DOCSLIB.ORG

Superfluidity in Strongly Correlated Systems

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Superfluidity in Strongly Correlated Systems Superfluidity in Strongly Correlated Systems A dissertation presented by Eun Gook Moon 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 2011 c 2011 - Eun Gook Moon All rights reserved. Thesis advisor Author Subir Sachdev Eun Gook Moon Superfluidity in Strongly Correlated Systems Abstract We study superfluidity in strongly correlated systems by focusing three features as follows. First, interplay between superfluidity and other order parameters near quantum critical points is studied. The onset positions of the order parameters with or without superconductivity determines how they interact with each other. For the spin density wave (SDW) transition, we find that the quantum critical point shifts by order ∆ , where ∆ is pairing amplitude, so that the region of SDW order is smaller j j in the superconductor than in the metal. This shift is larger than the ∆ 2 shift j j predicted by theories of competing orders which ignore Fermi surface effects. Second, we study a doped antiferromagnetic Mott insulator motivated by cop- per based high temperature superconductors. Based on spin and charge fraction- alization, the algebraic charge liquid phase whose bosonic spinons have energy gap but fermionic holons form Fermi surfaces and its superconductivity are studied. We show fluctuations of local SDW order orientation lead to d-wave superconductiv- ity, and its quantum critical pairing mechanisms are investigated. Also, a theory of bound states between spinons and holons is studied. We show that the fractional- ization induces a doubling electron-like quasiparticles, which naturally induces the fractionalized Fermi liquid. The bound state theory describes exotic properties of the underdoped Cuprates such as \nodal-antinodal dichotomy" at a mean field level description. At last, we study superfluidity of fermions in optical lattices near the Feshbach resonance. Due to divergence of scattering length at the resonance, universality is observed and characteristics of superfluidity has been studied. We extend such uni- versal properties by considering superfluid-insulator transition with an even integer number of fermions per unit cell. The resulting insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. iii Contents Title Page....................................i Abstract..................................... iii Table of Contents................................ iv Citations to Previously Published Work................... vi Acknowledgments................................ vii Dedication.................................... ix 1 Introduction1 1.1 Phase diagrams of cuprates and pnictides................4 1.2 Spin and charge fractionalization....................7 1.3 Superfluidity near the Feshbach resonance............... 10 1.4 Organization of this thesis........................ 14 2 Quantum critical point shifts under superconductivity: the pnictides and the cuprates 16 2.1 Introduction................................ 16 2.2 The spin-fermion model......................... 20 2.3 Pairing instabilities............................ 24 2.4 Microscopic symmetry and effective theory............... 26 2.5 Critical point shifts............................ 29 2.6 Conclusions................................ 36 3 Competition between spin density wave order and superconductivity in the underdoped cuprates 40 3.1 Introduction................................ 40 3.2 Eliashberg theory of pairing....................... 49 3.3 Shift of SDW ordering by superconductivity.............. 61 3.4 Conclusions................................ 66 4 Quantum-critical pairing with varying exponents 70 4.1 Introduction................................ 70 4.2 Review of the models........................... 74 iv Contents v 4.3 the MS model as the γ model with varying exponent γ ........ 80 4.4 the MS model at the SDW QCP { the equivalence with color super- conductivity................................ 88 4.5 Conclusions................................ 91 5 The underdoped cuprates as fractionalized Fermi liquids: transition to superconductivity 93 5.1 Introduction................................ 93 5.2 Effective Hamiltonian........................... 100 5.3 Invariant pairings and instability.................... 104 5.4 Spectral Gap............................... 108 5.5 Conclusions................................ 115 6 Superfluid-insulator transitions of the Fermi gas with near-unitary interactions in a periodic potential 119 6.1 Introduction................................ 119 6.2 Model Hamiltonian............................ 121 6.3 Discussion................................. 126 Citations to Previously Published Work Chapter2 has been previously published as \Quantum critical point shifts under superconductivity: the pnictides and the cuprates", E. G. Moon and S. Sachdev, Phys. Rev. B, 82, 104516 (2010), arXiv:1005.3312. Chapter3 has been recently published as \Competition between spin density wave order and superconductivity in the underdoped cuprates", E. G. Moon and Subir Sachdev, Phys. Rev. B, 80, 035117 (2009), arXiv:0905.2608. Chapter4 has been previously published as \Quantum-critical pairing with varying exponents", E. G. Moon and A. V. Chubukov, JLTP , 161, 263(2010), arXiv:1005.0356. Chapter5 has been recently submitted and accepted as \The underdoped cuprates as fractionalized fermi liquids : transition to superconductivity", E. G. Moon and Subir Sachdev, arXiv:1010.4567. Chapter6 has been previously published as \Superfluid-insulator transitions of the Fermi gas with near-unitary inter- actions in a periodic potential", E. G. Moon, P. Nikolic, and S. Sachdev, Phys. Rev. Lett., 99, 230403 (2007), arXiv:0707.2383. Electronic preprints (shown in typewriter font) are available on the Internet at the following URL: http://arXiv.org vi Acknowledgments It would have been impossible to complete this thesis without help from many people. I wish to thank them from my heart. Most of all, I would like to thank my advisor, Professor Subir Sachdev. I vividly remember the first moment of graduate years at Harvard when I got author's signature on his book. Since then it was a great experience to work with him. His deep understanding and intuition of physics guided me well. Discussions with him always made my understanding deeper. Writing papers together gave me great opportunities to learn his perspective and knowledge which I desire to reach. Without his help, I could not imagine finishing this thesis. Also, I would like to thank Professor Eugene Demler and Professor Markus Greiner for being on my thesis committee. I am grateful to them for providing me presentation opportunities though I have changed my subfield from the ultracold atoms. Discussions with many talented postdocs was one of the most effective ways to learn physics. I am especially grateful to Cenke Xu, Erez Berg, and Liang Fu. Cenke's theoretical viewpoint inspired me and motivated me to study topological objects in field theories. Erez not only taught me a number of phenomenologies but also showed me how one could understands physics in one's own way. Discussions with Liang always gave me chances to think different perspectives. I was impressed by his tendency to find easier ways to explain phenomena. I am indebted to my fellow students in the condensed matter group at Harvard: Yang Qi, Rudro Biswas, Max Metlitski, Yejin Huh, and Susanne Piewala, Takuya Kitagawa. I learned a lot of physics from discussions with them, and I appreciate their friendship. Particularly, Yang taught me useful numerics and his previous work on which I studied superconductivity in an exotic ground state based. Discussions with Max always became good motivations and helped me to understand physics more, and I would like to thank him. I wish to thank Yejin for being a wonderful office-mate and correcting my numerous English mistakes. I wish to thank all my friends I met during my Ph.D program. I am especially grateful to my Korean physics friends at Harvard and MIT: Eunmi Chae, Junhyun Lee, Jaehoon Lee, Jung Ook Hong, Sungkun Hong and Eunju Lee. I deeply appreciate their care, support, and friendship. Their preparation of my defense party was one vii Acknowledgments viii of the most moving events in my time at Harvard. I would like to thank Professors Yong-Baek Kim, Hae-Young Kee, and Eunah Kim for their advices, supports, and encouragements. I would also like to offer my thanks to Professors Junghun Han, Jun-Sung Kim, Jisoon Ihm, Gun-Sang Jeon, Kee-hoon Kim, Tae-won Noh, and Kwon Park and their group members for their hospitality, giving me chances to present my work during my visits to Korea. And I thank Sungwan, Changhyun, Daesu, Jaehyung, Youngkuk, Hosung, Seungeun, Hongki for their unchanging friendship. I deeply appreciate help from all secretaries. Sheila Ferguson helped a clueless international student and made him get through all hurdles to graduate. I would also like to thank William Walker and Heidi Kaye, who made it possible for me to travel. Lastly and most importantly, I would like to thank my parents, Byeong-Kil Moon and Geum-Hee Park. They bore me, raised me, taught me, and loved me. And I wish to thank my brother, Eun-Oh Moon, who always supported me, being the best friend in my life. To them I dedicate this thesis. Dedicated to my father Byeong-Kil Moon, my mother Geum-Hee Park, and my brother Eun-Oh Moon. ix Chapter 1 Introduction This thesis studies theory of superfluidity
Load more

Recommended publications
  • Diffractive Dissociation of Alpha Particles As a Test of Isophobic Short-Range Correlations Inside Nuclei ∗ Jennifer Rittenhouse West A, , Stanley J
    Physics Letters B 805 (2020) 135423 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Diffractive dissociation of alpha particles as a test of isophobic short-range correlations inside nuclei ∗ Jennifer Rittenhouse West a, , Stanley J. Brodsky a, Guy F. de Téramond b, Iván Schmidt c a SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USA b Laboratorio de Física Teórica y Computacional, Universidad de Costa Rica, 11501 San José, Costa Rica c Departamento de Física y Centro Científico Tecnológico de Valparáiso-CCTVal, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaíso, Chile a r t i c l e i n f o a b s t r a c t Article history: The CLAS collaboration at Jefferson Laboratory has compared nuclear parton distributions for a range Received 15 January 2020 of nuclear targets and found that the EMC effect measured in deep inelastic lepton-nucleus scattering Received in revised form 9 April 2020 has a strongly “isophobic” nature. This surprising observation suggests short-range correlations between Accepted 9 April 2020 neighboring n and p nucleons in nuclear wavefunctions that are much stronger compared to p − p or n − Available online 14 April 2020 n correlations. In this paper we propose a definitive experimental test of the nucleon-nucleon explanation Editor: W. Haxton of the isophobic nature of the EMC effect: the diffractive dissociation on a nuclear target A of high energy 4 He nuclei to pairs of nucleons n and p with high relative transverse momentum, α + A → n + p + A + X. The comparison of n − p events with p − p and n − n events directly tests the postulated breaking of isospin symmetry.
    [Show full text]
  • Unit VI Superconductivity JIT Nashik Contents
    Unit VI Superconductivity JIT Nashik Contents 1 Superconductivity 1 1.1 Classification ............................................. 1 1.2 Elementary properties of superconductors ............................... 2 1.2.1 Zero electrical DC resistance ................................. 2 1.2.2 Superconducting phase transition ............................... 3 1.2.3 Meissner effect ........................................ 3 1.2.4 London moment ....................................... 4 1.3 History of superconductivity ...................................... 4 1.3.1 London theory ........................................ 5 1.3.2 Conventional theories (1950s) ................................ 5 1.3.3 Further history ........................................ 5 1.4 High-temperature superconductivity .................................. 6 1.5 Applications .............................................. 6 1.6 Nobel Prizes for superconductivity .................................. 7 1.7 See also ................................................ 7 1.8 References ............................................... 8 1.9 Further reading ............................................ 10 1.10 External links ............................................. 10 2 Meissner effect 11 2.1 Explanation .............................................. 11 2.2 Perfect diamagnetism ......................................... 12 2.3 Consequences ............................................. 12 2.4 Paradigm for the Higgs mechanism .................................. 12 2.5 See also ...............................................
    [Show full text]
  • Surface Pair-Density-Wave Superconducting and Superfluid States
    Surface Pair-Density-Wave Superconducting and Superfluid States Mats Barkman,1 Albert Samoilenka,1 and Egor Babaev1 1Department of Physics, Royal Institute of Technology, SE-106 91 Stockholm, Sweden Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO) predicted inhomogeneous superconducting and superfluid ground states, spontaneously breaking translation symmetries. In this Letter, we demon- strate that the transition from the FFLO to the normal state as a function of temperature or increased Fermi surface splitting is not a direct one. Instead the system has an additional phase transition to a different state where pair-density-wave superconductivity (or superfluidity) exists only on the boundaries of the system, while the bulk of the system is normal. The surface pair- density-wave state is very robust and exists for much larger fields and temperatures than the FFLO state. In regular BCS theory, the formation of Cooper pairs The Ginzburg-Landau description of superconductors binding together two electrons with opposite spin and op- in the presence of Zeeman splitting was derived from mi- posite momentum results in a uniform superconducting croscopic theory in Ref. [31]. The free energy functional state [1,2]. In 1964, Fulde and Ferrell [3] and Larkin and R d reads F [ ] = Ω d x where the free energy density is Ovchinnikov [4] (FFLO) independently predicted that F F under certain conditions there should appear an inho- =α 2 + β 2 + γ 4 + δ 2 2+ mogeneous state in the presence of a strong magnetic F j j jr jµ j j jr j (1) µ 2 2 + ( ∗)2( )2 + c.c. + ν 6; field, where Zeeman splitting of the Fermi surfaces leads j j jr j 8 r j j to the formation of Cooper pairs with nonzero total mo- mentum.
    [Show full text]
  • Three-Flavor Color Superconductivity
    Three-Flavor Color Superconductivity Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften vorgelegt beim Fachbereich Physik der Johann Wolfgang Goethe-Universit¨at in Frankfurt am Main von Hossein Malekzadeh aus dem Iran Frankfurt am Main, Dezember 2007 (D 30) 2 vom Fachbereich Physik der Johann Wolfgang Goethe–Universit¨at als Dissertation angenommen. Dekan: Prof. Dr. W. Aßmus Gutachter: Prof. Dr. D.-H. Rischke, Prof. Dr. Adrian Dumitru Datum der Disputation: Dezember 7, 2007. Acknowledgements I would like to express my special thanks to Prof. Dirk Rischke for all the generous supports that during my Ph.D thesis he gave mentally and practically to me. I learned a lot of things from him which will be certainly very useful for me in future as well. Without his helps and encouragements it would be difficult to come to the end of this thesis. Thank you Dirk! I am also very grateful to Prof. Igor Shovkovy for very instructive discussions we had. He was the one who taught this stimulating field to me. Also, I had a lot of fun with him during lunch breaks and in other occasions. Since I wanted to take ten watermelons with my tow hands, I needed to work harder. On other words, along my Ph.D thesis, I wanted to work on other fields as well, although the project were not published. I had great times when I was collaborating with Prof. Adrian Dumitru and Prof. Michael Strickland. I thank both of you for teaching me those fascinating topics. I also had a wonderful chance to talk to Prof.
    [Show full text]
  • Conventional Superconductors 1 Bogoliubov-De
    Conventional superconductors 1 Bogoliubov-de Gennes equation for inhomogeneous superconductivity: application to vortex core states, (De Gennes’s book ) Caroli, De Gennes, Matricon, Phys. Lett. 9; 307 (1964). 2 “Concept of off-diagonal long range order and the quantum phases of liquid He and of superconductors”, C. N. Yang, Rev. Mod. Phys 34, 694, 1962. 3 Anderson theorem for disordered superconductors, “Theory of dirty superconductors”, J. Phys. Chem. Solids, 11, 26 (1959). 4 Yu-Shiba state: magnetic impurity in superconductor, Yu L. Acta Phys. Sinica, 21, 75 1965; H. Shiba, Prog. Theor. Phys. 40, 435 1968. 5 McMillan formula, “Transition Temperature of Strong-Coupled Superconductors”, Physical Review, vol. 167, 331-344(1968). 6 FFLO state, Inhomogeneous superconductivity in condensed matter and QCD Roberto Casalbuoni and Giuseppe Nardulli, Rev. Mod. Phys. 76, 263 (2004). 7 Superconductivity in fullerides O. Gunnarsson, Rev. Mod. Phys. 69, 575 – Published 31 March 1997 He-3 and other p-wave systems 8 A deeper study on He-3, “A theoretical description of the new phases of liquid He-3”, Anthony Leggett, RMP 47, 331 (1975). 9 p-wave pairing, “The superconductivity of Sr2RuO4 and the physics of spin triplet pairing”, Rev. Mod. Physics 75, 657, (2003). 10 Toplogical defect in He-3, “Quantized vortices in superfluid He3”, M. M. Salomaa and G. E. Volovik, Rev. Mod. Phys. 59, 533 (1987). 11 Majorana fermions, arXiv:cond-mat/0010440, “Unpaired Majorana fermions in quantum wires”, Alexei Kitaev High Tc superconductivity 12 Effective models of high Tc: Zhang-Rice singlet of high Tc, Phys. Rev. B, 37, 3759 (1988); Emery, Thoery of high Tc superconductivity in oxides, PRL 58, 2794 (1987).
    [Show full text]
  • Color Superconductivity in Quark Matter Mark Alford Washington University Saint Louis, USA
    Fedora GNU/Linux; LATEX 2ǫ; xfig Color superconductivity in quark matter Mark Alford Washington University Saint Louis, USA 1 Outline I Quarks at high density Cooper pairing, color superconductivity II Color superconducting phases Pairing vs. the strange quark mass III Compact stars Transport properties and signatures IV Looking to the future M. Alford, K. Rajagopal, T. Sch¨afer, A. Schmitt, arXiv:0709.4635 (RMP review) 2 I. Quarks at high density Quarks: Building blocks of matter atom: nucleus & electrons Quarks have color and flavor (“up” or “down”) proton: uud, uud, uud neutron: udd, udd, udd neutron/proton: 3 quarks bound by color force, Quantum Chromo Dynamics (QCD) 3 Interactions between Quarks Dominant interaction between quarks is the strong interaction, described by SU(3) “color” non-Abelian gauge theory (QCD). Properties of QCD • Short distances, r ≪ 1 fm, asymptotically free : g gauge coupling g ≪ 1, single gluon exchange dom- inates, the theory is analytically tractable. g • Long distances r > 1 fm, QCD confines : color electric fields form flux tubes, only color-neutral states, baryons and mesons, exist. baryon meson 4 Cooper pairing in quark matter: color superconductivity At sufficiently high density and low temperature, there is a Fermi sea of almost free quarks. Any attractive quark-quark interaction causes pairing instability of the Fermi surface: BCS mechanism of superconductivity. dF F = E − µN =0 µ = EF dN E QCD attractive quark-quark interaction p in color-antisymmetric channel: - single gluon exchange - instanton interaction - strong coupling: count flux tubes - confinement is attraction BCS in quark matter: Ivanenko and Kurdgelaidze, Lett. Nuovo Cim.
    [Show full text]
  • Light Tetraquarks and the Chiral Phase Transition
    Light tetraquarks and the chiral phase transition Vladimir Skokov, RIKEN/BNL Research Center & RDP: 1606.04111 XYZ, Pc states: strong evidence for tetraquark & pentaquark states, composed of both light and heavy quarks Why do we need heavy quarks to see tetraquark states? Jaffe ’79…Schechter…Close…Tornqvist…Maiani…Giacosa….Peleaz ’15: “the” σ meson is “a” tetraquark (diquark anti-diquark). But situation murky…. Punchline: tetraquarks must be included to understand the phase diagram of QCD (versus quark mass, plane of temperature T and baryon chemical potential μ) Tetraquarks: for three (not two) flavors of very light quarks, tetraquarks may generate a second chiral phase transition For QCD, in the plane of T & μ plane: direct connection between tetraquarks and color superconductivity in effective modesl, need tetraquarks to determine the Critical EndPoint Tetraquarks for two light flavors: meh, fuh gedda ‘boud it Chiral symmetry for two flavors Classically, chiral symmetry Gcl = SU(2)L x SU(2)R x U(1)A = O(4) x O(2) Use φ, complex 4-component vector φ =(σ + i ⌘ , ~a + i ~⇡ ) Linear σ model for exact χ symmetry: 0 cl 1 2 1 2 2 = (@ φ) + m φ⇤ φ + λ (φ⇤ φ) + ... L 2 µ 2 · · Quantum mechanically, axial anomaly reduces U(1)A -> Z(2)A : φ → (−) φ Simplest term which is only Z(2)A invariant: A =+m2 (Im φ)2 + ... L A With Gcl , η degenerate with π . With axial anomaly, η splits from massless π Directly induced by instantons + … Diquarks and tetraquarks for two flavors Jaffe ’79: most attractive channel for quark-quark scattering is antisym.
    [Show full text]
  • Nonperturbative Phenomena in QCD at Finite Temperature
    Physics of Atomic Nuclei, Vol. 68, No. 5, 2005, pp. 723–747. Translated from Yadernaya Fizika, Vol. 68, No. 5, 2005, pp. 755–779. Original Russian Text Copyright c 2005 by Agasian. Nonperturbative Phenomena in QCD at Finite Temperature N. O. Agasian* Institute of Theoretical and Experimental Physics, Bol’shaya Cheremushkinskaya ul. 25, Moscow, 117259 Russia Received July 26, 2004 Abstract—The main objective of the present study is to analyze various nonperturbative phenomena in QCDboth at low, T<Tc, and at high, T>Tc, temperatures. New methods are developed that make it possible, on one hand, to describe data obtained by numerically simulating QCDon a lattice and, on the other hand, to study new physical phenomena in QCDat finite temperature. c 2005 Pleiades Publish- ing, Inc. 1. INTRODUCTION which was predicted theoretically in recent years (for an overview, see [3–5]), can be realized. The physics of strong interactions, QCD, has been flourishing over the past three decades. For many Quantum chromodynamics is a quantum the- years, investigations into the behavior of strongly in- ory of Yang–Mills gauge fields interacting with quark fermion fields. The asymptotic-freedom phe- teracting matter under various external effects have nomenon [6, 7] and a topologically nontrivial struc- been of great topical interest. In the real world, these ture of the vacuum of non-Abelian gauge theories [8– are primarily temperature and the baryon density. In- 12] were discovered in the 1970s. A further devel- terest in the behavior of matter under extreme con-
    [Show full text]
  • Light Tetraquarks and the Chiral Phase Transition
    Light tetraquarks and the chiral phase transition Vladimir Skokov, RIKEN/BNL Research Center & RDP: 1606.04111 XYZ, Pc states: strong evidence for tetraquark & pentaquark states, composed of both light and heavy quarks Why do we need heavy quarks to see tetraquark states? Jaffe ’79…Schechter…Close…Tornqvist…Maiani…Giacosa….Peleaz ’15: “the” ! meson is “a” tetraquark (diquark anti-diquark). But situation murky…. Punchline: tetraquarks must be included to understand the phase diagram of QCD (versus quark mass, plane of temperature T and baryon chemical potential ") Tetraquarks: for three (not two) flavors of very light quarks, tetraquarks may generate a second chiral phase transition For QCD, in the plane of T & " plane: direct connection between tetraquarks and color superconductivity in effective modesl, need tetraquarks to determine the Critical EndPoint Need tetraquarks to find the critical endpoint Kovacs, Szep, & Wolf, 1601.05291: Use linear ! model + Polyakov loop model And add vector mesons (good!). But do not include tetraquarks. Find a critical endpoint (CEP), but T so low, CEP would have been seen exp’y! T! !!CEP "baryon" Tetraquarks for two light flavors: meh, fuh gedda ‘boud it Chiral symmetry for two flavors Classically, chiral symmetry Gcl = SU(2)L x SU(2)R x U(1)A = O(4) x O(2) Use #, complex 4-component vector φ =(σ + i η , a + i π ) Linear ! model for exact $ symmetry: 0 cl 1 2 1 2 2 = (∂ φ) + m φ∗ φ + λ (φ∗ φ) + ... L 2 µ 2 · · Quantum mechanically, axial anomaly reduces U(1)A -> Z(2)A : # " (') # Simplest term which is only Z(2)A invariant: A =+m2 (Im φ)2 + ..
    [Show full text]
  • Two Lectures on Color Superconductivity
    Two lectures on color superconductivity∗ Igor A. Shovkovy† Frankfurt Institute for Advanced Studies and Institut f¨ur Theoretische Physik, Johann Wolfgang Goethe-Universit¨at, D-60054 Frankurt am Main, Germany February 4, 2008 Abstract The first lecture provides an introduction to the physics of color superconductivity in cold dense quark matter. The main color su- perconducting phases are briefly described and their properties are listed. The second lecture covers recent developments in studies of color superconducting phases in neutral and β-equilibrated matter. The properties of gapless color superconducting phases are discussed. arXiv:nucl-th/0410091v2 8 Nov 2004 ∗Lectures delivered at the IARD 2004 conference, Saas Fee, Switzerland, June 12 - 19, 2004, and at the Helmholtz International Summer School and Workshop on Hot points in Astrophysics and Cosmology, JINR, Dubna, Russia, August 2 - 13, 2004. †On leave from Bogolyubov Institute for Theoretical Physics, 03143, Kiev, Ukraine. 1 Contents 1 Introduction into color superconductivity 3 1.1 Densebaryonicmatter . .. .. 3 1.1.1 Weakly interacting quark matter . 4 1.2 Cooper instability and color superconductivity . ... 5 1.3 Two-flavor color superconductivity (Nf =2).......... 7 1.3.1 Color and flavor structure of the condensate . 10 1.3.2 Quark propagator in the Nambu-Gorkov basis . 11 1.3.3 One-gluon exchange interaction . 12 1.3.4 GapequationinQCD . 15 1.3.5 GapequationintheNJLmodel . 17 1.3.6 Properties of quark matter in the 2SC phase . 19 1.4 Color-flavor locked phase (Nf =3) ............... 21 1.4.1 Properties of quark matter in the CFL phase . 23 1.4.2 Low-energyeffectiveaction.
    [Show full text]
  • Summary of Activities in 2009
    II Summary of activities in 2009 1. THEORETICAL NUCLEAR PHYSICS GROUP 1 Theoretical Nuclear Physics Group Subjects: Structure and reactions of unstable nuclei, Monte Carlo Shell Model, Molecular Orbit Method, Mean Field Calculations, Quantum Chaos Quark-Gluon Plasma, Lattice QCD simulations, Structure of Hadrons, Color superconductivity, cold atoms, graphene Relativistic Heavy Ion Collisions, Relativistic Hydrodynamics, Color Glass Con- densate Member: Takaharu Otsuka, Tetsuo Hatsuda, Tetsufumi Hirano, Noritaka Shimizu and Shoichi Sasaki In the nuclear theory group, a wide variety of subjects are studied. The subjects are divided into three major categories: Nuclear Structure Physics, Quantum Hadron Physics and High Energy Hadron Physics. Nuclear Structure Physics In the Nuclear Structure group (T. Otsuka and N. Shimizu), quantum many-body problems for atomic nuclei, various issues on nuclear forces and their combinations are studied theoretically from many angles. The major subjects are the structure of unstable exotic nuclei, shell model calculations including Monte Carlo Shell Model, reactions between heavy nuclei, Bose-Einstein condensation, symmetries and quantum chaos, etc. The structure of unstable nuclei is the major focus of our interests, and examples of the current subjects are the disappearance of conventional magic numbers and appearance of new ones. These phenomena are due to the change of the shell structure (shell evolution), and are largely due to nuclear forces such as the tensor force and the three-body force. Many papers with strong impacts have been published by our group in recent years, such as [1]. The structure of such unstable nuclei have been calculated by Monte Carlo Shell Model and conventional shell model [2], and their applications have been made in collaborations with experimentalists [3, 4].
    [Show full text]
  • Exotics: Heavy Pentaquarks and Tetraquarks Arxiv:1706.00610V2
    DESY 17-071 Exotics: Heavy Pentaquarks and Tetraquarks Ahmed Ali,1 Jens S¨orenLange,2 and Sheldon Stone3 1DESY Theory Group, Notkestrasse 85, D-22607 Hamburg, Germany 2Justus-Liebig-Universit¨atGiessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany 3Physics Department, 201 Physics Building, Syracuse University, Syracuse, NY 13244-1130, USA July 31, 2017 Abstract For many decades after the invention of the quark model in 1964 there was no evidence that hadrons are formed from anything other than the simplest pairings of quarks and antiquarks, mesons being formed of a quark-antiquark pair and baryons from three quarks. In the last decade, however, in an explosion of data from both e+e− and hadron colliders, there are many recently observed states that do not fit into this picture. These new particles are called generically \ex- otics". They can be either mesons or baryons. Remarkably, they all decay into at least one meson formed of either a cc or bb pair. In this review, after the introduction, we explore each of these new discoveries in detail first from an experimental point of view, then subsequently give a theo- retical discussion. These exotics can be explained if the new mesons contain two-quarks and two- antiquarks (tetraquarks), while the baryons contain four-quarks plus an antiquark (pentaquarks). The theoretical explanations for these states take three divergent tracks: tightly bound objects, just as in the case of normal hadrons, but with more constituents, or loosely bound \molecules" similar to the deuteron, but formed from two mesons, or a meson or baryon, or more wistfully, they are not multiquark states but appear due to kinematic effects caused by different rescatterings of virtual particles; most of these models have all been post-dictions.
    [Show full text]