The Path to Type-II Superconductivity
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Lecture Notes: BCS Theory of Superconductivity
Lecture Notes: BCS theory of superconductivity Prof. Rafael M. Fernandes Here we will discuss a new ground state of the interacting electron gas: the superconducting state. In this macroscopic quantum state, the electrons form coherent bound states called Cooper pairs, which dramatically change the macroscopic properties of the system, giving rise to perfect conductivity and perfect diamagnetism. We will mostly focus on conventional superconductors, where the Cooper pairs originate from a small attractive electron-electron interaction mediated by phonons. However, in the so- called unconventional superconductors - a topic of intense research in current solid state physics - the pairing can originate even from purely repulsive interactions. 1 Phenomenology Superconductivity was discovered by Kamerlingh-Onnes in 1911, when he was studying the transport properties of Hg (mercury) at low temperatures. He found that below the liquifying temperature of helium, at around 4:2 K, the resistivity of Hg would suddenly drop to zero. Although at the time there was not a well established model for the low-temperature behavior of transport in metals, the result was quite surprising, as the expectations were that the resistivity would either go to zero or diverge at T = 0, but not vanish at a finite temperature. In a metal the resistivity at low temperatures has a constant contribution from impurity scattering, a T 2 contribution from electron-electron scattering, and a T 5 contribution from phonon scattering. Thus, the vanishing of the resistivity at low temperatures is a clear indication of a new ground state. Another key property of the superconductor was discovered in 1933 by Meissner. -
R. C. Hanna, Brother of Geoffrey Hanna 1945 Brian Pippard 1945
R. C. Hanna, brother of Geoffrey Hanna 1945 My elder brother Geoffrey graduated in 1941 along with Brian. The two of them were awarded DSIR studentships to be taken up after the war. PhD's were to be few ! Next memory is of them sharing accommodation at ADRDE Malvern with another physicist, John Robson. What talent! Two went to Canada where John measured the half life of the neutron, Geoff, with Bruno Pontecorvo, set an upper limit to the mass of the (electron) neutrino and much more. Brian I knew again when I returned to Cambridge for a PhD. He acted as compere of the entertainments presented at the Cavendish Dinner. He urged the singers to relax."This is not Bach!" I remember a couplet from one song. "And when I've ceased contributing to knowledge “Then I can be the master of a Cambridge college". Untrue ! Considering the whole of the material presented, Professor Bragg took on the role of Queen Victoria. Brian Pippard 1945 It was towards the end of the war, and an advertisement came out that Pembroke wanted to appoint some Stokes Students for research in physics; and John Ashmead (who was my superior in Malvern) suggested I should try for this. So I went in for it, and in due course I was invited for interview. There were five or six of us in the Master’s Lodge, waiting to be interviewed by the committee, which consisted of Prof. Bragg, and Prof. Todd, and Prof. Norrish, and the Master of Pembroke, and that sort of thing—pretty formidable. -
The Superconductor-Metal Quantum Phase Transition in Ultra-Narrow Wires
The superconductor-metal quantum phase transition in ultra-narrow wires Adissertationpresented by Adrian Giuseppe Del Maestro to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts May 2008 c 2008 - Adrian Giuseppe Del Maestro ! All rights reserved. Thesis advisor Author Subir Sachdev Adrian Giuseppe Del Maestro The superconductor-metal quantum phase transition in ultra- narrow wires Abstract We present a complete description of a zero temperature phasetransitionbetween superconducting and diffusive metallic states in very thin wires due to a Cooper pair breaking mechanism originating from a number of possible sources. These include impurities localized to the surface of the wire, a magnetic field orientated parallel to the wire or, disorder in an unconventional superconductor. The order parameter describing pairing is strongly overdamped by its coupling toaneffectivelyinfinite bath of unpaired electrons imagined to reside in the transverse conduction channels of the wire. The dissipative critical theory thus contains current reducing fluctuations in the guise of both quantum and thermally activated phase slips. A full cross-over phase diagram is computed via an expansion in the inverse number of complex com- ponents of the superconducting order parameter (equal to oneinthephysicalcase). The fluctuation corrections to the electrical and thermal conductivities are deter- mined, and we find that the zero frequency electrical transport has a non-monotonic temperature dependence when moving from the quantum critical to low tempera- ture metallic phase, which may be consistent with recent experimental results on ultra-narrow MoGe wires. Near criticality, the ratio of the thermal to electrical con- ductivity displays a linear temperature dependence and thustheWiedemann-Franz law is obeyed. -
The Development of the Science of Superconductivity and Superfluidity
Universal Journal of Physics and Application 1(4): 392-407, 2013 DOI: 10.13189/ujpa.2013.010405 http://www.hrpub.org Superconductivity and Superfluidity-Part I: The development of the science of superconductivity and superfluidity in the 20th century Boris V.Vasiliev ∗Corresponding Author: [email protected] Copyright ⃝c 2013 Horizon Research Publishing All rights reserved. Abstract Currently there is a common belief that the explanation of superconductivity phenomenon lies in understanding the mechanism of the formation of electron pairs. Paired electrons, however, cannot form a super- conducting condensate spontaneously. These paired electrons perform disorderly zero-point oscillations and there are no force of attraction in their ensemble. In order to create a unified ensemble of particles, the pairs must order their zero-point fluctuations so that an attraction between the particles appears. As a result of this ordering of zero-point oscillations in the electron gas, superconductivity arises. This model of condensation of zero-point oscillations creates the possibility of being able to obtain estimates for the critical parameters of elementary super- conductors, which are in satisfactory agreement with the measured data. On the another hand, the phenomenon of superfluidity in He-4 and He-3 can be similarly explained, due to the ordering of zero-point fluctuations. It is therefore established that both related phenomena are based on the same physical mechanism. Keywords superconductivity superfluidity zero-point oscillations 1 Introduction 1.1 Superconductivity and public Superconductivity is a beautiful and unique natural phenomenon that was discovered in the early 20th century. Its unique nature comes from the fact that superconductivity is the result of quantum laws that act on a macroscopic ensemble of particles as a whole. -
Introduction to Superconductivity Theory
Ecole GDR MICO June, 2010 Introduction to Superconductivity Theory Indranil Paul [email protected] www.neel.cnrs.fr Free Electron System εεε k 2 µµµ Hamiltonian H = ∑∑∑i pi /(2m) - N, i=1,...,N . µµµ is the chemical potential. N is the total particle number. 0 k k Momentum k and spin σσσ are good quantum numbers. F εεε H = 2 ∑∑∑k k nk . The factor 2 is due to spin degeneracy. εεε 2 µµµ k = ( k) /(2m) - , is the single particle spectrum. nk T=0 εεεk/(k BT) nk is the Fermi-Dirac distribution. nk = 1/[e + 1] 1 T ≠≠≠ 0 The ground state is a filled Fermi sea (Pauli exclusion). µµµ 1/2 Fermi wave-vector kF = (2 m ) . 0 kF k Particle- and hole- excitations around kF have vanishingly 2 2 low energies. Excitation spectrum EK = |k – kF |/(2m). Finite density of states at the Fermi level. Ek 0 k kF Fermi Sea hole excitation particle excitation Metals: Nearly Free “Electrons” The electrons in a metal interact with one another with a short range repulsive potential (screened Coulomb). The phenomenological theory for metals was developed by L. Landau in 1956 (Landau Fermi liquid theory). This system of interacting electrons is adiabatically connected to a system of free electrons. There is a one-to-one correspondence between the energy eigenstates and the energy eigenfunctions of the two systems. Thus, for all practical purposes we will think of the electrons in a metal as non-interacting fermions with renormalized parameters, such as m →→→ m*. (remember Thierry’s lecture) CV (i) Specific heat (C V): At finite-T the volume of πππ 2∆∆∆ 2 ∆∆∆ excitations ∼∼∼ 4 kF k, where Ek ∼∼∼ ( kF/m) k ∼∼∼ kBT. -
GROSS, Rudolf
Personal Details Name: Prof. Dr. Rudolf Gross Office address: Walther-Meißner-Institut Bayerische Akademie der Wissenschaften Walther-Meißner-Str. 8, 85748 Garching Phone: +49 – 89 289 14201 Fax: +49 – 89 289 14206 E-Mail: [email protected] Web: www.wmi.badw.de Education and Scientific Career 1976 – 1982 Study of Physics, University of Tübingen 1983 Diploma Degree in Physics, University of Tübingen 1987 Ph.D. Degree in Physics, University of Tübingen 1987 Visiting Scientist, Electrotechnical Laboratory, Tsukuba, Japan 1988 – 1989 Postdoctoral Research Associate, University of Tübingen 1989 – 1990 Visiting Scientist, IBM T.J. Watson Research Center, Yorktown Heights, New York, USA 1990 – 1993 Postdoctoral Research Associate, University of Tübingen 1993 Habilitation, University of Tübingen 1993 – 1995 Assistant Professor, University of Tübingen 1996 – 2000 Full Professor, Chair for Applied Physics, II. Physikalisches Institut, Uni- versity of Cologne Principal Investigator and Board Member of the DFG Collaborative Re- search Center (SFB) 341 on ``Physics of Mesoscopic and Low Dimen- sional Metallic Systems’’ (Cologne, Aachen, Jülich) since 2000 Full Professor, Chair for Technical Physics (E 23), Technische Universität München Director of the Walther-Meißner-Institute for Low Temperature Re- search of the Bavarian Academy of Sciences and Humanities 2004 – 2010 Principal Investigator of the DFG Research Unit 538 on ``Doping De- pendence of Phase Transitions and Ordering Phenomena in Copper-Ox- ygen Superconductors’’ 2003 – 2015 Spokesman of the DFG Collaborative Research Center (SFB) 631 on ``Solid State Quantum Information Processing: Physical Concepts and Material Aspects’’ since 2006 Member of the Excellence Center "Nanosystems Initiative Munich", Board member and Coordinator of Research Area 1 on Quantum Nanosystems Fellowships, Awards and Services to the Community 1984 Prof. -
Superconductivity and SQUID Magnetometer
11 Superconductivity and SQUID magnetometer Basic knowledge Superconductivity (critical temperature, BCS-Theory, Cooper pairs, Type 1 and Type 2 superconductor, Penetration Depth, Meissner-Ochsenfeld effect, etc), High temperature superconductors, Weak links and Josephson effects (DC and AC), the voltage-current U(I) characteristic, SQUID: structure, applications, sensitivity, functionality, screening current, voltage-magnetic flux characteristic) Literature [1] Ibach, Lüth, Festkörperphysik, Springer Verlag [2] Buckel, Supraleitung, VCH Weinheim [3] Sawaritzki, Supraleitung, Harri Deutsch [4] C. Kittel, Introduction of the Solid State Physics, John Wiley & Sons Inc. [5] N. W. Ashcroft and N. D. Mermin, “Solid State Physics” [6] STAR Cryoelectronics, Mr. SQUID® User’s Guide [7] http://en.wikipedia.org/wiki/Superconductor [8] http://www.physnet.uni-hamburg.de/home/vms/reimer/htc/pt3.html [9] http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/scond.html#c1 [10] http://www.lancs.ac.uk/ug/murrays1/bcs.html [11] http://www.superconductors.org/Type1.htm Experiment 11, Page 1 Content: 1. Introduction………………………………..…………………………… 3 2. Basic knowledge………………………………………..………………4 Superconductivity BCS theory Cooper pairs Type I and Type II superconductors Meissner-Ochsenfeld effect Josephson contacts Josephson effects U-I characteristic Dc SQUID 3. Experimental setup………………………………………….….….13 4. Experiment…………………………………….………………….…14 4.1 Preparing the SQUID 4.2 Determination of the critical temperature of the YBCO-SQUID 4.3 Voltage – current characteristic 4.4 Voltage – magnetic flux characteristic 4.5 Qualitative experiments 5. Schedule and analysis………………………………..………....19 Questions……………………………………………...……….……….19 Experiment 11, Page 2 1. Introduction The aim of the present experiment is to give an insight into the main properties of superconductivity in connection with the description of SQUID. -
Cond-Mat.Mes-Hall] 28 Feb 2007 R Opligraost Eiv Htti Si Fact [7] Heeger in and Is Schrieffer Su, This Dimension, a That That One Showed Believe in to There So
Anyons in a weakly interacting system C. Weeks, G. Rosenberg, B. Seradjeh and M. Franz Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada V6T 1Z1 (Dated: June 30, 2018) In quantum theory, indistinguishable particles in three-dimensional space behave in only two distinct ways. Upon interchange, their wavefunction maps either to itself if they are bosons, or to minus itself if they are fermions. In two dimensions a more exotic possibility arises: upon iθ exchange of two particles called “anyons” the wave function acquires phase e =6 ±1. Such fractional exchange statistics are normally regarded as the hallmark of strong correlations. Here we describe a theoretical proposal for a system whose excitations are anyons with the exchange phase θ = π/4 and charge −e/2, but, remarkably, can be built by filling a set of single-particle states of essentially noninteracting electrons. The system consists of an artificially structured type-II superconducting film adjacent to a 2D electron gas in the integer quantum Hall regime with unit filling fraction. The proposal rests on the observation that a vacancy in an otherwise periodic vortex lattice in the superconductor creates a bound state in the 2DEG with total charge −e/2. A composite of this fractionally charged hole and the missing flux due to the vacancy behaves as an anyon. The proposed setup allows for manipulation of these anyons and could prove useful in various schemes for fault-tolerant topological quantum computation. I. INTRODUCTION particle states. It has been pointed out very recently [9] that a two-dimensional version of the physics underly- Anyons and fractional charges appear in a variety of ing the above effect could be observable under certain theoretical models involving electron or spin degrees of conditions in graphene. -
Fritz London a Scientific Biography
Fritz London a scientific biography Kostas Gavroglu University of Athens, Greece CAMBRIDGE UNIVERSITY PRESS Contents Preface page xni Acknowledgements xxi 1 From philosophy to physics 1 The years that left nothing unaffected 2 The appeal of ideas 5 Goethe as a scientist 7 How absolute is our knowledge? 8 Acquiring knowledge 10 London's teachers in philosophy: Alexander Pfander and Erich Becher 11 Husserl's teachings 12 Abhorrence of reductionist schemata 14 The philosophy thesis 15 Tolman's principle of similitude 23 The necessary clarifications 25 Work on quantum theory 26 Transformation theory 28 Unsuccessful attempts at unification 31 2 The years in Berlin and the beginnings of quantum chemistry 38 The mysterious bond 39 London in Zurich 42 Binding forces 44 The Pauli exclusion principle 48 [ix] X FRITZ LONDON The early years in Berlin 49 Reactions to the Heitler—London paper 51 Polyelectronic molecules and the application of group theory to problems of chemical valence 53 Chemists as physicists? 57 London's first contacts in Berlin 59 Marriage 61 Job offers 64 Intermolecular forces 66 The book which could not be written 69 Leningrad and Rome 71 Difficulties with group theory 74 Linus Pauling's resonance structures 75 Robert Mulliken's molecular orbitals 78 Trying to save what could not be saved 82 3 Oxford and superconductivity 96 The rise of the Nazis 97 The changes at the University 102 Going to Oxford 105 Lindemann, Simon and Heinz London 106 Electricity in the very cold 110 The end of old certainties 113 The thermodynamic treatment -
Lecture Notes 18: Magnetic Monopoles/Magnetic Charges
UIUC Physics 435 EM Fields & Sources I Fall Semester, 2007 Lecture Notes 18 Prof. Steven Errede LECTURE NOTES 18 MAGNETIC MONOPOLES – FUNDAMENTAL / POINTLIKE MAGNETIC CHARGES No fundamental, point-like isolated separate North or South magnetic poles – i.e. N or S magnetic charges have ever been conclusively / reproducibly observed. In principle, there is no physical law, or theory, that forbids their existence. So we may well ask, why did “nature” not “choose” to have magnetic monopoles in our universe – or, if so, why are they so extremely rare, given that many people (including myself) have looked for / tried to detect their existence… If magnetic monopoles / fundamental point magnetic charges did exist in nature, they would obey a Coulomb-type force law (just as electric charges do): ⎛⎞μ ggtest src test ommˆ Frmmm()== gBr () ⎜⎟ 2 r ⎝⎠4π r Source point Sr′( ′) src src test Where: gm = magnetic charge of source particle gm r =−rr′ gm test gm = magnetic charge of test particle zˆ gm ≡+ g() ≡ North pole r′ r gm ≡− g() ≡ South pole SI units of magnetic charge g = Ampere-meters (A-m) ϑ yˆ xˆ Field / observation point Pr( ) 2 ⎛⎞μomg −7 Newtons N Units check: Fm () Newtons = ⎜⎟2 μπo =×410 22 ⎝⎠4π r Ampere( A ) 2 ⎛⎞NN()Am− ⎛⎞A2 − m2 Newton = N = ⎜⎟22= ⎜⎟ = N ⎝⎠Am ⎝⎠A2 m2 Newton Then (the radial) B -field of a magnetic monopole is: 1 Tesla ≡1 Ampere− meter ⎛⎞μ g src N N omˆ Brm ()= ⎜⎟2 r (SI units = Tesla = ) 1 T = 1 ⎝⎠4π r Am− Am− NN⎛⎞A2 − m N Units check: Tesla == = gm = Ampere-meters (A-m) ⎜⎟2 2 Am− ⎝⎠A m Am− © Professor Steven Errede, Department of Physics, University of Illinois at Urbana-Champaign, Illinois 1 2005-2008. -
Transport in Quantum Hall Systems : Probing Anyons and Edge Physics
Transport in Quantum Hall Systems : Probing Anyons and Edge Physics by Chenjie Wang B.Sc., University of Science and Technology of China, Hefei, China, 2007 M.Sc., Brown University, Providence, RI, 2010 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Department of Physics at Brown University PROVIDENCE, RHODE ISLAND May 2012 c Copyright 2012 by Chenjie Wang This dissertation by Chenjie Wang is accepted in its present form by Department of Physics as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date Prof. Dmitri E. Feldman, Advisor Recommended to the Graduate Council Date Prof. J. Bradley Marston, Reader Date Prof. Vesna F. Mitrovi´c, Reader Approved by the Graduate Council Date Peter M. Weber, Dean of the Graduate School iii Curriculum Vitae Personal Information Name: Chenjie Wang Date of Birth: Feb 02, 1984 Place of Birth: Haining, China Education Brown University, Providence, RI, 2007-2012 • - Ph.D. in physics, Department of Physics (May 2012) - M.Sc. in physics, Department of Physics (May 2010) University of Science and Technology of China, Hefei, China, 2003- • 2007 - B.Sc. in physics, Department of Modern Physics (July 2007) Publications 1. Chenjie Wang, Guang-Can Guo and Lixin He, Ferroelectricity driven by the iv noncentrosymmetric magnetic ordering in multiferroic TbMn2O5: a first-principles study, Phys. Rev. Lett. 99, 177202 (2007) 2. Chenjie Wang, Guang-Can Guo, and Lixin He, First-principles study of the lattice and electronic structures of TbMn2O5, Phys. Rev B 77, 134113 (2008) 3. Chenjie Wang and D. E. Feldman, Transport in line junctions of ν = 5/2 quantum Hall liquids, Phys. -
The London Equations Aria Yom Abstract: the London Equations Were the First Successful Attempt at Characterizing the Electrodynamic Behavior of Superconductors
The London Equations Aria Yom Abstract: The London Equations were the first successful attempt at characterizing the electrodynamic behavior of superconductors. In this paper we review the motivation, derivation, and modification of the London equations since 1935. We also mention further developments by Pippard and others. The shaping influences of experiments on theory are investigated. Introduction: Following the discovery of superconductivity in supercooled mercury by Heike Onnes in 1911, and its subsequent discovery in various other metals, the early pioneers of condensed matter physics were faced with a mystery which continues to be unraveled today. Early experiments showed that below a critical temperature, a conventional conductor could abruptly transition into a superconducting state, wherein currents seemed to flow without resistance. This motivated a simple model of a superconductor as one in which charges were influenced only by the Lorentz force from an external field, and not by any dissipative interactions. This would lead to the following equation: 푚 푑퐽 = 퐸 (1) 푛푒2 푑푡 Where m, e, and n are the mass, charge, and density of the charge carriers, commonly taken to be electrons at the time this equation was being considered. In the following we combine these variables into a new constant both for convenience and because the mass, charge, and density of the charge carriers are often subtle concepts. 푚 Λ = 푛푒2 This equation, however, seems to imply that the crystal lattice which supports superconductivity is somehow invisible to the superconducting charges themselves. Further, to suggest that the charges flow without friction implies, as the Londons put it, “a premature theory.” Instead, the Londons desired a theory more in line with what Gorter and Casimir had conceived [3], whereby a persistent current is spontaneously generated to minimize the free energy of the system.