DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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]
  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.
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
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.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 59 works
Citation information provided by
Web of Science

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

Save / Share:

Works referenced in this record:

Topological Phases in the Zeroth Landau Level of Bilayer Graphene
journal, January 2014


Charge 2 e Skyrmions in Bilayer Graphene
journal, August 2009


Optically Pumped NMR Evidence for Finite-Size Skyrmions in GaAs Quantum Wells near Landau Level Filling ν = 1
journal, June 1995


Tunable fractional quantum Hall phases in bilayer graphene
journal, July 2014


Measurement of the electronic compressibility of bilayer graphene
journal, July 2010


The electronic properties of bilayer graphene
journal, April 2013


Canted Antiferromagnetic Phase of the ν = 0 Quantum Hall State in Bilayer Graphene
journal, July 2012


Broken-symmetry states and divergent resistance in suspended bilayer graphene
journal, September 2009

  • Feldman, Benjamin E.; Martin, Jens; Yacoby, Amir
  • Nature Physics, Vol. 5, Issue 12
  • DOI: 10.1038/nphys1406

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

  • Maher, P.; Dean, C. R.; Young, A. F.
  • Nature Physics, Vol. 9, Issue 3
  • DOI: 10.1038/nphys2528

Capacitance measurements of a quantized two-dimensional electron gas in the regime of the quantum Hall effect
journal, May 1985


Intra-Landau-Level Cyclotron Resonance in Bilayer Graphene
journal, August 2008


Breaking of Particle-Hole Symmetry by Landau Level Mixing in the ν = 5 / 2 Quantized Hall State
journal, March 2011


Single-electron capacitance spectroscopy of discrete quantum levels
journal, May 1992


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

  • Young, A. F.; Dean, C. R.; Wang, L.
  • Nature Physics, Vol. 8, Issue 7
  • DOI: 10.1038/nphys2307

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


Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene
journal, September 2012


Broken-Symmetry States in Doubly Gated Suspended Bilayer Graphene
journal, October 2010


Competing ordered states with filling factor two in bilayer graphene
journal, July 2014

  • Velasco Jr, J.; Lee, Y.; Zhang, F.
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5550

Nonabelions in the fractional quantum hall effect
journal, August 1991


Quantum Hall ferromagnetic phases in the Landau level N = 0 of a graphene bilayer
journal, March 2013


Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer
journal, October 2016

  • Sanchez-Yamagishi, Javier D.; Luo, Jason Y.; Young, Andrea F.
  • Nature Nanotechnology, Vol. 12, Issue 2
  • DOI: 10.1038/nnano.2016.214

Quantum spin-valley Hall effect in AB-stacked bilayer silicene
journal, December 2019


Charge 2e skyrmions in bilayer graphene
text, January 2009


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


The electronic properties of bilayer graphene
text, January 2012


Topological Phases in the Zeroth Landau Level of Bilayer Graphene
text, January 2013


Tunable Fractional Quantum Hall Phases in Bilayer Graphene
text, January 2014


Observation of Quantum Hall Valley Skyrmions
text, January 2005


Works referencing / citing this record:

Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect
journal, June 2019


Optical control of the layer degree of freedom through Wannier–Stark states in polar 3R MoS 2
journal, May 2019

  • Park, Jaehong; Yeu, In Won; Han, Gyuseung
  • Journal of Physics: Condensed Matter, Vol. 31, Issue 31
  • DOI: 10.1088/1361-648x/ab1d0f

A review of the quantum Hall effects in MgZnO/ZnO heterostructures
journal, March 2018


Energy levels of graphene magnetic circular quantum dot
journal, January 2020

  • Belouad, Abdelhadi; Lemaalem, Bouchaib; Jellal, Ahmed
  • Materials Research Express, Vol. 7, Issue 1
  • DOI: 10.1088/2053-1591/ab6d2f

Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene
journal, September 2019


Influence of minivalleys and Berry curvature on electrostatically induced quantum wires in gapped bilayer graphene
journal, October 2018


Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime
journal, July 2019


Quantum Effects in the Capacitance of Field-Effect Transistors with a Double Quantum Well
journal, September 2019


Evidence for a topological "exciton Fermi sea" in bilayer graphene
text, January 2018


Spin-orbit driven band inversion in bilayer graphene by van der Waals proximity effect
text, January 2019


Electronic Compressibility of Magic-Angle Graphene Superlattices
text, January 2019


Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene
text, January 2019


Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.