The Enigma of Supersolidity Sebastien Balibar1
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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. -
Arxiv:0807.2458V2 [Cond-Mat.Dis-Nn] 29 Oct 2008 Se Oee,Tevr Eetwr Eotdi E.7)
Theory of the superglass phase Giulio Biroli,1 Claudio Chamon,2 and Francesco Zamponi3 1Institut de Physique Th´eorique, CEA, IPhT, F-91191 Gif-sur-Yvette, France CNRS, URA 2306, F-91191 Gif-sur-Yvette, France 2Physics Department, Boston University, Boston, MA 02215, USA 3CNRS-UMR 8549, Laboratoire de Physique Th´eorique, Ecole´ Normale Sup´erieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France (Dated: October 29, 2008) A superglass is a phase of matter which is characterized at the same time by superfluidity and a frozen amorphous structure. We introduce a model of interacting bosons in three dimensions that displays this phase unambiguously and that can be analyzed exactly or using controlled approxima- tions. Employing a mapping between quantum Hamiltonians and classical Fokker-Planck operators, we show that the ground state wavefunction of the quantum model is proportional to the Boltzmann measure of classical hard spheres. This connection allows us to obtain quantitative results on static and dynamic quantum correlation functions. In particular, by translating known results on the glassy dynamics of Brownian hard spheres we work out the properties of the superglass phase and of the quantum phase transition between the superfluid and the superglass phase. I. INTRODUCTION Solids do not flow. This apparently tautological statement can be wrong in two ways. First, solidity is in general a timescale-dependent phenomenon. Crystal or glasses, well known solids on most experimentally relevant timescales, do flow if one waits long enough (see Ref. 1 for example). Second, at very small temperatures, quantum solids may become superfluids as suggested theoretically in the early seventies2–4. -
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. -
Insulation Solutions Guide
Creating Intelligent Environments Insulation Solutions Guide Has anyone ever put more thought into insulation? Our world has changed. The way we live is affecting our planet more than ever, and the buildings we construct need to address this – now. 2 Technical Department: 0808 1645 134 It’s time to think carefully about our future. All our futures. What we do today will have an immeasurable impact on tomorrow. And if we do the right thing, we’ll all benefit. As will the next generation. Superglass may be a brand with 40 years behind it, but our thinking is light years ahead. We create intelligent insulation solutions that enable comfortable living and working environments. And that protect our global environment by saving energy and using recycled glass. A global leader We may still be based in Scotland, but we’re part of global leader in roofing, waterproofing and insulation TECHNONICOL – a business with over 6500 people, 51 manufacturing plants and offices in 79 countries, dedicated to researching and investing in new energy saving solutions to improve the lives of millions of people worldwide. So while insulation is what we make, what we contribute makes an important difference to our planet. www.superglass.co.uk 3 The smartest way to use energy is to not use it at all. That’s the underlying principle behind Superglass thinking. It drives everything we do – from creating new ways of insulating to helping housebuilders make best use of resources. 4 Technical Department: 0808 1645 134 We’ve long been innovators – bringing new ideas, products and thinking to the construction industry. -
Bose-Einstein Condensation in Quantum Glasses
Bose-Einstein condensation in quantum glasses Giuseppe Carleo,1 Marco Tarzia,2 and Francesco Zamponi3, 4 1SISSA – Scuola Internazionale Superiore di Studi Avanzati and CNR-INFM DEMOCRITOS – National Simulation Center, via Beirut 2-4, I-34014 Trieste, Italy. 2Laboratoire de Physique Th´eorique de la Mati`ere Condens´ee, Universit´ePierre et Marie Curie-Paris 6, UMR CNRS 7600, 4 place Jussieu, 75252 Paris Cedex 05, France. 3Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA 4Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, UMR CNRS 8549, 24 Rue Lhomond, 75231 Paris Cedex 05, France. The role of geometrical frustration in strongly interacting bosonic systems is studied with a com- bined numerical and analytical approach. We demonstrate the existence of a novel quantum phase featuring both Bose-Einstein condensation and spin-glass behaviour. The differences between such a phase and the otherwise insulating “Bose glasses” are elucidated. Introduction. Quantum particles moving in a disor- frustrated magnets [10], valence-bond glasses [11] and dered environment exhibit a plethora of non-trivial phe- the order-by-disorder mechanism inducing supersolidity nomena. The competition between disorder and quan- on frustrated lattices [12]. Another prominent manifes- tum fluctuations has been the subject of vast literature tation of frustration is the presence of a large number [1, 2] in past years, with a renewed interest following of metastable states that constitutes the fingerprint of from the exciting frontiers opened by the experimental spin-glasses. When quantum fluctuations and geomet- research with cold-atoms [3, 4]. One of the most striking rical frustration meet, their interplay raises nontrivial features resulting from the presence of a disordered ex- questions on the possible realisation of relevant phases ternal potential is the appearance of localized states [1]. -
Quantum Fluctuations Can Promote Or Inhibit Glass Formation
LETTERS PUBLISHED ONLINE: 9 JANUARY 2011 | DOI: 10.1038/NPHYS1865 Quantum fluctuations can promote or inhibit glass formation Thomas E. Markland1, Joseph A. Morrone1, Bruce J. Berne1, Kunimasa Miyazaki2, Eran Rabani3* and David R. Reichman1* Glasses are dynamically arrested states of matter that do not 0.7 1–4 exhibit the long-range periodic structure of crystals . Here Glass 0.7 we develop new insights from theory and simulation into the 0.6 impact of quantum fluctuations on glass formation. As intuition may suggest, we observe that large quantum fluctuations serve 0.6 φ 0.5 to inhibit glass formation as tunnelling and zero-point energy 0.4 allow particles to traverse barriers facilitating movement. 0.3 However, as the classical limit is approached a regime is 10¬2 10¬1 100 φ 0.5 observed in which quantum effects slow down relaxation Λ∗ making the quantum system more glassy than the classical system. This dynamical ‘reentrance’ occurs in the absence of obvious structural changes and has no counterpart in the phenomenology of classical glass-forming systems. 0.4 Although a wide variety of glassy systems ranging from metallic to colloidal can be accurately described using classical theory, Liquid quantum systems ranging from molecular, to electronic and 5,6 0.3 magnetic form glassy states . Perhaps the most intriguing of these 10¬2 10¬1 100 is the coexistence of superfluidity and dynamical arrest, namely Λ∗ the `superglass' state suggested by recent numerical, theoretical and experimental work7–9. Although such intriguing examples exist, Figure 1 j Dynamic phase diagram calculated from the QMCT for a at present there is no unifying framework to treat the interplay hard-sphere fluid. -
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. -
Bose-Einstein Condensation in Quantum Glasses
Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Bose-Einstein condensation in Quantum Glasses Giuseppe Carleo, Marco Tarzia, and Francesco Zamponi∗ Phys. Rev. Lett. 103, 215302 (2009) Collaborators: Florent Krzakala, Laura Foini, Alberto Rosso, Guilhem Semerjian ∗Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, 24 Rue Lhomond, 75231 Paris Cedex 05 March 29, 2010 Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Outline 1 Motivations Supersolidity of He4 Helium 4: Monte Carlo results 2 The quantum cavity method Regular lattices, Bethe lattices and random graphs Recursion relations Bose-Hubbard models on the Bethe lattice 3 A lattice model for the superglass Extended Hubbard model on a random graph Results A variational argument 4 Discussion Disordered Bose-Hubbard model: the Bose glass 3D spin glass model with quenched disorder Quantum Biroli-M´ezard model: a lattice glass model 5 Conclusions Motivations The quantum cavity method A lattice model for the superglass Discussion Conclusions Outline 1 Motivations Supersolidity of He4 Helium 4: Monte Carlo results 2 The quantum cavity method Regular lattices, Bethe lattices and random graphs Recursion relations Bose-Hubbard models on the Bethe lattice 3 A lattice model for the superglass Extended Hubbard model on a random graph Results A variational argument 4 Discussion Disordered Bose-Hubbard model: the Bose glass 3D spin glass model with quenched disorder Quantum Biroli-M´ezard model: a lattice glass model 5 Conclusions Experimental Results Discovery by Kim & Chan in He4 (Nature & Science 2004). Motivations• The quantumExperimental cavity method A lattice modelResults for the superglass Discussion Conclusions Reproduced after by many4 other groups. -
Quantum Spin Glasses on the Bethe Lattice
Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions Quantum Spin Glasses on the Bethe lattice Francesco Zamponi∗ with C.R.Laumann, S. A. Parameswaran, S.L.Sondhi, PRB 81, 174204 (2010) with G.Carleo and M.Tarzia, PRL 103, 215302 (2009) ∗Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, 24 Rue Lhomond, 75231 Paris Cedex 05 June 2, 2010 Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions Outline 1 Introduction Classical spin glasses Random lattices and the cavity method Ising antiferromagnet on a random graph 2 AKLT states on the Bethe lattice AKLT states: mapping on a classical model AKLT models on the tree AKLT models on the random graph Phase diagram Spectrum of the quantum spin glass phase 3 A lattice model with a superglass phase Extended Hubbard model on a random graph Results A variational argument 4 Conclusions Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions Outline 1 Introduction Classical spin glasses Random lattices and the cavity method Ising antiferromagnet on a random graph 2 AKLT states on the Bethe lattice AKLT states: mapping on a classical model AKLT models on the tree AKLT models on the random graph Phase diagram Spectrum of the quantum spin glass phase 3 A lattice model with a superglass phase Extended Hubbard model on a random graph Results A variational argument 4 Conclusions Introduction AKLT states on the Bethe lattice A lattice model with a superglass phase Conclusions -
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.