Evolution of Landau levels into edge states in graphene

Li, Guohong; Luican‐Mayer, Adina; Abanin, Dmitry A.; Levitov, L. S.; Andrei, Eva Y.

doi:10.1038/ncomms2767

Cited by 68 publications

(76 citation statements)

References 62 publications

(126 reference statements)

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“…It is feasible to observe the effect experimentally. The traditional difficulties of good contact between metals and 2D gas can be circumvented if utilizing the edge channels in graphene [18,19]. The best setup is likely the one with the external circuit, provided the impedances involved can be controlled on chip, proving the scaling predicted by (14).…”

Section: Prl 118 177001 (2017) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 91%

Supercurrents in Unidirectional Channels Originate from Information Transfer in the Opposite Direction: A Theoretical Prediction

Huang

Nazarov

2017

Phys. Rev. Lett.

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It has been thought that the long chiral edge channels cannot support any supercurrent between the superconducting electrodes. We show theoretically that the supercurrent can be mediated by a non-local interaction that facilitates a long-distance information transfer in the direction opposite to electron flow. We compute the supercurrent for several interaction models, including that of an external circuit.

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Section: Prl 118 177001 (2017) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 91%

Supercurrents in Unidirectional Channels Originate from Information Transfer in the Opposite Direction: A Theoretical Prediction

Huang

Nazarov

2017

Phys. Rev. Lett.

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“…Finally, another promising direction is to study the structure of the FQH edge states in graphene. Owing to the atomically sharp confinement 57 , it is possible to avoid edge reconstruction 56 . A recent theoretical study 56 suggests that this might enable the observation of universal Luttinger liquid behavior at the edges of FQH states.…”

Section: Future Directionsmentioning

confidence: 99%

Fractional and integer quantum Hall effects in the zeroth Landau level in graphene

et al. 2013

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Experiments on the fractional quantized Hall effect in the zeroth Landau level of graphene have revealed some striking differences between filling factors in the ranges 0 < |ν| < 1 and 1 < |ν| < 2. We argue that these differences can be largely understood as a consequence of the effects of terms in the Hamiltonian which break SU (2) valley symmetry, which we find to be important for |ν| < 1 but negligible for |ν| > 1. The effective absence of valley anisotropy for |ν| > 1 means that states with odd numerator, such as |ν| = 5/3 or 7/5 can accommodate charged excitations in the form of large radius valley skyrmions, which should have a low energy cost, and may be easily induced by coupling to impurities. The absence of observed quantum Hall states at these fractions is likely due to the effects of valley skyrmions. For |ν| < 1, the anisotropy terms favor phases in which electrons occupy states with opposite spins, similar to the antiferromagnetic state previously hypothesized to be the ground state at ν = 0. The anisotropy and Zeeman energies suppress large-area skyrmions, so that quantized Hall states can be observable at a set of fractions similar to those in GaAs twodimensional electron systems. In a perpendicular magnetic field B, the competition between the Coulomb energy, which varies as B 1/2 , and the Zeeman energy, which varies as B, can explain the observation of apparent phase transitions as a function of B for fixed ν, as transitions between states with different degrees of spin polarization. In addition to an analysis of various fractional states from this point of view, and an examination of the effects of disorder on valley skyrmions, we present new experimental data for the energy gaps at integer fillings ν = 0 and ν = −1, as a function of magnetic field, and we examine the possibility that valley-skyrmions may account for the smaller energy gaps observed at ν = −1.

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“…Detailed numerical calculations 35,41,44 show that the edge reconstruction occurs quite generally in the FQH regime, except in some new 2DEG systems, such as graphene. 45,46 For the FQH state at filling fraction ν in the thermodynamic limit, the radius of the droplet is defined as R 0 = √ 2N orb = 2N/ν * where the ν * = ν − [ν] = 1/2 is the valence Landau level filling for 5/2 state. However, for finite size systems, the number of orbitals N orb has a shift N orb = 2N − 2 such that…”

Section: Edge Modes Near Reconstructionmentioning

confidence: 99%

Identification of the fractional quantum Hall edge modes by density oscillations

Jiang

2016

Phys. Rev. B

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The neutral fermionic edge mode is essential to the non-Abelian topological property and its experimental detection in Z k fractional quantum Hall (FQH) state for k > 1. Usually, the identification of the edge modes in a finite size system is difficult, especially near the region of the edge reconstruction, due to mixing with the bosonic edge mode and the bulk states as well. We study the edge-mode excitations of the Moore-Read (MR) and Read-Rezayi (RR) states by using Jack polynomials in the truncated subspace. It is found that the electron density, as a detector, has marked different behaviors between the bosonic and fermionic edge modes. As an application, it helps us to identify them near the edge reconstruction and in the RR edge spectrum. On the other hand, we systematically study the edge excitations for the RR state, extrapolate the edge velocities and their related coherence length and temperature in the interferometer experiments.

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Evolution of Landau levels into edge states in graphene

Cited by 68 publications

References 62 publications

Supercurrents in Unidirectional Channels Originate from Information Transfer in the Opposite Direction: A Theoretical Prediction

Supercurrents in Unidirectional Channels Originate from Information Transfer in the Opposite Direction: A Theoretical Prediction

Fractional and integer quantum Hall effects in the zeroth Landau level in graphene

Identification of the fractional quantum Hall edge modes by density oscillations

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