Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference

Randeria, Mallika T.; Feldman, Benjamin E.; Wu, Fengcheng; Ding, Hao; Gyenis, András; Ji, Huiwen; Cava, R. J.; MacDonald, Allan H.; Yazdani, Ali

doi:10.1038/s41567-018-0148-2

Title: Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference

Abstract

States with spontaneously broken symmetry can form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Materials with several degenerate regions in the Brillouin zone-called valleys-offer a rich setting for the emergence of such states, which have potential electronic and optical applications. To date, identification of these broken-symmetry phases has mostly relied on macroscopic transport or optical properties. Here we demonstrate a direct approach by visualizing the wavefunctions of bismuth surface states with a scanning tunnelling microscope. Strong spin-orbit coupling on the surface of bismuth leads to six degenerate, teardrop-shaped, hole valleys. Our spectroscopic measurements reveal that exchange interactions fully lift this degeneracy at high magnetic field, and we are able to determine the nature of the valley ordering by imaging the broken-symmetry Landau level wavefunctions. The spatial features of singly degenerate Landau level wavefunctions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. As a result, our observations confirm the recent prediction that interactions in strongly anisotropic valley systems favour the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth.

Authors:

Randeria, Mallika T. ^[1];

^[2]; Wu, Fengcheng ^[3];

^[1]; Gyenis, András ^[1]; Ji, Huiwen ^[1]; Cava, R. J. ^[1]; MacDonald, Allan H. ^[4];

^[1]

Princeton Univ., Princeton, NJ (United States)
Princeton Univ., Princeton, NJ (United States); Stanford Univ., Stanford, CA (United States)
Argonne National Lab. (ANL), Argonne, IL (United States)
The Univ. of Texas, Austin, TX (United States)

Publication Date:: Mon May 14 00:00:00 EDT 2018

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Gordon and Betty Moore Foundation; U.S. Army Research Laboratory, U.S. Army Research Office (ARO); Welch Foundation

OSTI Identifier:: 1466366

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: Nature Physics

Additional Journal Information:: Journal Volume: 14; Journal Issue: 8; Journal ID: ISSN 1745-2473

Publisher:: Nature Publishing Group (NPG)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Randeria, Mallika T., Feldman, Benjamin E., Wu, Fengcheng, Ding, Hao, Gyenis, András, Ji, Huiwen, Cava, R. J., MacDonald, Allan H., and Yazdani, Ali. Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference.  United States: N. p., 2018. 
Web.  doi:10.1038/s41567-018-0148-2.

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                    Randeria, Mallika T., Feldman, Benjamin E., Wu, Fengcheng, Ding, Hao, Gyenis, András, Ji, Huiwen, Cava, R. J., MacDonald, Allan H., & Yazdani, Ali. Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference.  United States.  https://doi.org/10.1038/s41567-018-0148-2

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                    Randeria, Mallika T., Feldman, Benjamin E., Wu, Fengcheng, Ding, Hao, Gyenis, András, Ji, Huiwen, Cava, R. J., MacDonald, Allan H., and Yazdani, Ali. Mon .  
"Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference".  United States.  https://doi.org/10.1038/s41567-018-0148-2.  https://www.osti.gov/servlets/purl/1466366.

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@article{osti_1466366,

  title        = {Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference},

  author       = {Randeria, Mallika T. and Feldman, Benjamin E. and Wu, Fengcheng and Ding, Hao and Gyenis, András and Ji, Huiwen and Cava, R. J. and MacDonald, Allan H. and Yazdani, Ali},

  abstractNote = {States with spontaneously broken symmetry can form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Materials with several degenerate regions in the Brillouin zone-called valleys-offer a rich setting for the emergence of such states, which have potential electronic and optical applications. To date, identification of these broken-symmetry phases has mostly relied on macroscopic transport or optical properties. Here we demonstrate a direct approach by visualizing the wavefunctions of bismuth surface states with a scanning tunnelling microscope. Strong spin-orbit coupling on the surface of bismuth leads to six degenerate, teardrop-shaped, hole valleys. Our spectroscopic measurements reveal that exchange interactions fully lift this degeneracy at high magnetic field, and we are able to determine the nature of the valley ordering by imaging the broken-symmetry Landau level wavefunctions. The spatial features of singly degenerate Landau level wavefunctions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. As a result, our observations confirm the recent prediction that interactions in strongly anisotropic valley systems favour the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth.},

  doi          = {10.1038/s41567-018-0148-2},

  journal      = {Nature Physics},

  number       = 8,

  volume       = 14,

  place        = {United States},

  year         = {Mon May 14 00:00:00 EDT 2018},

  month        = {Mon May 14 00:00:00 EDT 2018}

}

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Title: Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference

Abstract

Citation Formats

Order by disorder and by doping in quantum Hall valley ferromagnets journal, January 2016

Tight-binding theory of surface spin states on bismuth thin films journal, January 2016

Strong Spin-Orbit Splitting on Bi Surfaces journal, July 2004

Giant Anisotropy of Spin-Orbit Splitting at the Bismuth Surface journal, November 2012

Quantum Hall effects in graphene-based two-dimensional electron systems journal, January 2012

Spin and pseudospins in layered transition metal dichalcogenides journal, April 2014

Spin and valley quantum Hall ferromagnetism in graphene journal, May 2012

Role of Spin-Orbit Coupling and Hybridization Effects in the Electronic Structure of Ultrathin Bi Films journal, October 2006

Thin-film ferroelectric materials and their applications journal, November 2016

Valley-degenerate two-dimensional electrons in the lowest Landau level journal, January 2014

Discovery of robust in-plane ferroelectricity in atomic-thick SnTe journal, July 2016

Surface Landau levels and spin states in bismuth (111) ultrathin films journal, March 2016

Topological crystalline insulator states in Pb1−xSnxSe journal, September 2012

Giant Out-of-Plane Spin Component and the Asymmetry of Spin Polarization in Surface Rashba States of Bismuth Thin Film journal, April 2011

Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state journal, December 2013

Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy journal, October 2001

Physics of thin-film ferroelectric oxides journal, October 2005

Evidence for a spin phase transition at charge neutrality in bilayer graphene journal, January 2013

Topological crystalline insulators in the SnTe material class journal, January 2012

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Observation of Quantum Hall “Valley Skyrmions” journal, August 2005

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Imaging standing waves in a two-dimensional electron gas journal, June 1993

Spin-valley skyrmions in graphene at filling factor ν = − 1 journal, June 2017

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Fermi Surface of Bi(111) Measured by Photoemission Spectroscopy text, January 2001

Nematic Valley Ordering in Quantum Hall Systems text, January 2010

Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems text, January 2011

Spin and valley quantum Hall ferromagnetism in graphene text, January 2012

Topological crystalline insulator states in Pb(1-x)Sn(x)Se text, January 2012

Giant Anisotropy of Spin-Orbit Splitting at the Bismuth Surface text, January 2012

Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state text, January 2013

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Observation of Quantum Hall Valley Skyrmions text, January 2005

Two-dimensional electrons occupying multiple valleys in AlAs text, January 2006

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A modular ultra-high vacuum millikelvin scanning tunneling microscope text, January 2019

Order by disorder and by doping in quantum Hall valley ferromagnets
journal, January 2016

Tight-binding theory of surface spin states on bismuth thin films
journal, January 2016

Strong Spin-Orbit Splitting on Bi Surfaces
journal, July 2004

Giant Anisotropy of Spin-Orbit Splitting at the Bismuth Surface
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Quantum Hall effects in graphene-based two-dimensional electron systems
journal, January 2012

Spin and pseudospins in layered transition metal dichalcogenides
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Spin and valley quantum Hall ferromagnetism in graphene
journal, May 2012

Role of Spin-Orbit Coupling and Hybridization Effects in the Electronic Structure of Ultrathin Bi Films
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Thin-film ferroelectric materials and their applications
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Valley-degenerate two-dimensional electrons in the lowest Landau level
journal, January 2014

Discovery of robust in-plane ferroelectricity in atomic-thick SnTe
journal, July 2016

Surface Landau levels and spin states in bismuth (111) ultrathin films
journal, March 2016

Topological crystalline insulator states in Pb1−xSnxSe
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Giant Out-of-Plane Spin Component and the Asymmetry of Spin Polarization in Surface Rashba States of Bismuth Thin Film
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Physics of thin-film ferroelectric oxides
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Topological crystalline insulators in the SnTe material class
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Design and performance of an ultra-high vacuum scanning tunneling microscope operating at dilution refrigerator temperatures and high magnetic fields
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Observation of a nematic quantum Hall liquid on the surface of bismuth
journal, October 2016

Observation of Quantum Hall “Valley Skyrmions”
journal, August 2005

Nematic valley ordering in quantum Hall systems
journal, July 2010

Imaging standing waves in a two-dimensional electron gas
journal, June 1993

Spin-valley skyrmions in graphene at filling factor $ν = - 1$
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Field-induced polarization of Dirac valleys in bismuth
journal, October 2011

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Nematic Valley Ordering in Quantum Hall Systems
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Quantum Hall Effects in Graphene-Based Two-Dimensional Electron Systems
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