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

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.

doi:10.1038/s41467-017-00824-w

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

Journal Article · Mon Oct 16 00:00:00 EDT 2017 · Nature Communications

DOI:https://doi.org/10.1038/s41467-017-00824-w· OSTI ID:1529936

Hunt, B. M. ^[1];

^[2]; Zibrov, A. A. ^[3]; Wang, L. ^[4]; Taniguchi, T. ^[5];

^[5]; Hone, J. ^[4]; Dean, C. R. ^[4]; Zaletel, M. ^[6]; Ashoori, R. C. ^[7]; Young, A. F. ^[8]

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
Columbia Univ., New York, NY (United States). Dept. of Physics
Univ. of California, Santa Barbara, CA (United States). Dept. of Physics
Columbia Univ., New York, NY (United States)
National Inst. for Materials Science (NIMS), Tsukuba (Japan)
Microsoft Research, Santa Barbara, CA (United States). Station Q
Massachusetts Inst. of Tech., Cambridge, MA (United States)
Massachusetts Inst. of Tech., Cambridge, MA (United States); Univ. of California, Santa Barbara, CA (United States)

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.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-08ER46514

OSTI ID:: 1529936

Alternate ID(s):: OSTI ID: 1545718

Journal Information:: Nature Communications, Vol. 8, Issue 1; ISSN 2041-1723

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 60 works

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