LANDAU FERMI-LIQUID THEORY Concepts and Applications

Total Page:16

File Type:pdf, Size:1020Kb

LANDAU FERMI-LIQUID THEORY Concepts and Applications LANDAU FERMI-LIQUID THEORY Concepts and Applications GORDON BAYM University of Illinois at Urbana-Champaign and CHRISTOPHER PETHICK Nordita, Copenhagen and University of Illinois at Urbana-Champaign WI LEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA This Page Intentionally Left Blank LANDAU FERMI-LIQUID THEORY Concepts and Applications GORDON BAYM University of Illinois at Urbana-Champaign and CHRISTOPHER PETHICK Nordita, Copenhagen and University of Illinois at Urbana-Champaign WI LEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA This Page Intentionally Left Blank All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free oferrors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: Applied for British Library Cataloging-in-Publication Data: A catalogue record for this book is available I)om the British Library Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Ribliothek lists this publication in the Deutsche Nationalbibliogratie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. 0 199 I by John Wiley & Sons, Inc. 0 2004 WII,T:Y-Vc'I I Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those oftranslation into other languages). No part or this book may be reproduced in any form ~ nor transmitted or translated into machinc language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printed in the Federal Republic of Germany Printed on acid-free paper Printing Strauss CimbH, Miirlenbach Bookbinding Litgcs & Dopf Buchbinderei Gmbl I, I leppenheim ISBN-13: 978-0-47 1-824 1 8-3 ISBN-10: 0-47 1-824 18-6 This Page Intentionally Left Blank CONTENTS Preface vii 1 Landau Fermi-Liquid Theory and Law Temperature Properties of Normal Liquid %e I Introduction, 1 1.1 Static Properties, 2 1.1.1 Quasiparticles, 2 1.1.2 Quasiparticle Energy and Interactions, 4 1.1.3 Equilibrium Properties, 10 1.2 Nonequilibrium Properties, 16 1.2.1 Quasiparticle Energies and Interaction, 16 1.2.2 The Kinetic Equation, 18 1.2.3 The Conservation Laws, 21 1.2.4 Transport Coefficients, 25 1.3 Collective Effects, 45 1.3.1 Sound in Fermi Liquids, 45 1.3.2 Spin Waves and Related Phenomena, 56 1.3.3 Response Functions, Inequalities, and Form Factors, 69 1.4 Scattering of Quasiparticles and Finite Temperature Effects, 76 1.4.1 Landau Parameters and Scattering Amplitudes, 76 1.4.2 The Low Temperature Transport Coefficients of Liquid 3He; Theory and Experiment, 85 1.4.3 Finite Temperature Transport Coefficients, 86 1.4.4 Finite Temperature Contributions to the Specific Heat and Magnetic Susceptibility, 95 1.5 Concluding Remarks, 113 Appendix A: Some Useful Fermi Integrals, 114 Appendix B: Properties of Q,,, 116 V vi CONTENTS Appendix C Fermi Liquid Parameters for Liquid 3He, 117 2 Low Temperature Properties of Dilute Solutions of 'He in Superhid 4He 123 Introduction, 123 2.1 Elementary Excitations of Dilute Solutions, 125 2.2 Properties of one 3He Atom in 4He at T = 0, 128 2.2.1 Volume Occupied by 3He, 128 2.2.2 3He Effective Mass, 130 2.3 Interactions of the 3He at Very Low Temperature, 131 2.3.1 'He Landau Parameters, 131 2.3.2 Low Temperature Properties of Dilute Solutions, 134 2.3.3 Phenomenological Effective Interaction, 138 2.3.4 Microscopic Approaches to the Effective Interaction, 142 2.4 Interaction Between the 3He and 4He, 146 2.4.1 Effectives of Superfluid Flow on 'He Quasiparticles, 147 2.4.2 Interaction of 3He Quasiparticles with Long-Wavelength Phonons, 149 2.4.3 Scattering of Phonons by 'He Quasiparticles, 155 2.4.4 First Sound in Dilute Solutions, 158 2.4.5 Second Sound, 167 2.4.6 Transport Properties, 168 3 Further Developments 177 Introduction, 177 3.1 Liquid 3He, 177 3.1.1 Quasiparticle Spectrum and Thermodynamic Properties, 177 3.1.2 Measurements of Transport Properties, 178 3.1.3 Density and Spin Fluctuations, 179 3.1.4 Calculations of Scattering Amplitudes, 180 3.1.5 Superfluid 3He and the Landau Theory of Fermi Liquids, 181 3.2 Dilute Solutions of 'He in Superfluid 4He, 183 3.2.1 Equilibrium and Transport Properties, 183 3.2.2 Higher-Momentum Excitations, 184 3.3 Spin-Polarized Systems, 185 3.3.1 Spin-Polarized 'He, 185 3.3.2 Dilute Solutions of 3He in 4He, 186 3.3.3 Other Systems, 187 3.4 Nuclear Applications, 187 3.4.1 Particles and Quasiparticles, 188 3.4.2 Quasiparticle Interactions in Nuclei and Nuclear Matter, 189 3.5 Electrons in Metals, 191 INDEX 201 Landau’s theory of Fermi liquids, advanced in 1956, stands out as one of the high points of modern theoretical physics, a theory whose profun- dity goes beyond mere phenomenology. Although strongly interacting many-particle systems are very difficult to describe in general, Landau saw, with great insight, that at low temperature an exact simplicity arises, enabling one to describe the properties of extended systems in terms of a dilute collection of elementary excitations. These elementary excitations, or “quasiparticles,” are not merely the motion of single particles, but represent the motion of many particles of the system simultaneously. As Landau realized, one can keep track of the thermodynamic and transport properties, that is, do the bookkeeping on conserved quantities and their currents, in terms of the elementary excitations; the detailed proof of this picture requires extensive use of field theory, including conservation laws, associated Ward identities, and renormalization theory. At the same time that the Landau theory has deep conceptual roots, it is a useful and practical tool for accounting for the low temperature properties of Fermi liquids in terms of a rather small number of parameters. Beyond being a vital part of a condensed matter physicist’s culture, the theory is a necessary skill for the practitioner. The major emphasis in this book is on the practical development and application of the theory, rather than on the description of its microscopic derivation. The first chapter delineates the basic theory of the thermody- namic and nonequilibrium properties of Fermi liquids, with application to liquid 3He in its normal state. The second chapter discusses the important and tractable extension of the Fermi liquid theory to dilute solutions of 3He in superfluid 4He, an experimentally rich system where, in addition to Fermi excitations, boson degrees of freedom-of the 4He-play a role. viii PREFACE The basis of this book, two review articles on the Landau Fermi-liquid theory and the application to dilute solutions of 3He in superfluid 4He, were originally written as part of a collection of articles in the books, The Physics of Liquid and Solid Helium, edited by K. H. Bennemann and J. B. Ketterson (Wiley, Part 1, 1976, and Part 2, 1978). In retrospect, because of the general utility of the Landau Fermi-liquid theory, it appeared to be valuable to make them more widely available in the present format. Despite the passing of over a decade, the two review articles remain timely, having been written to emphasize the fundamental ideas of the theory. Experiments on normal ’He in the intervening years have contin- ued to confirm the general theory, and provide information on its exten- sion to higher temperatures. In addition, the theory has found further application in other areas, such as nuclear and neutron star matter, superfluid ’He, and modern problems in superconductivity. To avoid resetting type for the entire book, we have chosen to give a brief summary of the developments in the physics of Fermi liquids since the writing of the original text in an added final Chapter 3, and at the same time have made minor modifications to the introductory sections of the two original chap- ters. Citations in Chapter 3 references in earlier chapters are given in the format “[Chap. 1: 46, 1021.’’ We would like to take this opportunity to thank our colleagues in Urbana and Copenhagen for the many interesting and provocative conver- sations over the years that have helped to shape this monograph. The supportive environment of Nordita, and the continued funding by the U.S. National Science Foundation of our research in low temperature physics, have both contributed greatly to our writing of the present volume. We dedicate this book to the memory of our friend and colleague, John Wheatley, whose virtuosity in extracting the physics of Fermi liquids, through both his imaginative experiments and his challenging and probing interactions with theorists, made the field for us vital and exciting. GORDONBAYM CHRISTOPHERPETHICK Urbana, Illinois Covenhagen, Denmurk 1 LANDAU FERMI-LIQUID THEORY AND LOW TEMPERATURE PROPERTIES OF NORMAL LIQUID 3He INTRODUCTION Landau advanced his theory of normal Fermi liquids [l,21 in 1956, and by the early 1960s, experiments indicated that the predictions of the Landau theory were satisfied, at least qualitatively, by liquid 3He. During the past three decades, precision measurements of the properties of liquid 3 He have been carried out at temperatures below 100 mK, where the Landau theory enables one to calculate. More recent theoretical and experimental attention has turned to properties at higher temperatures, and phenomena that vary rapidly in space and time. We shall focus our attention here chiefly on theoretical deveIopments and related experi- ments. A detailed account of experimental work on Fermi liquid proper- ties of 3He is given by Wheatley in his review article [3].
Recommended publications
  • Lecture 3: Fermi-Liquid Theory 1 General Considerations Concerning Condensed Matter
    Phys 769 Selected Topics in Condensed Matter Physics Summer 2010 Lecture 3: Fermi-liquid theory Lecturer: Anthony J. Leggett TA: Bill Coish 1 General considerations concerning condensed matter (NB: Ultracold atomic gasses need separate discussion) Assume for simplicity a single atomic species. Then we have a collection of N (typically 1023) nuclei (denoted α,β,...) and (usually) ZN electrons (denoted i,j,...) interacting ∼ via a Hamiltonian Hˆ . To a first approximation, Hˆ is the nonrelativistic limit of the full Dirac Hamiltonian, namely1 ~2 ~2 1 e2 1 Hˆ = 2 2 + NR −2m ∇i − 2M ∇α 2 4πǫ r r α 0 i j Xi X Xij | − | 1 (Ze)2 1 1 Ze2 1 + . (1) 2 4πǫ0 Rα Rβ − 2 4πǫ0 ri Rα Xαβ | − | Xiα | − | For an isolated atom, the relevant energy scale is the Rydberg (R) – Z2R. In addition, there are some relativistic effects which may need to be considered. Most important is the spin-orbit interaction: µ Hˆ = B σ (v V (r )) (2) SO − c2 i · i × ∇ i Xi (µB is the Bohr magneton, vi is the velocity, and V (ri) is the electrostatic potential at 2 3 2 ri as obtained from HˆNR). In an isolated atom this term is o(α R) for H and o(Z α R) for a heavy atom (inner-shell electrons) (produces fine structure). The (electron-electron) magnetic dipole interaction is of the same order as HˆSO. The (electron-nucleus) hyperfine interaction is down relative to Hˆ by a factor µ /µ 10−3, and the nuclear dipole-dipole SO n B ∼ interaction by a factor (µ /µ )2 10−6.
    [Show full text]
  • Unconventional Hund Metal in a Weak Itinerant Ferromagnet
    ARTICLE https://doi.org/10.1038/s41467-020-16868-4 OPEN Unconventional Hund metal in a weak itinerant ferromagnet Xiang Chen1, Igor Krivenko 2, Matthew B. Stone 3, Alexander I. Kolesnikov 3, Thomas Wolf4, ✉ ✉ Dmitry Reznik 5, Kevin S. Bedell6, Frank Lechermann7 & Stephen D. Wilson 1 The physics of weak itinerant ferromagnets is challenging due to their small magnetic moments and the ambiguous role of local interactions governing their electronic properties, 1234567890():,; many of which violate Fermi-liquid theory. While magnetic fluctuations play an important role in the materials’ unusual electronic states, the nature of these fluctuations and the paradigms through which they arise remain debated. Here we use inelastic neutron scattering to study magnetic fluctuations in the canonical weak itinerant ferromagnet MnSi. Data reveal that short-wavelength magnons continue to propagate until a mode crossing predicted for strongly interacting quasiparticles is reached, and the local susceptibility peaks at a coher- ence energy predicted for a correlated Hund metal by first-principles many-body theory. Scattering between electrons and orbital and spin fluctuations in MnSi can be understood at the local level to generate its non-Fermi liquid character. These results provide crucial insight into the role of interorbital Hund’s exchange within the broader class of enigmatic multiband itinerant, weak ferromagnets. 1 Materials Department, University of California, Santa Barbara, CA 93106, USA. 2 Department of Physics, University of Michigan, Ann Arbor, MI 48109, USA. 3 Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA. 4 Institute for Solid State Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany.
    [Show full text]
  • Landau Effective Interaction Between Quasiparticles in a Bose-Einstein Condensate
    PHYSICAL REVIEW X 8, 031042 (2018) Landau Effective Interaction between Quasiparticles in a Bose-Einstein Condensate A. Camacho-Guardian* and Georg M. Bruun Department of Physics and Astronomy, Aarhus University, Ny Munkegade, DK-8000 Aarhus C, Denmark (Received 19 December 2017; revised manuscript received 28 February 2018; published 15 August 2018) Landau’s description of the excitations in a macroscopic system in terms of quasiparticles stands out as one of the highlights in quantum physics. It provides an accurate description of otherwise prohibitively complex many-body systems and has led to the development of several key technologies. In this paper, we investigate theoretically the Landau effective interaction between quasiparticles, so-called Bose polarons, formed by impurity particles immersed in a Bose-Einstein condensate (BEC). In the limit of weak interactions between the impurities and the BEC, we derive rigorous results for the effective interaction. They show that it can be strong even for a weak impurity-boson interaction, if the transferred momentum- energy between the quasiparticles is resonant with a sound mode in the BEC. We then develop a diagrammatic scheme to calculate the effective interaction for arbitrary coupling strengths, which recovers the correct weak-coupling results. Using this scheme, we show that the Landau effective interaction, in general, is significantly stronger than that between quasiparticles in a Fermi gas, mainly because a BEC is more compressible than a Fermi gas. The interaction is particularly large near the unitarity limit of the impurity-boson scattering or when the quasiparticle momentum is close to the threshold for momentum relaxation in the BEC.
    [Show full text]
  • Attractive Fermi Polarons at Nonzero Temperatures with a Finite Impurity
    PHYSICAL REVIEW A 98, 013626 (2018) Attractive Fermi polarons at nonzero temperatures with a finite impurity concentration Hui Hu, Brendan C. Mulkerin, Jia Wang, and Xia-Ji Liu Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia (Received 29 June 2018; published 25 July 2018) We theoretically investigate how quasiparticle properties of an attractive Fermi polaron are affected by nonzero temperature and finite impurity concentration in three dimensions and in free space. By applying both non- self-consistent and self-consistent many-body T -matrix theories, we calculate the polaron energy (including decay rate), effective mass, and residue, as functions of temperature and impurity concentration. The temperature and concentration dependencies are weak on the BCS side with a negative impurity-medium scattering length. Toward the strong attraction regime across the unitary limit, we find sizable dependencies. In particular, with increasing temperature the effective mass quickly approaches the bare mass and the residue is significantly enhanced. At temperature T ∼ 0.1TF ,whereTF is the Fermi temperature of the background Fermi sea, the residual polaron-polaron interaction seems to become attractive. This leads to a notable down-shift in the polaron energy. We show that, by taking into account the temperature and impurity concentration effects, the measured polaron energy in the first Fermi polaron experiment [Schirotzek et al., Phys.Rev.Lett.102, 230402 (2009)] could be better theoretically explained. DOI: 10.1103/PhysRevA.98.013626 I. INTRODUCTION Experimentally, the first experiment on attractive Fermi polarons was carried out by the Zwierlein group at Mas- Over the past two decades, ultracold atomic gases have pro- sachusetts Institute of Technology (MIT) in 2009 using 6Li vided an ideal platform to understand the intriguing quantum many-body systems [1].
    [Show full text]
  • Electron-Electron Interactions(Pdf)
    Contents 2 Electron-electron interactions 1 2.1 Mean field theory (Hartree-Fock) ................ 3 2.1.1 Validity of Hartree-Fock theory .................. 6 2.1.2 Problem with Hartree-Fock theory ................ 9 2.2 Screening ..................................... 10 2.2.1 Elementary treatment ......................... 10 2.2.2 Kubo formula ............................... 15 2.2.3 Correlation functions .......................... 18 2.2.4 Dielectric constant ............................ 19 2.2.5 Lindhard function ............................ 21 2.2.6 Thomas-Fermi theory ......................... 24 2.2.7 Friedel oscillations ............................ 25 2.2.8 Plasmons ................................... 27 2.3 Fermi liquid theory ............................ 30 2.3.1 Particles and holes ............................ 31 2.3.2 Energy of quasiparticles. ....................... 36 2.3.3 Residual quasiparticle interactions ................ 38 2.3.4 Local energy of a quasiparticle ................... 42 2.3.5 Thermodynamic properties ..................... 44 2.3.6 Quasiparticle relaxation time and transport properties. 46 2.3.7 Effective mass m∗ of quasiparticles ................ 50 0 Reading: 1. Ch. 17, Ashcroft & Mermin 2. Chs. 5& 6, Kittel 3. For a more detailed discussion of Fermi liquid theory, see G. Baym and C. Pethick, Landau Fermi-Liquid Theory : Concepts and Ap- plications, Wiley 1991 2 Electron-electron interactions The electronic structure theory of metals, developed in the 1930’s by Bloch, Bethe, Wilson and others, assumes that electron-electron interac- tions can be neglected, and that solid-state physics consists of computing and filling the electronic bands based on knowldege of crystal symmetry and atomic valence. To a remarkably large extent, this works. In simple compounds, whether a system is an insulator or a metal can be deter- mined reliably by determining the band filling in a noninteracting cal- culation.
    [Show full text]
  • Non-Fermi Liquids in Oxide Heterostructures
    UC Santa Barbara UC Santa Barbara Previously Published Works Title Non-Fermi liquids in oxide heterostructures Permalink https://escholarship.org/uc/item/1cn238xw Journal Reports on Progress in Physics, 81(6) ISSN 0034-4885 1361-6633 Authors Stemmer, Susanne Allen, S James Publication Date 2018-06-01 DOI 10.1088/1361-6633/aabdfa Peer reviewed eScholarship.org Powered by the California Digital Library University of California Reports on Progress in Physics KEY ISSUES REVIEW Non-Fermi liquids in oxide heterostructures To cite this article: Susanne Stemmer and S James Allen 2018 Rep. Prog. Phys. 81 062502 View the article online for updates and enhancements. This content was downloaded from IP address 128.111.119.159 on 08/05/2018 at 17:09 IOP Reports on Progress in Physics Reports on Progress in Physics Rep. Prog. Phys. Rep. Prog. Phys. 81 (2018) 062502 (12pp) https://doi.org/10.1088/1361-6633/aabdfa 81 Key Issues Review 2018 Non-Fermi liquids in oxide heterostructures © 2018 IOP Publishing Ltd Susanne Stemmer1 and S James Allen2 RPPHAG 1 Materials Department, University of California, Santa Barbara, CA 93106-5050, United States of America 062502 2 Department of Physics, University of California, Santa Barbara, CA 93106-9530, United States of America S Stemmer and S J Allen E-mail: [email protected] Received 18 July 2017, revised 25 January 2018 Accepted for publication 13 April 2018 Published 8 May 2018 Printed in the UK Corresponding Editor Professor Piers Coleman ROP Abstract Understanding the anomalous transport properties of strongly correlated materials is one of the most formidable challenges in condensed matter physics.
    [Show full text]
  • Boiling a Unitary Fermi Liquid
    PHYSICAL REVIEW LETTERS 122, 093401 (2019) Editors' Suggestion Featured in Physics Boiling a Unitary Fermi Liquid Zhenjie Yan,1 Parth B. Patel,1 Biswaroop Mukherjee,1 Richard J. Fletcher,1 Julian Struck,1,2 and Martin W. Zwierlein1 1MIT-Harvard Center for Ultracold Atoms, Department of Physics, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2D´epartement de Physique, Ecole Normale Sup´erieure/PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France (Received 1 November 2018; published 6 March 2019) We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T. In this regime, we observe a characteristic T2 dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝ T−1=2. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons. DOI: 10.1103/PhysRevLett.122.093401 Landau’s Fermi liquid theory provides a quasiparticle the quantum critical region.
    [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]
  • UC Berkeley UC Berkeley Electronic Theses and Dissertations
    UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids Permalink https://escholarship.org/uc/item/9kw3g8gg Author Bahri, Yasaman Publication Date 2017 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids by Yasaman Bahri A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Ashvin Vishwanath, Chair Professor Joel Moore Professor K. Birgitta Whaley Spring 2017 Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids Copyright 2017 by Yasaman Bahri 1 Abstract Quantum Phenomena in Interacting Many-Body Systems: Topological Protection, Localization, and Non-Fermi Liquids by Yasaman Bahri Doctor of Philosophy in Physics University of California, Berkeley Professor Ashvin Vishwanath, Chair This dissertation establishes and investigates new phenomena in diverse interacting many- body quantum systems guided by three distinct, but complementary, themes: (i) symmetry and topology, (ii) localization, and (iii) non-Fermi liquids. The first theme concerns how the interplay of symmetry and topology can offer robust protection for a many-body system. We investigate low-dimensional quantum fermionic mod- els from a general structural perspective. These phases can exhibit fractionalized Majorana zero-energy modes on their boundary. We devise experimentally relevant nonlocal measure- ments that can be used to detect these topological phases. While our primary focus is on quantum systems, topologically protected behavior can arise in classical mechanical models as well.
    [Show full text]
  • Probing Luttinger Liquid Plasmons in Single Walled Carbon Nanotubes
    Probing Luttinger Liquid Plasmons in Single Walled Carbon Nanotubes By Sheng Wang A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Feng Wang, Chair Professor Michael F. Crommie Professor Eli Yablonovitch Spring 2020 Abstract Probing Luttinger Liquid Plasmons in Single Walled Carbon Nanotubes By Sheng Wang Doctor of Philosophy in Physics University of California, Berkeley Professor Feng Wang, Chair Single walled carbon nanotubes (SWNTs) are one-dimensional (1D) rolled-up hollow cylinders composed of graphene sheets. Since their discovery about three decades ago, they have been one of the most fascinating and unique nanoscale structures. There have been tremendous and still ongoing research on SWNTs for both fundamental science as well as technological devices. SWNTs have been a good platform to study electron-electron interaction in solid state systems, including Coulomb blockage effect and Luttinger liquid formulism. SWNTs exhibit unique electrical, mechanical and thermal properties, making them potentially useful in a variety of applications including nano-electronics, optics, energy storage, and nanomedicine. Notably, carbon nanotube field-effect transistor-based digital circuits may be a viable route for next- generation beyond-silicon electronic systems for post-Moore’s Law era. Recent major advance includes a 16-bit computer built entirely from carbon nanotube transistors. Despite the intense established research, SWNTs have never ceased to surprise researchers with their emerging properties and potential applications. During the past decade, advances in the synthesis and processing have enabled the controlled growth of high quality ultralong SWNTs on different substrates even with desirable chirality.
    [Show full text]
  • Breakdown of Fermi-Liquid Theory in a Copper-Oxide Superconductor
    articles Breakdown of Fermi-liquid theory in a copper-oxide superconductor R. W. Hill*, Cyril Proust*³, Louis Taillefer*, P. Fournier²³ & R. L. Greene² * Canadian Institute for Advanced Research, Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada ² Center for Superconductivity Research, Department of Physics, University of Maryland, College Park, Maryland 20742, USA ............................................................................................................................................................................................................................................................................ The behaviour of electrons in solids is well described by Landau's Fermi-liquid theory, which predicts that although electrons in a metal interact, they can still be treated as well de®ned fermions, which are called `quasiparticles'. At low temperatures, the ability of quasiparticles to transport heat is given strictly by their ability to transport charge, as described by a universal relation known as the Wiedemann±Franz law, which hitherto no material has been known to violate. High-temperature superconductors have long been thought to fall outside the realm of Fermi-liquid theory, as suggested by several anomalous properties, but this has yet to be shown conclusively. Here we report an experimental test of the Wiedemann±Franz law in the normal state of a copper-oxide superconductor, (Pr,Ce)2CuO4, which reveals that the elementary excitations that carry heat in this material are not fermions. This is compelling evidence for the breakdown of Fermi-liquid theory in high-temperature superconductors. Landau's Fermi-liquid theory is the de®nitive theory of electrons in Theoretically, electrons are predicted to obey the WF law at T ! 0 metals1, or more generally fermions in condensed matter, and is a in a very wide range of environments4: in both three dimensions or major landmark of twentieth-century physics.
    [Show full text]
  • Propagation of Shear Stress in Strongly Interacting Metallic Fermi Liquids Enhances Transmission of Terahertz Radiation D
    www.nature.com/scientificreports OPEN Propagation of shear stress in strongly interacting metallic Fermi liquids enhances transmission of terahertz radiation D. Valentinis1,2, J. Zaanen3 & D. van der Marel1* A highlight of Fermi-liquid phenomenology, as explored in neutral 3He, is the observation that in the collisionless regime shear stress propagates as if one is dealing with the transverse phonon of a solid. The existence of this “transverse zero sound” requires that the quasiparticle mass enhancement exceeds a critical value. Could such a propagating shear stress also exist in strongly correlated electron systems? Despite some noticeable diferences with the neutral case in the Galilean continuum, we arrive at the verdict that transverse zero sound should be generic for mass enhancement higher than 3. We present an experimental setup that should be exquisitely sensitive in this regard: the transmission of terahertz radiation through a thin slab of heavy-fermion material will be strongly enhanced at low temperature and accompanied by giant oscillations, which refect the interference between light itself and the “material photon” being the actual manifestation of transverse zero sound in the charged Fermi liquid. Te elucidation of the Fermi liquid as a unique state of matter is a highlight of twentieth century physics 1. It has a precise identity only at strictly zero temperature. At times large compared to /(kBT) it can be adiabatically con- tinued to the high-temperature limit and it is therefore indistinguishable from a classical fuid—the “collision-full regime”. However, at energies ω>kBT (the “collisionless regime”) the unique nature of the zero-temperature state can be discerned, being diferent from either the non-interacting Fermi gas or a thermal fuid.
    [Show full text]