconductors
More informationCritical Current Anisotropy in High Temperature Superconductors
Critical Current Anisotropy in High Temperature Superconductors John Hay Durrell Jesus College Cambridge A dissertation submitted for the degree of Doctor of Philosophy at the University of Cambridge April
More informationSRF FUNDAMENTALS. Jean Delayen. First Mexican Particle Accelerator School Guanajuato. 26 Sept 3 Oct 2011
First Mexican Particle Accelerator School Guanajuato 6 Sept 3 Oct 011 SRF FUNDAMENTALS Jean Delayen Center for Accelerator Science Old Dominion University and Thomas Jefferson National Accelerator Facility
More information1 Quantum Theory of Matter
Quantum Theory of Matter: Superfluids & Superconductors Lecturer: Derek Lee Condensed Matter Theory Blackett 809 Tel: 020 7594 7602 dkk.lee@imperial.ac.uk Level 4 course: PT4.5 (Theory Option) http://www.cmth.ph.ic.ac.uk/people/dkk.lee/teach/qtm
More informationContents. 6 Summary Sumenvatting 67. List of abbreviations 71. References 75. Curriculum Vitae 82. List of publications 84
i Contents 1 Introduction 1 1.1 Phase slip phenomenon in 1D superconductors 4 1.1.1 Time dependent Ginzburg-Landau theory 4 1.1.2 Phase slip mechanisms 7 1.1.3 Application of the Ginzburg-Landau theory
More information6.763 Applied Superconductivity Lecture 1
1 6.763 Applied Superconductivity Lecture 1 Terry P. Orlando Dept. of Electrical Engineering MIT September 8, 2005 Outline What is a Superconductor? Discovery of Superconductivity Meissner Effect Type
More informationVortex Structure and Critical Parameters in Superconducting Thin Films with Arrays of Pinning Centers
UNIVERSITEIT ANTWERPEN Faculteit Wetenschappen Departement Fysica Vortex Structure and Critical Parameters in Superconducting Thin Films with Arrays of Pinning Centers Proefschrift voorgelegd tot het behalen
More informationSuperconductivity at nanoscale
Superconductivity at nanoscale Superconductivity is the result of the formation of a quantum condensate of paired electrons (Cooper pairs). In small particles, the allowed energy levels are quantized and
More informationCritical Current and Vortex Lattice Properties in Superconducting MgB 2
Critical Current and Vortex Lattice Properties in Superconducting MgB 2 KIMBERLY SCHLESINGER 2010 NSF/REU Program Physics Department, University of Notre Dame ADVISOR: Prof. Morten Eskildsen GRADUATE STUDENT
More informationVortices in superconductors: I. Introduction
Tutorial BEC and quantized vortices in superfluidity and superconductivity 6-77 December 007 Institute for Mathematical Sciences National University of Singapore Vortices in superconductors: I. Introduction
More information1 General Theory of High - Tc Superconductors
1 1 General Theory of High - Tc Superconductors Kaname Matsumoto Twenty years after the discovery of high-temperature superconductors, practical superconducting wires made of these materials are now being
More informationSuperconductivity at high magnetic field
Superconductivity at high magnetic field How can we achieve superconductivity at very high magnetic fields? What sort of materials should we choose to look at? Theory - introduction to superconductivity
More informationElectrodynamics of s-wave Superconductors Using First-Order Formalism
Article Electrodynamics of s-wave Superconductors Using First-Order Formalism Naoum Karchev Department of Physics, University of Sofia, Sofia 1164, Bulgaria; naoum@phys.uni-sofia.bg Academic Editor: Antonio
More informationZurich Open Repository and Archive. Current-Induced Critical State in NbN Thin-Film Structures
University of Zurich Zurich Open Repository and Archive Winterthurerstr. 190 CH-8057 Zurich http://www.zora.uzh.ch Year: 2008 Current-Induced Critical State in NbN Thin-Film Structures Il in, K; Siegel,
More informationSuperconductivity. Alexey Ustinov Universität Karlsruhe WS Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 1
Superconductivity Alexey Ustinov Universität Karlsruhe WS 2008-2009 Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 1 Lectures October 20 Phenomenon of superconductivity October 27 Magnetic properties
More informationSuperconductivity: approaching the century jubilee
SIMTECH KICK-OFF MEETING, March, 18, 2011 Superconductivity: approaching the century jubilee Andrey Varlamov Institute of Superconductivity & Innovative Materials (SPIN), Consiglio Nazionale delle Ricerche,
More informationSUPERCONDUCTIVITY IN ACCELERATORS PART II : MIXED STATE
SUPERCONDUCTIVITY IN ACCELERATORS PART II : MIXED STATE Cours supraconductivité M2 GI Claire ANTOINE MAGNETS AND RF CAVITIES WY DO VORTICES ARE SO IMPORTANT? Magnets RF Cavities!!!!!!!! Magnet (DC) : One
More informationGinzburg-Landau theory of supercondutivity
Ginzburg-Landau theory of supercondutivity Ginzburg-Landau theory of superconductivity Let us apply the above to superconductivity. Our starting point is the free energy functional Z F[Ψ] = d d x [F(Ψ)
More informationConfiguration-induced vortex motion in type II superconducting films with periodic magnetic dot arrays
Configuration-induced vortex motion in type II superconducting films with periodic magnetic dot arrays Qinghua Chen Prof. Shi Xue Dou 1 Outline: I. An Introduction of superconductor II. Overview of vortex
More informationA DSP-Enhanced AC Susceptometer for Characterisation of High Temperature Superconductors
A DSP-Enhanced AC Susceptometer for Characterisation of High Temperature Superconductors Sergio Stephane Babet Submitted in fulfillment of the Master of Science in Engineering to the Faculty of Engineering,
More informationPhysics 525, Condensed Matter Homework 8 Due Thursday, 14 th December 2006
Physics 525, Condensed Matter Homework 8 Due Thursday, 14 th December 2006 Jacob Lewis Bourjaily Problem 1: Little-Parks Experiment Consider a long, thin-walled, hollow cylinder of radius R and thickness
More informationSuperconductivity. Superconductivity. Superconductivity was first observed by HK Onnes in 1911 in mercury at T ~ 4.2 K (Fig. 1).
Superconductivity Superconductivity was first observed by HK Onnes in 9 in mercury at T ~ 4. K (Fig. ). The temperature at which the resistivity falls to zero is the critical temperature, T c. Superconductivity
More informationarxiv: v1 [cond-mat.supr-con] 13 Jun 2017
arxiv:1706.04002v1 [cond-mat.supr-con] 13 Jun 2017 The Dynamics of Magnetic Vortices in Type II Superconductors with Pinning Sites Studied by the Time Dependent Ginzburg-Landau Model Mads Peter Sørensen
More informationA Appendix. A.1 Description of Equilibrium State
A Appendix A.1 Description of Equilibrium State Here we shall derive the force balance equation on flux lines in a usual transverse magnetic field after the method of Josephson [1] and also discuss the
More informationWhat was the Nobel Price in 2003 given for?
What was the Nobel Price in 2003 given for? Krzysztof Byczuk Instytut Fizyki Teoretycznej Uniwersytet Warszawski December 18, 2003 2003 Nobel Trio Alexei A. Abrikosov, born 1928 (75 years) in Moscow, the
More informationEnergy Levels Zero energy. From Last Time Molecules. Today. n- and p-type semiconductors. Energy Levels in a Metal. Junctions
Today From Last Time Molecules Symmetric and anti-symmetric wave functions Lightly higher and lower energy levels More atoms more energy levels Conductors, insulators and semiconductors Conductors and
More informationCritical Dynamics of The Superconductor Transition
1 INTRODUCTION 1 Critical Dynamics of The Superconductor Transition T. Siegfried Ip Department of Physics University of Illinois, Urbana Champaign This paper aims to be a brief survey to recent development
More informationDISSERTATION VORTEX PHASES IN TYPE-I SUPERCONDUCTORS. Submitted by. Mark Sweeney. Department of Physics. Doctor of Philosophy
DISSERTATION VORTEX PHASES IN TYPE-I SUPERCONDUCTORS Submitted by Mark Sweeney Department of Physics In partial fulfillment of the requirements for the degree of Doctor of Philosophy Colorado State University
More informationDemonstration Some simple theoretical models Materials How to make superconductors Some applications
Superconductivity Demonstration Some simple theoretical models Materials How to make superconductors Some applications How do we show superconductivity? Superconductors 1. have an electrical resistivity
More informationTRIBUTE TO LEV GORKOV
TRIBUTE TO LEV GORKOV 81 = 9 x 9 LANDAU S NOTEBOOK To solve the Problem of Critical Phenomena using Diagrammatics To find the level statistics in nuclei taking into account their mutual repulsion
More informationWhat s so super about superconductivity?
What s so super about superconductivity? Mark Rzchowski Physics Department Electrons can flow through the wire when pushed by a battery. Electrical resistance But remember that the wire is made of atoms.
More informationAdvances in Physics Theories and Applications ISSN X (Paper) ISSN (Online) Vol.27, 2014
Influence of Vortex-Antivortex Annihilation on the Potential Curve for Josephson Junction Based on The Modified Time Dependent Ginzburg-Landau Equations Abstract Hari Wisodo 1, 2, *, Arif Hidayat 1, Pekik
More information(Color-)magnetic flux tubes in dense matter
Seattle, Apr 17, 2018 1 Andreas Schmitt Mathematical Sciences and STAG Research Centre University of Southampton Southampton SO17 1BJ, United Kingdom (Color-)magnetic flux tubes in dense matter A. Haber,
More informationCollective Effects. Equilibrium and Nonequilibrium Physics
Collective Effects in Equilibrium and Nonequilibrium Physics: Lecture 4, April 7, 2006 1 Collective Effects in Equilibrium and Nonequilibrium Physics Website: http://cncs.bnu.edu.cn/mccross/course/ Caltech
More informationarxiv:cond-mat/ v1 [cond-mat.supr-con] 25 Apr 2005
Europhysics Letters PREPRINT arxiv:cond-mat/0504645v1 [cond-mat.supr-con] 25 Apr 2005 Field-enhanced critical parameters in magnetically nanostructured superconductors M. V. Milošević and F. M. Peeters
More informationSuperconductor. Superconductor Materials Materials Eng. Dep. Kufa Univ. Dr. Sabah M. Thahab
Superconductor Materials What's a superconductor? Superconductors have two outstanding features: 1). Zero electrical resistivity. This means that an electrical current in a superconducting ring continues
More informationUniversità degli Studi Roma Tre MICROWAVE COMPLEX RESPONSE IN SUPERCONDUCTING THIN FILMS IN MAGNETIC FIELDS. Nicola Pompeo
Dipartimento di Fisica E. Amaldi Università degli Studi Roma Tre Dottorato di Ricerca in Fisica - XVIII ciclo MICROWAVE COMPLEX RESPONSE IN SUPERCONDUCTING THIN FILMS IN MAGNETIC FIELDS Nicola Pompeo Chairperson
More informationSuperconductivity. Dirk van Delft and Peter Kes, "The discovery of superconductivity", Physics Today 63(9), 38, 2010.
Experiment Nr. 31 Superconductivity 1. Introduction When cooled down below a characteristic critical temperature T c a specific phase transition of electron system can be observed in certain materials.
More information