Emergent Phenomena in Quantum Critical Systems
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Quantum Fluctuations Across the Superconductor-Insulator Transition
Quantum Fluctuations Across the Superconductor-Insulator Transition Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Hasan Khan, B.S. Graduate Program in Physics The Ohio State University 2019 Dissertation Committee: Nandini Trivedi, Advisor Yuan-Ming Lu Rolando Vald´esAguilar Richard J. Furnstahl c Copyright by Hasan Khan 2019 Abstract Superconductivity has been at the heart of research into quantum phenomena since its discovery over a century ago. More recently efforts have been made to un- derstand the nature of the quantum phase transition (QPT) that separates the super- conducting and insulating phases in certain 2D materials at zero temperature. This superconductor-insulator transition (SIT) has been theoretically and experimentally proven to be driven by quantum fluctuations of the superconducting phase instead of the breakup of Cooper pairs. In this thesis we present a study of quantum fluctua- tions across the SIT and how they can be imaged in both theoretical simulations and experimental measurements. We begin with an overview of the field from a historical perspective, describing the development of the theory of SITs driven by experiments on thin films. We present the Josephson junction array (JJA) model as a paradigm to investigate the quantum phase fluctuation-driven SIT using quantum Monte Carlo (QMC) techniques. We explore the manifestation of quantum fluctuations across the SIT in three different local measurements: the diamagnetic susceptibility χ(r), two-particle den- sity of states P (r;!), and compressibility κ(r), revealed through their local maps and calculated via QMC. -
Bose-Einstein Condensation in Bacusi2o6
Institute of Physics Publishing Journal of Physics: Conference Series 51 (2006) 9–14 doi:10.1088/1742-6596/51/1/002 Yamada Conference LX on Research in High Magnetic Fields Bose-Einstein condensation in BaCuSi2O6 1N Harrison, 2,3S E Sebastian, 1C D Batista, 1MJaime,4L Balicas, 1P A Sharma, 5N Kawashima and 2IRFisher 1MST-NHMFL, Los Alamos National Laboratory, Los Alamos, NM 87545 2Department of Applied Physics, Geballe Laboratory for Advanced Materials, Stanford University, California 94305-4045 4National High Magnetic Field Laboratory, Tallahassee, FL 32310 5Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan Abstract. BaCuSi2O6 is a model spin dimer system in which a BEC QCP is realised. Universal BEC power law scaling is experimentally observed, with 3d critical behaviour above 0.5 K, but a crossover to 2d BEC critical scaling down to 30 mK. Here we briefly review and expand on the results presented in the recent Nature paper [8]. 1. Spin dimer systems Spin dimer materials have attracted considerable attention recently due to the realisation of Bose-Einstein condensate (BEC) physics in these systems [1, 2, 3, 4, 5, 6, 7, 8, 9]. The ground state of these systems comprises singlets with gapped triplet excitations. In an applied magnetic field, Zeeman splitting of the triplet levels lowers the energy of the lowest triplet, such that above critical field Hc1, a finite concentration of triplets is populated in the ground state. The ground state above Hc1 is an ordered XY antiferromagnet, separated from the disordered quantum paramagnet below Hc1 by a BEC quantum critical point (QCP) at 0 K. -
Matthias Vojta Subir Sachdev Quantum Phase Transitions in D
Quantum phase transitions in d-wave superconductors •C. Buragohain Matthias Vojta •Y. Zhang •A. Polkovnikov Subir Sachdev Transparencies on-line at http://pantheon.yale.edu/~subir Phys. Rev Lett. 83, 3916 (1999) Science 286, 2479 (1999) Phys. Rev. B 61, 15152 (2000) Phys. Rev. B 62, Sep 1 (2000) cond-mat/0005250 (review article) cond-mat/0007170 Yale University Quantum Phase Transitions Cambridge University Press Elementary excitations of a d-wave superconductor (A) S=0 Cooper pairs, phase fluctuations Negligible below Tc except near a T=0 superconductor-insulator transition. (B) S=1/2 Fermionic quasiparticles Ψ π π h : strongly paired fermions near ( ,0), (0, ) ∆ have an energy gap h ~ 30-40 meV Ψ 1,2 : gapless fermions near the nodes of the superconducting gap at (±±KK , ) with K =0.391π (C) S=1 Bosonic, resonant collective mode Represented by φ α , a vector Γ field measuring the strength of pure antiferromagnetic spin S(Q,ω) fluctuations near Q ≈ (,)ππ Damping is small at T=0 Γ≈ = pure 0 at T 0 (Theory generalizes to the cases with Γ≠ incommensurate Q and pure 0 ) ∆ ω res Constraints from momentum conservation π Ψ h Ψ 2 Ψ 1 φ Ψ α Ψ 0 h h Q φα Ψ 1 Ψ Q 2 Ψ −π h −π 0 π Ψ φ φ h : strongly coupled to α , but do not damp α ∆ ∆ as long as res < 2 h Ψ φ 1,2 : decoupled from α I. Zero temperature broadening of resonant collective mode φ α by impurities: comparison with neutron scattering experiments of Fong et al Phys. -
Computing Quantum Phase Transitions Preamble
COMPUTING QUANTUM PHASE TRANSITIONS Thomas Vojta Department of Physics, University of Missouri-Rolla, Rolla, MO 65409 PREAMBLE: MOTIVATION AND HISTORY A phase transition occurs when the thermodynamic properties of a material display a singularity as a function of the external parameters. Imagine, for instance, taking a piece of ice out of the freezer. Initially, its properties change only slowly with increasing temperature. However, at 0°C, a sudden and dramatic change occurs. The thermal motion of the water molecules becomes so strong that it destroys the crystal structure. The ice melts, and a new phase of water forms, the liquid phase. At the phase transition temperature of 0°C the solid (ice) and the liquid phases of water coexist. A finite amount of heat, the so-called latent heat, is required to transform the ice into liquid water. Phase transitions involving latent heat are called first-order transitions. Another well known example of a phase transition is the ferromagnetic transition of iron. At room temperature, iron is ferromagnetic, i.e., it displays a spontaneous magnetization. With rising temperature, the magnetization decreases continuously due to thermal fluctuations of the spins. At the transition temperature (the so-called Curie point) of 770°C, the magnetization vanishes, and iron is paramagnetic at higher temperatures. In contrast to the previous example, there is no phase coexistence at the transition temperature; the ferromagnetic and paramagnetic phases rather become indistinguishable. Consequently, there is no latent heat. This type of phase transition is called continuous (second-order) transition or critical point. Phase transitions play an essential role in shaping the world. -
Experimentally Testing Quantum Critical Dynamics Beyond The
ARTICLE https://doi.org/10.1038/s42005-020-0306-6 OPEN Experimentally testing quantum critical dynamics beyond the Kibble–Zurek mechanism ✉ ✉ Jin-Ming Cui1,2, Fernando Javier Gómez-Ruiz 3,4,5, Yun-Feng Huang1,2 , Chuan-Feng Li1,2 , ✉ Guang-Can Guo1,2 & Adolfo del Campo3,5,6,7 1234567890():,; The Kibble–Zurek mechanism (KZM) describes the dynamics across a phase transition leading to the formation of topological defects, such as vortices in superfluids and domain walls in spin systems. Here, we experimentally probe the distribution of kink pairs in a one- dimensional quantum Ising chain driven across the paramagnet-ferromagnet quantum phase transition, using a single trapped ion as a quantum simulator in momentum space. The number of kink pairs after the transition follows a Poisson binomial distribution, in which all cumulants scale with a universal power law as a function of the quench time in which the transition is crossed. We experimentally verified this scaling for the first cumulants and report deviations due to noise-induced dephasing of the trapped ion. Our results establish that the universal character of the critical dynamics can be extended beyond KZM, which accounts for the mean kink number, to characterize the full probability distribution of topological defects. 1 CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China. 2 CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China. 3 Donostia International Physics Center, E-20018 San Sebastián, Spain. 4 Departamento de Física, Universidad de los Andes, A.A. -
Order Parameter Fluctuations at a Buried Quantum Critical Point
Order parameter fluctuations at a buried quantum critical point Yejun Fenga,b,1, Jiyang Wangb, R. Jaramilloc, Jasper van Wezeld, S. Haravifarda,b, G. Srajera,Y.Liue,f, Z.-A. Xuf, P. B. Littlewoodg, and T. F. Rosenbaumb,1 aThe Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439; bThe James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637; cSchool of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138; dMaterials Science Division, Argonne National Laboratory, Argonne, IL 60439; eDepartment of Physics, Pennsylvania State University, University Park, PA 16802; fDepartment of Physics, Zhejiang University, Hangzhou 310027, People’s Republic of China; and gCavendish Laboratory, University of Cambridge, Cambridge CB3 OHE, United Kingdom Edited by Zachary Fisk, University of California, Irvine, CA, and approved March 9, 2012 (received for review February 9, 2012) Quantum criticality is a central concept in condensed matter phy- NbSe2 is a model two-dimensional CDW system (15–21) where sics, but the direct observation of quantum critical fluctuations negatively charged electrons and positively charged holes form has remained elusive. Here we present an X-ray diffraction study a spatially periodic arrangement below the transition tempera- H T ¼ 33 5 – of the charge density wave (CDW) in 2 -NbSe2 at high pressure ture CDW . K (15 21). NbSe2 also superconducts below T ¼ 7 2 and low temperature, where we observe a broad regime of order sc . K, and the electronic band structure supports both parameter fluctuations that are controlled by proximity to a quan- the CDW and superconductivity with some competition for elec- tum critical point. -
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. -
Quantum Phase Transitions
P1: GKW/UKS P2: GKW/UKS QC: GKW CB196-FM July 31, 1999 15:48 Quantum Phase Transitions SUBIR SACHDEV Professor of Physics Yale University iii P1: GKW/UKS P2: GKW/UKS QC: GKW CB196-FM July 31, 1999 15:48 PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK http://www.cup.cam.ac.uk 40 West 20th Street, New York, NY 10011-4211, USA http: //www.cup.org 10 Stamford Road, Oakleigh, Melbourne 3166, Australia Ruiz de Alarc´on 13, 28014 Madrid, Spain C Subir Sachdev 1999 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1999 Printed in the United States of America Typeface in Times Roman 10/12.5 pt. System LATEX2ε [TB] A catalog record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data Sachdev, Subir, 1961– Quantum phase transitions / Subir Sachdev. p. cm. Includes bibliographical references and index. ISBN 0-521-58254-7 1. Phase transformations (Statistical physics) 2. Quantum theory. I. Title. QC175. 16.P5S23 2000 530.4014 – dc21 99-12280 CIP ISBN 0 521 58254 7 hardback iv P1: GKW/UKS P2: GKW/UKS QC: GKW CB196-FM July 31, 1999 15:48 Contents Preface page xi Acknowledgments xv Part I: Introduction 1 1 Basic Concepts 3 1.1 What Is a Quantum Phase Transition? -
Superconducting and Excitonic Quantum Phase Transitions in Doped Dirac Electronic Systems ∗ Lizardo H.C.M
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Physics Letters A 376 (2012) 779–784 Contents lists available at SciVerse ScienceDirect Physics Letters A www.elsevier.com/locate/pla Superconducting and excitonic quantum phase transitions in doped Dirac electronic systems ∗ Lizardo H.C.M. Nunes a, , Ricardo L.S. Farias a, Eduardo C. Marino b a Departamento de Ciências Naturais, Universidade Federal de São João del Rei, 36301-000 São João del Rei, MG, Brazil b Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ, 21941-972, Brazil article info abstract Article history: We investigate the effect of superconducting and excitonic interactions, as well as their competition, on Received 10 June 2011 Dirac electrons on a bipartite planar lattice. It is shown that, at half-filling, Cooper pairs and excitons Received in revised form 1 December 2011 coexist if the superconducting and excitonic coupling parameters are equal and above a threshold cor- Accepted 17 December 2011 responding to a quantum critical point. In the case where only the excitonic interaction is present, we Available online 21 December 2011 obtain a critical chemical potential, as a function of the interaction strength. Conversely, if only the su- Communicated by A.R. Bishop perconducting interaction is considered, we show that the superconducting gap displays a characteristic Keywords: dome as charge carriers are doped into the system. We also show that, as the chemical potential in- Dirac electrons creases, superconductivity tends to suppress the excitonic order parameter. -
Quantum Phase Transitions the Following Article Appeared in Physics World, Vol
Quantum Phase Transitions The following article appeared in Physics World, vol. 12, no. 4, pg 33 (1999). Additional footnotes [9,10] have been added to the web version. Quantum Phase Transitions Subir Sachdev Phase transitions are normally associated with changes of temperature but a new type of transition - caused by quantum fluctuations near absolute zero - is possible, and can tell us more about a wide range of systems in condensed matter physics Contents 1 Introduction 2 Quantum Ising systems 3 High-temperature superconductors 4 Spins and stripes 5 Experiments on superconductors 6 Quantum Hall systems 7 Outlook Bibliography NEXT http://pantheon.yale.edu/~subir/physworld/index.html [8/5/2000 11:58:21 AM] refs.html PREVIOUS; TABLE OF CONTENTS References [1] Aeppli, G., Mason, T. E., Hayden, S. M., Mook, H. A., and Kulda, J. (1998) Nearly singular magnetic fluctuations in the normal state of a high-Tc cuprate superconductor, Science 278, 1432; cond-mat/9801169 [2] Bitko, D., Rosenbaum, T. F., and Aeppli, G. (1996) Quantum critical behaviour for a model magnet, Phys. Rev. Lett. 77, 940. [3] Das Sarma, S., Sachdev, S., and Zheng, L. (1998) Canted antiferromagnetic and spin singlet quantum Hall states in double-layer systems, Phys. Rev. B 58, 4672; cond-mat/9709315 [4] Hunt, A. W., Singer, P. M., Thurber, K. R., and Imai, T. (1999) 63Cu NQR measurement of stripe order parameter in La2-x Srx CuO4, Phys. Rev. Lett. 82, 4300; cond-mat/9902348 [5] Imai, T., Slichter, C. P., Yoshimura, K., and Kosuge, K. (1993) Low frequency spin dynamics in undoped and Sr-doped La2 CuO4, Phys. -
Locally Critical Quantum Phase Transitions in Strongly Correlated Metals
articles Locally critical quantum phase transitions in strongly correlated metals Qimiao Si*, Silvio Rabello*, Kevin Ingersent² & J. Lleweilun Smith* * Department of Physics & Astronomy, Rice University, Houston, Texas 77251-1892, USA ² Department of Physics, University of Florida, Gainesville, Florida 32611-8440, USA ............................................................................................................................................................................................................................................................................ When a metal undergoes a continuous quantum phase transition, non-Fermi-liquid behaviour arises near the critical point. All the low-energy degrees of freedom induced by quantum criticality are usually assumed to be spatially extended, corresponding to long-wavelength ¯uctuations of the order parameter. But this picture has been contradicted by the results of recent experiments on a prototype system: heavy fermion metals at a zero-temperature magnetic transition. In particular, neutron scattering from CeCu6-x Aux has revealed anomalous dynamics at atomic length scales, leading to much debate as to the fate of the local moments in the quantum-critical regime. Here we report our theoretical ®nding of a locally critical quantum phase transition in a model of heavy fermions. The dynamics at the critical point are in agreement with experiment. We propose local criticality to be a phenomenon of general relevance to strongly correlated metals. Quantum (zero-temperature) phase transitions are ubiquitous in over essentially the entire Brillouin zone. Finally, the dynamical spin strongly correlated metals (for a recent review, see ref. 1). The susceptibility exhibits q/T scaling. These experiments have led to extensive present interest in metals close to a second-order quantum much debate as to the nature of the QCPs in heavy-fermion metals, phase transition has stemmed largely from studies of high- especially concerning the fate of the local magnetic moments in the temperature superconductors. -
Table of Contents (Print, Part 1)
PERIODICALS PHYSICAL REVIEW BTM Postmaster send address changes to: For editorial and subscription correspondence, APS Subscription Services please see inside front cover Suite 1NO1 (ISSN: 1098-0121) 2 Huntington Quadrangle Melville, NY 11747-4502 THIRD SERIES, VOLUME 83, NUMBER 7 CONTENTS FEBRUARY 2011-15(I) EDITORIALS AND ANNOUNCEMENTS Editorial: Expanded Open Access and Creative Commons (2 pages)........................................ 070001 BRIEF REPORTS Electronic structure and strongly correlated systems Temperature and voltage driven tunable metal-insulator transition in individual Wx V1−x O2 nanowires (4 pages)........................................................................................... 073101 Tai-Lung Wu, Luisa Whittaker, Sarbajit Banerjee, and G. Sambandamurthy Activation gap in the specific heat measurements for 3He bilayers (4 pages) ................................. 073102 A. Ranc¸on-Schweiger, A. Benlagra, and C. Pepin´ Soft x-ray absorption spectroscopy study of Mo-rich SrMn1−x Mox O3 (x 0.5) (4 pages)..................... 073103 J. H. Hwang, D. H. Kim, J.-S. Kang, S. Kolesnik, O. Chmaissem, J. Mais, B. Dabrowski, J. Baik, H. J. Shin, Jieun Lee, Bongjae Kim, and B. I. Min Thermopower as a fingerprint of the Kondo breakdown quantum critical point (4 pages) ...................... 073104 K.-S. Kim and C. Pepin´ Intrinsic and extrinsic x-ray absorption effects in soft x-ray diffraction from the superstructure in magnetite (4 pages)........................................................................................... 073105 C. F. Chang, J. Schlappa, M. Buchholz, A. Tanaka, E. Schierle, D. Schmitz, H. Ott, R. Sutarto, T. Willers, P. Metcalf, L. H. Tjeng, and C. Schußler-Langeheine¨ Semiconductors I: bulk Boron acceptor concentration in diamond from excitonic recombination intensities (4 pages) .................. 073201 J. Barjon, T. Tillocher, N. Habka, O. Brinza, J. Achard, R. Issaoui, F.