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Title: Observing a scale anomaly and a universal quantum phase transition in graphene

Abstract

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe ‘Efimov physics’. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. Furthermore, the purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene.

Authors:
 [1];  [2];  [2];  [2];  [1]
  1. Technion-Israel Inst. of Tech., Haifa (Israel). Dept. of Physics
  2. Rutgers Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1473977
Grant/Contract Number:  
FG02-99ER45742
Resource Type:
Accepted Manuscript
Journal Name:
Nature Communications
Additional Journal Information:
Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 2041-1723
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Ovdat, O., Mao, Jinhai, Jiang, Yuhang, Andrei, E. Y., and Akkermans, Eric. Observing a scale anomaly and a universal quantum phase transition in graphene. United States: N. p., 2017. Web. doi:10.1038/s41467-017-00591-8.
Ovdat, O., Mao, Jinhai, Jiang, Yuhang, Andrei, E. Y., & Akkermans, Eric. Observing a scale anomaly and a universal quantum phase transition in graphene. United States. doi:10.1038/s41467-017-00591-8.
Ovdat, O., Mao, Jinhai, Jiang, Yuhang, Andrei, E. Y., and Akkermans, Eric. Mon . "Observing a scale anomaly and a universal quantum phase transition in graphene". United States. doi:10.1038/s41467-017-00591-8. https://www.osti.gov/servlets/purl/1473977.
@article{osti_1473977,
title = {Observing a scale anomaly and a universal quantum phase transition in graphene},
author = {Ovdat, O. and Mao, Jinhai and Jiang, Yuhang and Andrei, E. Y. and Akkermans, Eric},
abstractNote = {One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale-free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe ‘Efimov physics’. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. Furthermore, the purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realized in graphene.},
doi = {10.1038/s41467-017-00591-8},
journal = {Nature Communications},
number = 1,
volume = 8,
place = {United States},
year = {2017},
month = {9}
}

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Cited by: 11 works
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Works referenced in this record:

On the limit cycle for the 1/r2 potential in momentum space
journal, February 2006


Supercritical Coulomb impurities in gapped graphene
journal, August 2008


Attractive Inverse Square Potential, U ( 1 ) Gauge, and Winding Transitions
journal, February 2014


Energy levels arising from resonant two-body forces in a three-body system
journal, December 1970


Conformality lost
journal, December 2009


Singular potentials in nonrelativistic quantum mechanics
journal, November 1964


Quantum Anomaly in Molecular Physics
journal, November 2001


Geometric Scaling of Efimov States in a Li 6 Cs 133 Mixture
journal, December 2014


Critical Behavior in (2+1)-Dimensional QED
journal, June 1988


Observing Atomic Collapse Resonances in Artificial Nuclei on Graphene
journal, March 2013


Universality in few-body systems with large scattering length
journal, June 2006


Observation of the Second Triatomic Resonance in Efimov’s Scenario
journal, May 2014


Observation of Universality in Ultracold Li 7 Three-Body Recombination
journal, October 2009


A class of exactly solvable three-body quantum mechanical problems and the universal low energy behavior
journal, May 1981


Electric-Dipole-Induced Universality for Dirac Fermions in Graphene
journal, May 2014


Radio-Frequency Association of Efimov Trimers
journal, November 2010


Axial-Vector Vertex in Spinor Electrodynamics
journal, January 1969


Renormalization-group limit cycle for the 1 r 2 potential
journal, November 2004


Universality classes for line-depinning transitions
journal, November 1992


Effects of ion bombardment on a two-dimensional target: Atomistic simulations of graphene irradiation
journal, April 2010

  • Lehtinen, O.; Kotakoski, J.; Krasheninnikov, A. V.
  • Physical Review B, Vol. 81, Issue 15, Article No. 153401
  • DOI: 10.1103/PhysRevB.81.153401

Universality in Three- and Four-Body Bound States of Ultracold Atoms
journal, November 2009


Measurement of an Efimov Trimer Binding Energy in a Three-Component Mixture of Li 6
journal, April 2011


Singular Potentials
journal, December 1950


Evidence for Efimov quantum states in an ultracold gas of caesium atoms
journal, March 2006


Observation of the Efimov state of the helium trimer
journal, April 2015


Lifetime Matrix in Collision Theory
journal, April 1960


A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969


Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance
journal, June 2014


Nonrelativistic inverse square potential, scale anomaly, and complex extension
journal, February 2010


Coulomb Impurity Problem in Graphene
journal, October 2007


Realization of a tunable artificial atom at a supercritically charged vacancy in graphene
journal, February 2016

  • Mao, Jinhai; Jiang, Yuhang; Moldovan, Dean
  • Nature Physics, Vol. 12, Issue 6
  • DOI: 10.1038/nphys3665

Singular potentials and limit cycles
journal, September 2001


Atomic Collapse and Quasi–Rydberg States in Graphene
journal, December 2007


Twisted boundary conditions and transport in disordered systems
journal, April 1997

  • Akkermans, E.
  • Journal of Mathematical Physics, Vol. 38, Issue 4
  • DOI: 10.1063/1.531913

Tunable Kondo effect in graphene with defects
journal, April 2011

  • Chen, Jian-Hao; Li, Liang; Cullen, William G.
  • Nature Physics, Vol. 7, Issue 7, p. 535-538
  • DOI: 10.1038/nphys1962

Electron Capture by Polar Molecules
journal, January 1967


Electronic properties of graphene: a perspective from scanning tunneling microscopy and magnetotransport
journal, April 2012


    Works referencing / citing this record:

    Tuning a circular p–n junction in graphene from quantum confinement to optical guiding
    journal, September 2017

    • Jiang, Yuhang; Mao, Jinhai; Moldovan, Dean
    • Nature Nanotechnology, Vol. 12, Issue 11
    • DOI: 10.1038/nnano.2017.181

    On the landscape of scale invariance in quantum mechanics
    journal, September 2018

    • Brattan, Daniel K.; Ovdat, Omrie; Akkermans, Eric
    • Journal of Physics A: Mathematical and Theoretical, Vol. 51, Issue 43
    • DOI: 10.1088/1751-8121/aadfae

    Log-periodic quantum magneto-oscillations and discrete-scale invariance in topological material HfTe5
    journal, August 2019

    • Wang, Huichao; Liu, Yanzhao; Liu, Yongjie
    • National Science Review, Vol. 6, Issue 5
    • DOI: 10.1093/nsr/nwz110

    Effect of Coulomb screening on the discrete scale invariance of quasibound states in three-dimensional topological semimetals
    journal, November 2019


    Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
    journal, July 2019