Direct measurement of discrete valley and orbital quantum numbers in a multicomponent quantum Hall system

Abstract

Strongly interacting two dimensional electron systems (2DESs) host a complex landscape of broken symmetry states. The possible ground states are further expanded by internal degrees of freedom such as spin or valley-isospin. While direct probes of spin in 2DESs were demonstrated two decades ago, the valley quantum number has only been probed indirectly in semiconductor quantum wells, graphene mono- and bilayers, and transition-metal dichalcogenides. Here, we present the first direct experimental measurement of valley polarization in a two dimensional electron system, effected via the direct mapping of the valley quantum number onto the layer polarization in bilayer graphene at high magnetic fields. We find that the layer polarization evolves in discrete steps across 32 electric field-tuned phase transitions between states of different valley, spin, and orbital polarization. Our data can be fit by a model that captures both single particle and interaction induced orbital, valley, and spin anisotropies, providing the most complete model of this complex system to date. Among the newly discovered phases are theoretically unanticipated orbitally polarized states stabilized by skew interlayer hopping. The resulting roadmap to symmetry breaking in bilayer graphene 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, providing an essential direct probe that is a prerequisite for manipulating these new quantum degrees of freedom.

arXiv commentThis version (v3) updates a large portion of the theoretical treatment in previous versions and consequently has new Figs. 3 and 4 of the main text and a significant overhaul of the Supplementary Material

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• Tunable Coupling between Surface States of a Three-Dimensional Topological Insulator in the Quantum Hall Regime
• Gapless Spin Wave Transport through a Quantum Canted-Antiferromagnet
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• Metallic Phase and Temperature Dependence of the $\nu =0$ Quantum Hall State in Bilayer Graphene
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• A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene
• Gate-controlled transmission of quantum Hall edge states in bilayer graphene
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• Tunable Quantum Hall Edge Conduction in Bilayer Graphene through Spin-Orbit Interaction
• Evidence for a topological "exciton Fermi sea" in bilayer graphene
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• Large Landau level splitting with tunable one-dimensional graphene superlattice probed by magneto capacitance measurements
• An $O(N)$ $Abinitio$ Calculation Scheme for Large-Scale Moiré Structures
• Absence of heat flow in ν = 0 quantum Hall ferromagnet in bilayer graphene
• Dual-gated hBN/bilayer-graphene superlattices and the transitions between the insulating phases at the charge neutrality point
• Phase diagram of the $\nu =2$ quantum Hall state in bilayer graphene
• Valley and Zeeman Splittings in Multilayer Epitaxial Graphene Revealed by Circular Polarization Resolved Magneto-infrared Spectroscopy
• Energetics of complex phase diagram in a tunable bilayer graphene probed by quantum capacitance
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• Stabilizing the inverted phase of a WSe${}_2$/BLG/WSe${}_2$ heterostructure via hydrostatic pressure
• Fluctuating magnetism and Pomeranchuk effect in multilayer graphene
• Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene
• Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene
• High Precision, Low Excitation Capactiance Measurement Methods from 10 mK- to Room-Temperature
• Landau Levels of Bilayer Graphene in a WSe${}_2$/Bilayer Graphene van der Waals Heterostructure
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• Spectroscopic Characterization of Landau Level Splitting and the Intermediate v = 0 Phase in Bilayer Graphene
• Quantum Hall ferroelectric helix in bilayer graphene
• Deep learning extraction of band structure parameters from density of states: a case study on trilayer graphene
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• Many-body effects, orbital mixing and cyclotron resonance in bilayer graphene
• Interaction-driven quantum phase transitions between topological and crystalline orders of electrons
• Landau Level Phases in Bilayer Graphene under Pressure at Charge Neutrality
• $2{\mathbf{k}}_{\mathbf{F}}$ Density Wave Instability of Composite Fermi Liquid
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• Increasing the proximity induced spin-orbit coupling in bilayer graphene/WSe${}_2$ heterostructures with pressure
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