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.
Highlights
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
The single-particle energy spectrum of a two-dimensional electron system (2DES) in a large magnetic field collapses into Landau levels (LLs) containing NΦ degenerate states, with NΦ the number of magnetic flux quanta penetrating the sample
Electrons in valley +/− are localized near points K/K′ of the hexagonal Brillouin zone, while the index N is closely analogous to the LL-index of conventional LL systempsffi.ffiffiTffiffiffihffiffiffieffiffiffieffiffinffiffiffieffiffirgies of the LLs are approximately εσξN % hωcsignðNÞ NðN À 1Þ, where ħωc is the cyclotron energy, leading to an eight-fold nearly degenerate zero energy Landau level (ZLL) comprising the N = 0 and N = 1 orbitals and all possible spin and valley isospin combinations
Summary
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. Past experiments[5,6,7,8,9,10,11,12,13, 17] have observed numerous phase transitions between gapped ground states at both integer[6,7,8,9, 12, 13, 17] and fractional[10, 11, 13] filling These experiments are insufficient to constrain realistic theoretical models, in which the preferred ordering is determined by a combination of the Zeeman energy, which splits the spins; Coulomb interactions and band structure effects, both of which distinguish between the N = 0, 1 orbitals; and several.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
