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Register a new userTunable Fractional Quantum Hall Phases in Bilayer Graphene
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Symmetry breaking in a quantum system often leads to complex emergent behavior. In bilayer graphene (BLG), an electric field applied perpendicular to the basal plane breaks the inversion symmetry of the lattice, opening a band gap at the charge neutrality point. In a quantizing magnetic field electron interactions can cause spontaneous symmetry breaking within the spin and valley degrees of freedom, resulting in quantum Hall states (QHS) with complex order. Here we report fractional quantum Hall states (FQHS) in bilayer graphene which show phase transitions that can be tuned by a transverse electric field. This result provides a model platform to study the role of symmetry breaking in emergent states with distinct topological order.
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The multi-component nature of bilayer graphene (BLG), together with the ability to controllably tune between the various ground state orders, makes it a rich system in which to explore interaction driven phenomena. In the fractional quantum Hall effect (FQHE) regime, the unique Landau level spectrum of BLG is anticipated to support a non-Abelian even-denominator state that is tunable by both electric and magnetic fields. However, observation of this state, which is anticipated to be stronger than in conventional systems, has been conspicuously difficult. Here we report transport measurements of a robust even denominator FQHE in high-mobility, dual gated BLG devices. We confirm that the stability of the energy gap can be sensitively tuned and map the phase diagram. Our results establish BLG as a dynamic new platform to study topological ground states with possible non-Abelian excitations.
Electron spin and pseudospin degrees of freedom play a critical role in many-body phenomena through exchange interactions, the understanding and control of which enable the construction of states with complex topological orders and exotic excitations. In this work, we demonstrate fine control of the valley isospin in high-quality bilayer graphene devices and its profound impact in realizing fractional quantum Hall effect with different ground state orders. We present evidence for a new even-denominator fractional quantum Hall state in bilayer graphene, its spontaneous valley polarization in the limit of zero valley Zeeman energy, and the breaking of particle-hole symmetry. These observations support the Moore-Read anti-Pfaffian order. Our experiments establish valley isospin in bilayer graphene to be a powerful experimental knob and open the door to engineering non-Abelian states and quantum information processes in a quantum Hall platform.
The quantum anomalous Hall (QAH) effect - a macroscopic manifestation of chiral band topology at zero magnetic field - has only been experimentally realized by magnetic doping of topological insulators (1 - 3) and delicate design of Moire heterostructures (4 - 8). However, the seemingly simple bilayer graphene without magnetic doping or Moire engineering has long been predicted to host competing ordered states with QAH effects (9 - 11). Here, we explore states in bilayer graphene with conductance of 2 e2/h that not only survive down to anomalously small magnetic fields and up to temperatures of 5 K, but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital magnetism driven QAH behavior with a Chern number tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations due to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley, and spin-valley Hall behavior.
Protected edge modes are the cornerstone of topological states of matter. The simplest example is provided by the integer quantum Hall state at Landau level filling unity, which should feature a single chiral mode carrying electronic excitations. In the presence of a smooth confining potential it was hitherto believed that this picture may only be partially modified by the appearance of additional counterpropagating integer-charge modes. Here, we demonstrate the breakdown of this paradigm: The system favors the formation of edge modes supporting fractional excitations. This accounts for previous observations, and leads to additional predictions amenable to experimental tests.
We have measured the quantum Hall activation gaps in bilayer graphene at filling factors $ u=pm4$ and $ u=pm8$ in high magnetic fields up to 30 T. We find that energy levels can be described by a 4-band relativistic hyperbolic dispersion. The Landau level width is found to contain a field independent background due to an intrinsic level broadening and a component which increases linearly with magnetic field.
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