Superconductivity the Structure Scale of the Universe (Elastic Resonant Symmetric Medium by Self-Energy) A
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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. -
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. -
J. Robert Schrieffer Strange Quantum Numbers in Condensed Matter
Wednesday, May 1, 2002 3:00 pm APS Auditorium, Building 402, Argonne National Laboratory APS Colloquium home J. Robert Schrieffer Nobel Laureate National High Magnetic Field Laboratory Florida State University, Tallahassee [email protected] http://www.physics.fsu.edu/research/NHMFL.htm Strange Quantum Numbers in Condensed Matter Physics The origin of peculiar quantum numbers in condensed matter physics will be reviewed. The source of spin-charge separation and fractional charge in conducting polymers has to do with solitons in broken symmetry states. For superconductors with an energy gap, which is odd under time reversal, reverse spin-orbital angular momentum pairing occurs. In the fractional quantum Hall effect, quasi particles of fractional charge occur. In superfluid helium 3, a one-way branch of excitations exists if a domain wall occurs in the system. Many of these phenomena occur due to vacuum flow of particles without crossing the excitation of the energy gap. John Robert Schrieffer received his bachelor's degree from Massachusetts Institute of Technology in 1953 and his Ph.D. from the University of Illinois in 1957. In addition, he holds honorary Doctor of Science degrees from universities in Germany, Switzerland, and Israel, and from the University of Pennsylvania, the University of Cincinnati, and the University of Alabama. Since 1992, Dr. Schrieffer has been a professor of Physics at Florida State University and the University of Florida and the Chief Scientist of the National High Magnetic Field Laboratory. He also holds the FSU Eminent Scholar Chair in Physics. Before moving to Florida in 1991, he served as director for the Institute for Theoretical Physics from 1984-1989 and was the Chancellor's Professor at the University of California in Santa Barbara from 1984-1991. -
Title: the Distribution of an Illustrated Timeline Wall Chart and Teacher's Guide of 20Fh Century Physics
REPORT NSF GRANT #PHY-98143318 Title: The Distribution of an Illustrated Timeline Wall Chart and Teacher’s Guide of 20fhCentury Physics DOE Patent Clearance Granted December 26,2000 Principal Investigator, Brian Schwartz, The American Physical Society 1 Physics Ellipse College Park, MD 20740 301-209-3223 [email protected] BACKGROUND The American Physi a1 Society s part of its centennial celebration in March of 1999 decided to develop a timeline wall chart on the history of 20thcentury physics. This resulted in eleven consecutive posters, which when mounted side by side, create a %foot mural. The timeline exhibits and describes the millstones of physics in images and words. The timeline functions as a chronology, a work of art, a permanent open textbook, and a gigantic photo album covering a hundred years in the life of the community of physicists and the existence of the American Physical Society . Each of the eleven posters begins with a brief essay that places a major scientific achievement of the decade in its historical context. Large portraits of the essays’ subjects include youthful photographs of Marie Curie, Albert Einstein, and Richard Feynman among others, to help put a face on science. Below the essays, a total of over 130 individual discoveries and inventions, explained in dated text boxes with accompanying images, form the backbone of the timeline. For ease of comprehension, this wealth of material is organized into five color- coded story lines the stretch horizontally across the hundred years of the 20th century. The five story lines are: Cosmic Scale, relate the story of astrophysics and cosmology; Human Scale, refers to the physics of the more familiar distances from the global to the microscopic; Atomic Scale, focuses on the submicroscopic This report was prepared as an account of work sponsored by an agency of the United States Government. -
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. -
ANTIMATTER a Review of Its Role in the Universe and Its Applications
A review of its role in the ANTIMATTER universe and its applications THE DISCOVERY OF NATURE’S SYMMETRIES ntimatter plays an intrinsic role in our Aunderstanding of the subatomic world THE UNIVERSE THROUGH THE LOOKING-GLASS C.D. Anderson, Anderson, Emilio VisualSegrè Archives C.D. The beginning of the 20th century or vice versa, it absorbed or emitted saw a cascade of brilliant insights into quanta of electromagnetic radiation the nature of matter and energy. The of definite energy, giving rise to a first was Max Planck’s realisation that characteristic spectrum of bright or energy (in the form of electromagnetic dark lines at specific wavelengths. radiation i.e. light) had discrete values The Austrian physicist, Erwin – it was quantised. The second was Schrödinger laid down a more precise that energy and mass were equivalent, mathematical formulation of this as described by Einstein’s special behaviour based on wave theory and theory of relativity and his iconic probability – quantum mechanics. The first image of a positron track found in cosmic rays equation, E = mc2, where c is the The Schrödinger wave equation could speed of light in a vacuum; the theory predict the spectrum of the simplest or positron; when an electron also predicted that objects behave atom, hydrogen, which consists of met a positron, they would annihilate somewhat differently when moving a single electron orbiting a positive according to Einstein’s equation, proton. However, the spectrum generating two gamma rays in the featured additional lines that were not process. The concept of antimatter explained. In 1928, the British physicist was born. -
Appendix E • Nobel Prizes
Appendix E • Nobel Prizes All Nobel Prizes in physics are listed (and marked with a P), as well as relevant Nobel Prizes in Chemistry (C). The key dates for some of the scientific work are supplied; they often antedate the prize considerably. 1901 (P) Wilhelm Roentgen for discovering x-rays (1895). 1902 (P) Hendrik A. Lorentz for predicting the Zeeman effect and Pieter Zeeman for discovering the Zeeman effect, the splitting of spectral lines in magnetic fields. 1903 (P) Antoine-Henri Becquerel for discovering radioactivity (1896) and Pierre and Marie Curie for studying radioactivity. 1904 (P) Lord Rayleigh for studying the density of gases and discovering argon. (C) William Ramsay for discovering the inert gas elements helium, neon, xenon, and krypton, and placing them in the periodic table. 1905 (P) Philipp Lenard for studying cathode rays, electrons (1898–1899). 1906 (P) J. J. Thomson for studying electrical discharge through gases and discover- ing the electron (1897). 1907 (P) Albert A. Michelson for inventing optical instruments and measuring the speed of light (1880s). 1908 (P) Gabriel Lippmann for making the first color photographic plate, using inter- ference methods (1891). (C) Ernest Rutherford for discovering that atoms can be broken apart by alpha rays and for studying radioactivity. 1909 (P) Guglielmo Marconi and Carl Ferdinand Braun for developing wireless telegraphy. 1910 (P) Johannes D. van der Waals for studying the equation of state for gases and liquids (1881). 1911 (P) Wilhelm Wien for discovering Wien’s law giving the peak of a blackbody spectrum (1893). (C) Marie Curie for discovering radium and polonium (1898) and isolating radium. -
3: Applications of Superconductivity
Chapter 3 Applications of Superconductivity CONTENTS 31 31 31 32 37 41 45 49 52 54 55 56 56 56 56 57 57 57 57 57 58 Page 3-A. Magnetic Separation of Impurities From Kaolin Clay . 43 3-B. Magnetic Resonance Imaging . .. ... 47 Tables Page 3-1. Applications in the Electric Power Sector . 34 3-2. Applications in the Transportation Sector . 38 3-3. Applications in the Industrial Sector . 42 3-4. Applications in the Medical Sector . 45 3-5. Applications in the Electronics and Communications Sectors . 50 3-6. Applications in the Defense and Space Sectors . 53 Chapter 3 Applications of Superconductivity INTRODUCTION particle accelerator magnets for high-energy physics (HEP) research.l The purpose of this chapter is to assess the significance of high-temperature superconductors Accelerators require huge amounts of supercon- (HTS) to the U.S. economy and to forecast the ducting wire. The Superconducting Super Collider timing of potential markets. Accordingly, it exam- will require an estimated 2,000 tons of NbTi wire, ines the major present and potential applications of worth several hundred million dollars.2 Accelerators superconductors in seven different sectors: high- represent by far the largest market for supercon- energy physics, electric power, transportation, indus- ducting wire, dwarfing commercial markets such as trial equipment, medicine, electronics/communica- MRI, tions, and defense/space. Superconductors are used in magnets that bend OTA has made no attempt to carry out an and focus the particle beam, as well as in detectors independent analysis of the feasibility of using that separate the collision fragments in the target superconductors in various applications. -
Memories of Julian Schwinger
Memories of Julian Schwinger Edward Gerjuoy* ABSTRACT The career and accomplishments of Julian Schwinger, who shared the Nobel Prize for physics in 1965, have been reviewed in numerous books and articles. For this reason these Memories, which seek to convey a sense of Schwinger’s remarkable talents as a physicist, concentrate primarily (though not entirely) on heretofore unpuBlished pertinent recollections of the youthful Schwinger by this writer, who first encountered Schwinger in 1934 when they both were undergraduates at the City College of New York. *University of Pittsburgh Dept. of Physics and Astronomy, Pittsburgh, PA 15260. 1 Memories of Julian Schwinger Julian Seymour Schwinger, who shared the 1965 Nobel prize in physics with Richard Feynman and Sin-itiro Tomonaga, died in Los Angeles on July 16, 1994 at the age of 76. He was a remarkably talented theoretical physicist, who—through his own publications and through the students he trained—had an enormous influence on the evolution of physics after World War II. Accordingly, his life and work have been reviewed in a number of publications [1-3, inter alia]. There also have been numerous published obituaries, of course [4-5, e.g.] These Memories largely are the text of the Schwinger portion of a colloquium talk, “Recollections of Oppenheimer and Schwinger”, which the writer has given at a number of universities, and which can be found on the web [6]. The portion of the talk devoted to J. Robert Oppenheimer—who is enduringly famous as director of the Los Alamos laboratory during World War II—has been published [7], but the portion devoted to Julian is essentially unpublished; references 7-9 describe the basically trivial exceptions to this last assertion. -
Does Physics History Matter? by Robert H
HistoryN E W S L E T T E R of Physics A F O R U M O F T H E A M E R I C A N P H Y S I C A L S O C I E T Y • V O L U M E I X N O . 6 • S P R I N G 2 0 0 6 Report From The Chair Does Physics History Matter? by Robert H. Romer, Amherst College, Forum Chair Perhaps the title got your attention, so let me promptly explain leading experimental results. It might just help them to understand what I mean. Is it important that serious history of physics be that the fact that Darwinian or neo-Darwinian evolution does not included in the professional education of physicists? I think that explain every last detail of every living organism does not mean for many of us who belong to and support the APS history forum, that some other idea, untested or untestable, has an equal claim to even — or perhaps especially — for those like me who are not time in the science classroom, that the fact that none of us were professional historians of physics, it is almost an article of faith present at the big bang does not mean that the big bang is “just a that the answer to my question is an unqualified “yes.” I said as theory” with no successful explanations to its credit, that someone much myself several years ago, in my election statement when I else’s creation myth is just as deserving of our attention. -
John Robert Schrieffer Daniel Arovas, Greg Boebinger, and Nick Bonesteel
John Robert Schrieffer Daniel Arovas, Greg Boebinger, and Nick Bonesteel Citation: Physics Today 73, 1, 63 (2020); doi: 10.1063/PT.3.4395 View online: https://doi.org/10.1063/PT.3.4395 View Table of Contents: https://physicstoday.scitation.org/toc/pto/73/1 Published by the American Institute of Physics ARTICLES YOU MAY BE INTERESTED IN Gaurang Bhaskar Yodh Physics Today 73, 64 (2020); https://doi.org/10.1063/PT.3.4396 Johannes Kepler’s pursuit of harmony Physics Today 73, 36 (2020); https://doi.org/10.1063/PT.3.4388 Rare earths in a nutshell Physics Today 73, 66 (2020); https://doi.org/10.1063/PT.3.4397 The sounds around us Physics Today 73, 28 (2020); https://doi.org/10.1063/PT.3.4387 Charles Kittel Physics Today 72, 73 (2019); https://doi.org/10.1063/PT.3.4326 The usefulness of GRE scores Physics Today 73, 10 (2020); https://doi.org/10.1063/PT.3.4376 OBITUARIES made when Cooper solved the problem John Robert Schrieffer of two electrons above a quiescent Fermi towering figure in theoretical con- sea. He took into account the effective at- densed-matter physics, John Robert tractive interaction mediated by phonons, ASchrieffer died on 27 July 2019 in Tal- which resulted in a bound state of elec- lahassee, Florida. He is best known for trons. Schrieffer’s focus crystallized on his crucial contributions to the theory of finding a many-electron theory that superconductivity, a problem that since could incorporate Cooper’s bound pairs, its discovery in 1911 had vexed physi- which, though not quite bosons, some- cists searching for a microscopic expla- how needed to be condensed.