DOCSLIB.ORG

Strongly Correlated Quantum Matter January 14 2020

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Strongly Correlated Quantum Matter January 14 2020 Quantum Matter: Concepts and Models Brief introduction to the ”third module”: Strongly correlated quantum matter January 14 2020 Strongly correlated quantum matter bosonic systems fermionic systems … … electronic correlations major focus in condensed matter physics Bob Laughlin from Laughlin’s Nobel Prize talk 1998 Bob Laughlin … on length scales from a few nanometers to ~ human scales from Laughlin’s Nobel Prize talk 1998 Bob Laughlin not so relevant for condensed matter Major problem: The ”Theory of Everything” Hamiltonian 1 can’t be solved accurately for more than (at most) ~ 10 particles. A catastrophe of dimension! N # of particles Required size of computer memory: m required memory size to represent theDOS wave function of one particle Waiting for a quantum computer, what to do? B~ = A~ What we have always done: r⇥ Make approximations & caricatures guided by experiments! pφ =( i~/r)@φ n n +1 − ! Ey h ⇢yx = Φ0 = (flux quantum) jx e M =0 M =0 6 ⇢xx ⌫ =0 ⌫ =1 P =0modeP= e/2 mod e a =1 w =0 v =0 v =0 w =0 6 6 2 2 2 2 2 12 1 T =(UT K) = UT K = UT = n n = n n ⇥ ⇥ 2 2 2 2 2 T =(UT K) =(1n n ( iσy)) K =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ HF (k) u (k) = ✏ (k) u (k) | n i n | n i ⇡ ⇡ − a a n =1, 2: e↵ective time-independent two-band model ✏n kn=1 n =2 Start easy: • neglect the electron-electron (and ion-ion) interaction • treat the ions as fixed (Born-Oppenheimer approximation) wave functions built from Slater determinants wave of functions single-particle potential of a static lattice of background ions (”hard” quantum condensed matter) major schemes: nearly free electron approximation (Bloch state basis) tight-binding approximation (Wannier state basis) Band theory of metals, semimetals, semiconductors, and insulators (elementary textbook solid state physics) Still, lots of interesting physics! Even more so when bringing in effects from relativity, lattice distortions, confined geometries,…! topological band theory mesoscopic physics Next: adding the electron-electron interaction (the starting point of this course module!) popular approach: mean-field theory Hartree-Fock (”textbook”) Density Functional Theory (DFT) P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964) W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965) single-electron Kohn-Sham Hamiltonian powerful method for systems with weak electron correlations LDA W. Kohn P. Hohenberg L. Sham 1 Next: 2 ¯ 1/3 Ee-e e /d n 1/3 Adding the electron-electron interaction 2 2 2/3 = n− Ekin ⇠ ~ kF /m ⇠ n mN DOS 1 B~ = A~ 1 How to assess the importance of the electron-electron interaction?r⇥ When is its effect weak? When is it ”strong”? 2 ¯ 1/3 Ee-e e /d n 1/3 2 2 2/3 = n− Ekin ⇠ ~ kF /2m ⇠ n 2 ¯ 1/3 1 ”weak” Ee-e meN /d n 1/3 ⌧ ”Rule of thumb” (3D): = n− 2 2DOS 2/3 Ekin ⇠ ~ kF /2m ⇠ n (1) ”strong” ¯ N d average electron separation ⇠ O m n electron density DOS pφ =( i~/r)@φ n n +1 − ! B~ = A~ r⇥ B~ = A~ Ey h r⇥ ⇢yx = Φ0 = (flux quantum) jx e 1 1 M =0 M =0 ⌧ 6 ⌧ ⇢xx (1) (1) ⇠ O ⇠ O pφ =( i~/r)@φ n n +1 ⌫ =0 ⌫ =1 P =0modeP− = e/2 mod! e p =( i /r)@ n n +1 φ ~ φ Ey h − ! ⇢yx = Φ0 = (flux quantum) jx e M =0 M =0a =1 w =0 v =0 v =0 w =0 6 6 6 ⇢xx Ey h ⇢yx = Φ0 = (flux quantum) jx e 2 2 2 2 2 12 1 T =(UT K) = U⌫T=0K =⌫ =1UT =P =0modn n = ePn n= e/2 mod e M =0 M =0 ⇥ ⇥ 6 ⇢xx a =1 w =0 v =0 v =0 w =0 2 2 2 2 6 2 6 T =(UT K) =(1n n ( iσy)) K =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ 2 2 2 2 2 12 1 T =(UT K) = UT K = UT = n n = n n ⌫ =0 ⌫ =1 P =0modeP= e/2 mod e ⇥ ⇥ HF (k) u (k) = ✏ (k) u (k) 2 n 2 n n 2 2 2 T =(U|T K) =(i 1n n ( |iσy)) Ki =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ a =1 w =0 v =0 v =0 w =0 F 6 6 ⇡ H⇡ (k) un(k) = ✏n(k) un(k) | i | i − a a n =1, 2: e↵ective time-independent two-band model ⇡ ⇡ 2 2 2 2 2 12 1 − a a T =(UT K) = UT K = UT = n n = n n n =1, 2: e↵ective time-independent⇥ two-band⇥ model ✏n kn=1 n =2 ✏n kn=1 n =2 2 2 2 2 2 T =(UT K) =(1n n ( iσy)) K =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ HF (k) u (k) = ✏ (k) u (k) | n i n | n i ⇡ ⇡ − a a n =1, 2: e↵ective time-independent two-band model ✏n kn=1 n =2 1 Next: 2 ¯ 1/3 Ee-e e /d n 1/3 Adding the electron-electron interaction 2 2 2/3 = n− Ekin ⇠ ~ kF /m ⇠ n mN DOS 1 B~ = A~ 1 How to assess the importance of the electron-electron interaction?r⇥ When is its effect weak? When is it ”strong”? 2 ¯ 1/3 Ee-e e /d n 1/3 2 2 2/3 = n− Ekin ⇠ ~ kF /2m ⇠ n 2 ¯ 1/3 1 ”weak” Ee-e meN /d n 1/3 ⌧ ”Rule of thumb” (3D): = n− 2 2DOS 2/3 Ekin ⇠ ~ kF /2m ⇠ n (1) ”strong” ¯ N d average electron separation ⇠ O m n electron density DOS LDA+U,…? DFT fails pφ =( i~/r)@φ n n +1 − ! another, more modern, typeB~ =of mean-fieldA~ theory can sometimes be used r⇥ Dynamical mean-field theory E h B~ = A~ ⇢ = y Φ = (flux quantum)r⇥ W. Metzner and D. Vollhardt, Phys. Rev. Lett.yx 62, 324j (1989) 0 e A. Georges and G.Kotliar , Phys. Rev. B 45, 6479 (1992)x 1 1 MMapping=0 M the=0 full lattice problem to a time-dependent single-site ”mean⌧ field” problem 6 ⌧ ⇢xx usually treated by numerical methods (exact diagonalization, Monte Carlo,…) (1) (1) ⇠ O ⇠ O pφ =( i~/r)@φ n n +1 ⌫ =0 ⌫ =1 P =0modeP− = e/2 mod! e p =( i /r)@ n n +1 φ ~ φ Ey h − ! ⇢yx = Φ0 = (flux quantum) jx e M =0 M =0a =1 w =0 v =0 v =0 w =0 6 6 6 ⇢xx Ey h ⇢yx = Φ0 = (flux quantum) jx e 2 2 2 2 2 12 1 T =(UT K) = U⌫T=0K =⌫ =1UT =P =0modn n = ePn n= e/2 mod e M =0 M =0 ⇥ ⇥ 6 ⇢xx a =1 w =0 v =0 v =0 w =0 2 2 2 2 6 2 6 T =(UT K) =(1n n ( iσy)) K =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ 2 2 2 2 2 12 1 T =(UT K) = UT K = UT = n n = n n ⌫ =0 ⌫ =1 P =0modeP= e/2 mod e ⇥ ⇥ HF (k) u (k) = ✏ (k) u (k) 2 n 2 n n 2 2 2 T =(U|T K) =(i 1n n ( |iσy)) Ki =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ a =1 w =0 v =0 v =0 w =0 F 6 6 ⇡ H⇡ (k) un(k) = ✏n(k) un(k) | i | i − a a n =1, 2: e↵ective time-independent two-band model ⇡ ⇡ 2 2 2 2 2 12 1 − a a T =(UT K) = UT K = UT = n n = n n n =1, 2: e↵ective time-independent⇥ two-band⇥ model ✏n kn=1 n =2 ✏n kn=1 n =2 2 2 2 2 2 T =(UT K) =(1n n ( iσy)) K =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ HF (k) u (k) = ✏ (k) u (k) | n i n | n i ⇡ ⇡ − a a n =1, 2: e↵ective time-independent two-band model ✏n kn=1 n =2 1 2 ¯ 1/3 Ee-e e /d n 1/3 = n− E ⇠ 2k2 /2m ⇠ n2/3 kin ~ F 1 mN r ⇤ = ”high-energy”Next: cuto↵ DOS Adding the electron-electron interaction d¯ average2 ¯ electron1/3 separation Ee-e e /d n 1/3 n2 electron2 density2/3 = n− Ekin ⇠ ~ kF /2m ⇠ n e2 U(q) Alternative⇠ q2 strategy: perturbation theory 1 (”many-body theory”) 2...”Low-energy”¯ dr1/...3 approach, smear out the lattice: Uion(rj) const. Ee-e e /d! n = n 1/3 ! X2 2 Z 2/3 − Ekin ⇠ ~ kF /Second2m ⇠ n quantization: 1 kin = B~ = A~ Hkin = r⇥ H N 2 ¯ 1/3 m r Ee-e e /d n 1/3 2 2 2/3 = n− Ekin ⇠ ~ kF /2m ⇠ n ee = 1 H ⌧ mN rDOS e2 U(q) 2 ⇠ q (1) d¯ average electron separation ⇠ O n electronDOS density ... dr... ! Z d¯ average electron separation X pφ =( i~/r)@φ n n +1 n electron density − ! = Hkin mN r Ey h Uion(rj) const. ⇢yx = Φ0 = (flux quantum) ! j e DOS x M =0 M =0 d¯ average electron separation 6 n electron densityU (r ) ⇢const.B~ =, A~.... dr.... ion j ! xx r⇥ ! j X Z 1 B~ =⌧ A~ r⇥ ⌫ =0 ⌫ =1 P =0modeP= e/2 mod e (1) Uion(rj) const. ⇠ O ! 1 ⌧ a =1 w =0 v =0 v =0 w =0 B~ = A~ 6 6 pφ =( i~/r)@φ n n +1 r⇥ − (1) ! ⇠ O 1 2 2 2 2 2 12 1 E h ⌧ T =(UT K) = UT K = UT = n n = n n ⇢ = y Φ = (flux quantum) ⇥ ⇥ yx j 0 e pφ =(x i~/r)@φ n n +1 (1) − ! ⇠ O M =0 M =0 6 2 2 1 2 2 1 2 1 ⇢xx T =(UT K) =( n n ( iσy)) K =( n n ( iσy)) = 2n 2n pφ =( i~/r)@φ n n +1 ⇥ ⌦ − ⇥ ⌦ − − ⇥ Ey h − ! ⇢yx = Φ0 = (flux quantum) jx e E h ⇢ = y Φ = (flux quantum) F ⌫ =0 ⌫ =1 P =0modyx eP= 0e/2 mod e H (k) un(k) = ✏n(k) un(k) jx e | i | i M =0 M =0 6 ⇢xx a =1 w =0 v =0 v =0 w =0 6 6 ⌫ =0 ⌫ =1 P =0modeP= e/2 mod e 2 2 2 2 2 12 1 T =(UT K) = UT K = UT = n n = n n ⇥ ⇥ a =1 w =0 v =0 v =0 w =0 6 6 2 2 2 2 2 T =(UT K) =(1n n ( iσy)) K =(1n n ( iσy)) = 12n 2n ⇥ ⌦ − ⇥ ⌦ − − ⇥ First-order perturbative contribution to the groundstate energy: Second-order perturbative contribution to the groundstate energy: 1 ⇤ = ”high-energy” cuto↵ 2 ¯ 1/3 Ee-e e /d n 1/3 2 2 2/3 = n− Ekin ⇠ ~ kF /2m ⇠ n e2 U(q) ⇠ q2 ..
Load more

Recommended publications
  • Kondo Effect and Mesoscopic Fluctuations
    PRAMANA c Indian Academy of Sciences Vol. 77, No. 5 — journal of November 2011 physics pp. 769–779 Kondo effect and mesoscopic fluctuations DENIS ULLMO1,∗, SÉBASTIEN BURDIN2, DONG E LIU3 and HAROLD U BARANGER3 1LPTMS, Univ. Paris Sud, CNRS, 91405 Orsay Cedex, France 2Condensed Matter Theory Group, LOMA, UMR 5798, Université de Bordeaux I, 33405 Talence, France 3Department of Physics, Duke University, Box 90305, Durham, NC 27708-0305, USA ∗Corresponding author. E-mail: [email protected] Abstract. Two important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic fluctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic fluctuations; in particular, we consider a small quan- tum dot coupled to a finite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature TK which takes into account the mesoscopic fluctuations is a relevant concept: for instance, physical properties are universal functions of T/TK. Secondly, when the temperature is much less than the mean level spacing due to confinement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-defined single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-field technique, we connect the mesoscopic fluctuations of the quasiparticles in the weak coupling regime to those at strong coupling.
    [Show full text]
  • Mesoscopic Physics of Finite Temperature Superfluid Turbulence in He4: Models, Solutions and Prospects
    Mesoscopic physics of finite temperature superfluid turbulence in He4: models, solutions and prospects Demosthenes Kivotides University of Strathclyde Glasgow Demosthenes Kivotides Mesoscopic physics of finite temperature superfluid turbulence Prologue Quantize the Schroedinger equation to obtain a QFT of Galilean-relativistic, spin-0, bosonic, many-particle systems Corresponding field-theoretic Hamiltonian: 2 Z H^ = ~ d3xr ^y(x) · r ^(x) + 2m 1 Z d3xd3x0 ^y(x) ^y(x0)V (x; x0) ^(x0) ^(x) 2 Quantum Schroedinger field quanta [look also at soliton-like solutions of LSE (Zamboni-Rached, Becami JMP, 2012)] interact with each other via potential V LSE (V = 0) encodes matter inertia and a stress field (quantum potential) Demosthenes Kivotides Mesoscopic physics of finite temperature superfluid turbulence Prologue Motion under the quantum potential results in highly nontrivial pathlines Quantum potential effects topological defect formation in the superfluid, which are velocity-field vortices V not required for topological defect formation, but has important fluid dynamic effects, since it is the origin of fluid pressure Strongly-interacting liquid: Slater-Kirkwood potential (R = jx − x0j): V (R) = [770exp(−4:60R) − (1:49=R6)] × 10−12 erg (R in A˚). Demosthenes Kivotides Mesoscopic physics of finite temperature superfluid turbulence Prologue Breaking the rigid U(1) symmetry of quantum Schroedinger field leads to superfluidity (Nambu-Goldstone modes) The standard conservation principles lead to normal-fluid hydrodynamics The purpose of the mesoscopic model (MM) is
    [Show full text]
  • PHYSICS (PHY) Fall 2021
    PHYSICS (PHY) Fall 2021 Physics Chairperson Axel Drees, Physics Building C-104 (631) 632-8114 Graduate Program Director Matt Dawber, Physics Building P-107 (631) 632-4978 Assistant Graduate Program Director Donald J. Sheehan III, Physics Building P-110 (631) 632-8759 Degrees Awarded M.A. in Physics; M.S. in Physics in Scientific Instrumentation; Ph.D. in Physics; Ph.D. in Physics with Concentration in Astronomy; Ph.D. in Physics with Concentration in Physical Biology. Web Site https://www.stonybrook.edu/commcms/grad-physics-astronomy/ http://graduate.physics.sunysb.edu http://www.physics.sunysb.edu/Physics/ Application https://graduateadmissions.stonybrook.edu/apply/ General Description of the Graduate Program The Department of Physics and Astronomy in the College of Arts and Sciences offers courses of study and research that normally lead to the Ph.D. degree. The M.A degree is awarded either as a terminal degree, or to students on the way to the Ph.D. degree. The Master of Science in Scientific Instrumentation program is provided for those interested in instrumentation for physical research. A Master of Arts in Teaching program, from the School of Professional Development, is available for students seeking to teach physics in high schools. Students may find opportunities in various areas of physics not found in the department or in related disciplines at Stony Brook in such programs as Medical Physics, Chemical Physics, Atmospheric and Climate Modeling, Materials Science and at Cold Spring Harbor Laboratory. The entire faculty participates in teaching a rich curriculum of undergraduate, graduate, and professional development courses, including many courses on special topics of current interest.
    [Show full text]
  • Magnetic Quantum Phase Transitions in a Clean Dirac Metal
    arXiv:xxxx.xxxx Magnetic Quantum Phase Transitions in a Clean Dirac Metal D. Belitz1;2 and T. R. Kirkpatrick3 1 Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, OR 97403, USA 2 Materials Science Institute, University of Oregon, Eugene, OR 97403, USA 3 Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA (Dated: August 18, 2021) We consider clean Dirac metals where the linear band crossing is caused by a strong spin-orbit interaction, and study the quantum phase transitions from the paramagnetic phase to various mag- netic phases, including homogeneous ferromagnets, ferrimagnets, canted ferromagnets, and magnetic nematics. We show that in all of these cases the coupling of fermionic soft modes to the order param- eter generically renders the quantum phase transition first order, with certain gapless Dirac systems providing a possible exception. These results are surprising since a strong spin-orbit scattering sup- presses the mechanism that causes the first order transition in ordinary metals. The important role of chirality in generating a new mechanism for a first-order transition is stressed. I. INTRODUCTION is proportional to hd−1, and for d = 3 it is h2 ln h. This is a result of soft or massless excitations in the under- lying Dirac Fermi liquid that are rendered massive by a It has been known for a long time that the spin-orbit magnetic field. While the resulting nonanalyticity has interaction can lead to semimetals, that is, materials the same functional form as in an ordinary or Landau that in a well-defined sense are in between metals and Fermi liquid,12,13 this result came as a surprise since the 1–3 insulators.
    [Show full text]
  • Efficient Directional Excitation of Surface Plasmons by a Single
    Letter pubs.acs.org/NanoLett Efficient Directional Excitation of Surface Plasmons by a Single- Element Nanoantenna § † § † † † † ‡ † ‡ Wenjie Yao, , Shang Liu, , Huimin Liao,*, Zhi Li,*, Chengwei Sun, , Jianjun Chen, , † ‡ and Qihuang Gong , † School of Physics, Peking University, Beijing 100871, China ‡ State Key Laboratory for Mesoscopic Physics, Peking University, Beijing 100871, China *S Supporting Information ABSTRACT: Directional light scattering is important in basic research and real applications. This area has been successfully downscaled to wavelength and subwavelength scales with the development of optical antennas, especially single-element nano- antennas. Here, by adding an auxiliary resonant structure to a single-element plasmonic nanoantenna, we show that the highly efficient lowest-order antenna mode can be effectively transferred into inactive higher-order modes. On the basis of this mode conversion, scattered optical fields can be well manipulated by utilizing the interference between different antenna modes. Both broadband directional excitation of surface plasmon polaritons (SPPs) and inversion of SPP launching direction at different wavelengths are experimentally demonstrated as typical examples. The proposed strategy based on mode conversion and mode interference provides new opportunities for the design of nanoscale optical devices, especially directional nanoantennas. KEYWORDS: nanoantenna, surface plasmon polaritons, directional scattering, mode conversion, single-element ight field manipulation is a basic subject in optics and has generally cannot be excited as efficiently as the lowest mode L several important applications. With the development of by external optical fields because strong field gradients on the nano-optics, this area has been downscaled to nanoscales fi − nanoscales are required to match the complex modal elds of accompanied by several important progresses.1 3 Typical higher-order modes.
    [Show full text]
  • Towards Deep Integration of Electronics and Photonics
    applied sciences Review Towards Deep Integration of Electronics and Photonics Ivan A. Pshenichnyuk 1,* , Sergey S. Kosolobov 1 and Vladimir P. Drachev 1,2,* 1 Skolkovo Institute of Science and Technology, Center for Photonics and Quantum Materials, Nobelya 3, 121205 Moscow, Russia; [email protected] 2 Department of Physics, University of North Texas,1155 Union Circle, Denton, TX 76203, USA * Correspondence: [email protected] (I.A.P.); [email protected] (V.P.D.) Received: 15 September 2019; Accepted: 5 November 2019; Published: 12 November 2019 Abstract: A combination of computational power provided by modern MOSFET-based devices with light assisted wideband communication at the nanoscale can bring electronic technologies to the next level. Obvious obstacles include a size mismatch between electronic and photonic components as well as a weak light–matter interaction typical for existing devices. Polariton modes can be used to overcome these difficulties at the fundamental level. Here, we review applications of such modes, related to the design and fabrication of electro–optical circuits. The emphasis is made on surface plasmon-polaritons which have already demonstrated their value in many fields of technology. Other possible quasiparticles as well as their hybridization with plasmons are discussed. A quasiparticle-based paradigm in electronics, developed at the microscopic level, can be used in future molecular electronics and quantum computing. Keywords: plasmon; light-matter interaction; photonics; nano-electronics; quasiparticle 1. Introduction Further achievements in electronics and photonics imply their better integration. Usage of photons at the level of circuits and single chips has a huge potential to improve modern intelligent systems [1].
    [Show full text]
  • Persistent Current in a Mesoscopic Ring with Strongly Coupled Polarons
    Chapter 18 PERSISTENT CURRENT IN A MESOSCOPIC RING WITH STRONGLY COUPLED POLARONS M. Bayindir and I. O. Kulik Department of Physics, Bilkent University 06533 Bilkent, Ankaro, Thrkey Abstract We investigate influence of the electron-phonon interaction on persistent current in a mesoscopic ring threaded by a Aharonov-Bohm flux <P. We find that all thermodynamic quantities are still periodic in <P with a period <Po = he/e. In both cases, weak- and strong-coupling, effective mass of the electrons is increased and amplitude of persistent current is suppressed. In the latter case the amplitude decreases exponentially as a function of the electron-phonon coupling constant. 1. INTRODUCTION In classical electrodynamics, motion of a charged particle is completely determined by local electric field E and magnetic field B that act upon it. The scalar potential cp and vector potential A were first introduced as a mathematical tool for calculation concerning electromagnetic fields. However, in quantum theory these potentials appear in the Schrodinger equation explicitly and therefore they affect all physical quantities di­ rectly. Aharonov and Bohm [1] have shown that contrary to the conclu­ sion of classical electrodynamics, there exist effects of the potentials on the charged particles, even in the region where all fields vanish (hence, there is no force acting on the particles). The experiment of Chambers [2] proved the existence of Aharonov-Bohm (AB) effect and stimulated ex­ perimental and theoretical studies in this field [3, 4, 5]. This effect has purely quantum mechanical origin because it comes from the interfer­ ence phenomenon. The most well-known example of the AB effect is 283 I.
    [Show full text]
  • Singular Fermi Liquids, at Least for the Present Case Where the Singularities Are Q-Dependent
    Singular Fermi Liquids C. M. Varmaa,b, Z. Nussinovb, and Wim van Saarloosb aBell Laboratories, Lucent Technologies, Murray Hill, NJ 07974, U.S.A. 1 bInstituut–Lorentz, Universiteit Leiden, Postbus 9506, 2300 RA Leiden, The Netherlands Abstract An introductory survey of the theoretical ideas and calculations and the ex- perimental results which depart from Landau Fermi-liquids is presented. Common themes and possible routes to the singularities leading to the breakdown of Landau Fermi liquids are categorized following an elementary discussion of the theory. Sol- uble examples of Singular Fermi liquids include models of impurities in metals with special symmetries and one-dimensional interacting fermions. A review of these is followed by a discussion of Singular Fermi liquids in a wide variety of experimental situations and theoretical models. These include the effects of low-energy collective fluctuations, gauge fields due either to symmetries in the hamiltonian or possible dynamically generated symmetries, fluctuations around quantum critical points, the normal state of high temperature superconductors and the two-dimensional metallic state. For the last three systems, the principal experimental results are summarized and the outstanding theoretical issues highlighted. Contents 1 Introduction 4 1.1 Aim and scope of this paper 4 1.2 Outline of the paper 7 arXiv:cond-mat/0103393v1 [cond-mat.str-el] 19 Mar 2001 2 Landau’s Fermi-liquid 8 2.1 Essentials of Landau Fermi-liquids 8 2.2 Landau Fermi-liquid and the wave function renormalization Z 11
    [Show full text]
  • Single-Mode Characteristic of a Supermode Microcavity Raman Laser
    Single-mode characteristic of a supermode microcavity Raman laser Pei-Ji Zhanga,b,1, Qing-Xin Jia,1 , Qi-Tao Caoa,2, Heming Wanga,3 , Wenjing Liua,b , Qihuang Gonga,b,c,d, and Yun-Feng Xiaoa,b,c,d,2 aState Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, 100871 Beijing, China; bFrontiers Science Center for Nano-optoelectronics, Peking University, 100871 Beijing, China; cCollaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China; and dYangtze Delta Institute of Optoelectronics, Peking University, Nantong 226010, China Edited by Alexis T. Bell, University of California, Berkeley, CA, and approved April 29, 2021 (received for review January 27, 2021) Microlasers in near-degenerate supermodes lay the cornerstone supermode laser. When a tiny reflection is introduced and pro- for studies of non-Hermitian physics, novel light sources, and vides self-injection of the Raman laser, beating phenomena are advanced sensors. Recent experiments of the stimulated scat- observed and recognized as the transient interference during the tering in supermode microcavities reported beating phenomena, lasing switching between the supermodes. interpreted as dual-mode lasing, which, however, contradicts The Raman microlaser is generated by optically pumping a their single-mode nature due to the clamped pump field. Here, we WGM microcavity and propagates in both the clockwise (CW) investigate the supermode Raman laser in a whispering-gallery and counterclockwise (CCW) directions (Fig. 1A) (2, 26). The microcavity and demonstrate experimentally its single-mode las- intracavity counterpropagating waves are coupled by a scatterer ing behavior with a side-mode suppression ratio (SMSR) up to at the surface (8, 9, 21, 42), which forms a pair of standing-wave 37 dB, despite the emergence of near-degenerate supermodes supermodes, the symmetric a+ and antisymmetric a−, defined by the backscattering between counterpropagating waves.
    [Show full text]
  • Statistical and Dynamical Aspects of Mesoscopic Systems
    Lecture Notes in Physics 547 Statistical and Dynamical Aspects of Mesoscopic Systems Proceedings of the XVI Sitges Conference on Statistical Mechanics Held at Sitges, Barcelona, Spain, 7–11 June 1999 Bearbeitet von D Reguera, G Platero, L.L Bonilla, J.M Rubi 1. Auflage 2000. Buch. xii, 360 S. Hardcover ISBN 978 3 540 67478 8 Format (B x L): 15,5 x 23,5 cm Gewicht: 725 g Weitere Fachgebiete > Physik, Astronomie > Angewandte Physik Zu Inhaltsverzeichnis schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Preface One of the most significant developments in physics in recent years con- cerns mesoscopic systems, a subfield of condensed matter physics which has achieved proper identity. The main objective of mesoscopic physics is to un- derstand the physical properties of systems that are not as small as single atoms, but small enough that properties can differ significantly from those of a large piece of material. This field is not only of fundamental interest in its own right, but it also offers the possibility of implementing new generations of high-performance nano-scale electronic and mechanical devices. In fact, interest in this field has been initiated at the request of modern electronics which demands the development of more and more reduced structures. Un- derstanding the unusual properties these structures possess requires collabo- ration between disparate disciplines.
    [Show full text]
  • Mesoscopic Electronics in Solid State Nanostructures
    Thomas Heinzel Mesoscopic Electronics in Solid State Nanostructures Second, Completely Revised and Enlarged Edition WILEY-VCH Verlag GmbH & Co. KGaA This Page Intentionally Left Blank Thomas Heinzel Mesoscopic Electronics in Solid State Nanostructures Second, Completely Revised and Enlarged Edition WILEY-VCH Verlag GmbH & Co. KGaA 1807–2007 Knowledge for Generations Each generation has its unique needs and aspirations. When Charles Wiley first opened his small printing shop in lower Manhattan in 1807, it was a generation of boundless potential searching for an identity. And we were there, helping to define a new American literary tradition. Over half a century later, in the midst of the Second Industrial Revolution, it was a generation focused on building the future. Once again, we were there, supplying the critical scientific, technical, and engineering knowledge that helped frame the world. Throughout the 20th Century, and into the new millennium, nations began to reach out beyond their own borders and a new international community was born. Wiley was there, ex- panding its operations around the world to enable a global exchange of ideas, opinions, and know-how. For 200 years, Wiley has been an integral part of each generation’s journey, enabling the flow of information and understanding necessary to meet their needs and fulfill their aspirations. Today, bold new technologies are changing the way we live and learn. Wiley will be there, providing you the must-have knowledge you need to imagine new worlds, new possibilities, and new oppor- tunities. Generations come and go, but you can always count on Wiley to provide you the knowledge you need, when and where you need it! William J.
    [Show full text]
  • Surface-Plasmon-Induced Modification on the Spontaneous
    Letter pubs.acs.org/NanoLett Surface-Plasmon-Induced Modification on the Spontaneous Emission Spectrum via Subwavelength-Confined Anisotropic Purcell Factor † † † ‡ ‡ § Ying Gu,*, Luojia Wang, Pan Ren, Junxiang Zhang, Tiancai Zhang, Olivier J. F. Martin, † and Qihuang Gong*, † State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China ‡ State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China § Nanophotonics and Metrology Laboratory, Swiss Federal Institute of Technology Lausanne (EPFL), EPFL-STI-NAM, ELG Station 11, CH-1015 Lausanne, Switzerland *S Supporting Information ABSTRACT: The mechanism of using the anisotropic Purcell factor to control the spontaneous emission linewidths in a four-level atom is theoretically demonstrated; if the polar- ization angle bisector of the two dipole moments lies along the axis of large/small Purcell factor, destructive/constructive interference narrows/widens the fluorescence center spectral lines. Large anisotropy of the Purcell factor, confined in the subwavelength optical mode volume, leads to rapid spectral line narrowing of atom approaching a metallic nanowire, nanoscale line width pulsing following periodically varying decay rates near a periodic metallic nanostructure, and dramatic modification on the spontaneous emission spectrum near a custom-designed resonant plasmon nanostructure. The combined system opens a good perspective for applications in ultracompact active
    [Show full text]