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Register a new userObservation of Helical Edge States and Fractional Quantum Hall Effect in a Graphene Electron-hole Bilayer
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Added by
Javier Sanchez-Yamagishi
Publication date
2016
fields
Physics
and research's language is
English
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A quantum Hall edge state provides a rich foundation to study electrons in 1-dimension (1d) but is limited to chiral propagation along a single direction. Here, we demonstrate a versatile platform to realize new 1d systems made by combining quantum Hall edge states of opposite chiralities in a graphene electron-hole bilayer. Using this approach, we engineer helical 1d edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong nonlocal transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Moreover, we investigate these electron-hole bilayers in the fractional quantum Hall regime, where we observe conduction through fractional and integer edge states of opposite chiralities, paving the way towards the realization of 1d helical systems with fractional quantum statistics.
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When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions. However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena, despite concerted experimental efforts and intense theoretical interest. Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields.
We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by non-linear transformations to the spectra of quantum Hall edge--states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a hole-like edge state of one valley and a particle-like state of the other on the same edge, which may or may not cross depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends BOTH on boundary conditions and the energies of the bulk states.
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.
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.
We report observation of the fractional quantum Hall effect (FQHE) in high mobility multi-terminal graphene devices, fabricated on a single crystal boron nitride substrate. We observe an unexpected hierarchy in the emergent FQHE states that may be explained by strongly interacting composite Fermions with full SU(4) symmetric underlying degrees of freedom. The FQHE gaps are measured from temperature dependent transport to be up 10 times larger than in any other semiconductor system. The remarkable strength and unusual hierarcy of the FQHE described here provides a unique opportunity to probe correlated behavior in the presence of expanded quantum degrees of freedom.
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