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

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:
 [1] ; ORCiD logo [2] ;  [3] ; ORCiD logo [1] ;  [1] ;  [1] ;  [1] ;  [4] ; ORCiD logo [1]
  1. Princeton Univ., Princeton, NJ (United States)
  2. Princeton Univ., Princeton, NJ (United States); Stanford Univ., Stanford, CA (United States)
  3. Argonne National Lab. (ANL), Argonne, IL (United States)
  4. The Univ. of Texas, Austin, TX (United States)
Publication Date:
Grant/Contract Number:
AC02-06CH11357
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)
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
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1466366

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., Web. doi:10.1038/s41567-018-0148-2.
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. doi:10.1038/s41567-018-0148-2.
Randeria, Mallika T., Feldman, Benjamin E., Wu, Fengcheng, Ding, Hao, Gyenis, András, Ji, Huiwen, Cava, R. J., MacDonald, Allan H., and Yazdani, Ali. 2018. "Ferroelectric quantum Hall phase revealed by visualizing Landau level wave function interference". United States. doi:10.1038/s41567-018-0148-2.
@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 = {2018},
month = {5}
}

Works referenced in this record:

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

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