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Title: Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene

Abstract

The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.

Authors:
 [1]; ORCiD logo [2];  [3];  [4];  [5]; ORCiD logo [5];  [4];  [4];  [6];  [7];  [8]
+ Show Author Affiliations
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics; Columbia Univ., New York, NY (United States). Dept. of Physics; Carnegie Mellon Univ., Pittsburgh, PA (United States). Dept. of Physics
  2. Columbia Univ., New York, NY (United States). Dept. of Physics
  3. Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
  4. Columbia Univ., New York, NY (United States)
  5. National Inst. for Materials Science (NIMS), Tsukuba (Japan)
  6. Microsoft Research, Santa Barbara, CA (United States). Station Q
  7. Massachusetts Inst. of Tech., Cambridge, MA (United States)
  8. Massachusetts Inst. of Tech., Cambridge, MA (United States); Univ. of California, Santa Barbara, CA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1529936
Alternate Identifier(s):
OSTI ID: 1545718
Grant/Contract Number:  
FG02-08ER46514
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

Hunt, B. M., Li, J. I. A., Zibrov, A. A., Wang, L., Taniguchi, T., Watanabe, K., Hone, J., Dean, C. R., Zaletel, M., Ashoori, R. C., and Young, A. F. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene. United States: N. p., 2017. Web. doi:10.1038/s41467-017-00824-w.
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Hunt, B. M., Li, J. I. A., Zibrov, A. A., Wang, L., Taniguchi, T., Watanabe, K., Hone, J., Dean, C. R., Zaletel, M., Ashoori, R. C., & Young, A. F. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene. United States. https://doi.org/10.1038/s41467-017-00824-w
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Hunt, B. M., Li, J. I. A., Zibrov, A. A., Wang, L., Taniguchi, T., Watanabe, K., Hone, J., Dean, C. R., Zaletel, M., Ashoori, R. C., and Young, A. F. Mon . "Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene". United States. https://doi.org/10.1038/s41467-017-00824-w. https://www.osti.gov/servlets/purl/1529936.
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@article{osti_1529936,
title = {Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene},
author = {Hunt, B. M. and Li, J. I. A. and Zibrov, A. A. and Wang, L. and Taniguchi, T. and Watanabe, K. and Hone, J. and Dean, C. R. and Zaletel, M. and Ashoori, R. C. and Young, A. F.},
abstractNote = {The high magnetic field electronic structure of bilayer graphene is enhanced by the spin, valley isospin, and an accidental orbital degeneracy, leading to a complex phase diagram of broken symmetry states. Here, we present a technique for measuring the layer-resolved charge density, from which we directly determine the valley and orbital polarization within the zero energy Landau level. Layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital order, including previously unobserved orbitally polarized states stabilized by skew interlayer hopping. We fit our data to a model that captures both single-particle and interaction-induced anisotropies, providing a complete picture of this correlated electron system. The resulting roadmap to symmetry breaking paves the way for deterministic engineering of fractional quantum Hall states, while our layer-resolved technique is readily extendable to other two-dimensional materials where layer polarization maps to the valley or spin quantum numbers.},
doi = {10.1038/s41467-017-00824-w},
journal = {Nature Communications},
number = 1,
volume = 8,
place = {United States},
year = {2017},
month = {10}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1038/s41467-017-00824-w
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Figures / Tables:

Fig. 1 Fig. 1: Layer polarization of bilayer graphene at zero magnetic field. a Measurement schematic showing geometric gate capacitances ct and cb and interlayer capacitance c0. Capacitance is measured using a cryogenic bridge circuit by comparison with a standard capacitor Cstd, measured to be 404± 20 fF (see “Methods”). b Devicemore » image. Top gate (TG), back gate (BG), and contacts to bilayer graphene (G) are shown. Scale bar is 10 μm; device area is approximately 87 μm2. c CS measured at B= 0 and T= 1.6 K as a function of n0/c= vt + vb and p0/c= vt − vb. A p0-dependent band gap is visible as the dark region near n0= 0. d Line traces taken at different values of p0, corresponding to dashed lines in c. Band edge van Hove singularities and electron-hole asymmetry are both evident. e CA measured under the same conditions. A common, constant background has been subtracted to account for fixed parasitic capacitances. f Line traces at different values of p0 corresponding to dashed lines in e. g Integrated change in polarization, $\frac{c_{0}}{c}$∫CAd($\frac{n_{0}}{c}$) = Δp, with the constant of integration fixed to be zero at high |n0|. In accordance with single-particle band structure, wavefunctions are layer unpolarized for p0 = 0, while for large |p0| the polarization peaks at n0 = 0, where band wavefunctions are strongly layer polarized« less
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Quantum spin-valley Hall effect in AB-stacked bilayer silicene
journal, December 2019

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text, January 2009

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text, January 2012

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text, January 2012

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    Evidence for a topological "exciton Fermi sea" in bilayer graphene
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    Spin-orbit driven band inversion in bilayer graphene by van der Waals proximity effect
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    Electronic Compressibility of Magic-Angle Graphene Superlattices
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    Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene
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