Resonant suppression of the quantized Hall effect in ballistic junctions

Ford, C. J. B.; Washburn, S.; Newbury, R.; Knoedler, C. M.; Hong, Jongill

doi:10.1103/physrevb.43.7339

Cited by 44 publications

(8 citation statements)

References 23 publications

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“…Within a framework of traditional AB oscillation, our findings that the oscillation period is given by the conducting area rather than the total size of the ring would suggest that the electrons move through a phase-coherent path along counter-propagating edge channels at the inner edge and the outer edge, which are connected at one point. In this respect, they are similar to long-period oscillations observed in quantum dots, where electrons scattered from one edge channel to another pick up an extra AB phase 15,16 . In our case, electrons transferring a ring through such a path defined by an inner and outer edge pick up a phase, which is determined by the grey area in the right panels of Fig.…”

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confidence: 67%

Correlation-induced single-flux-quantum penetration in quantum rings

et al. 2010

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The confined electronic states of mesoscopic structures in a magnetic field are arranged in Landau levels consisting of spatially discrete eigenstates. These Landau orbits are the quantum mechanical analogue of classical cyclotron orbits. Here we present magnetoconductance oscillations in semiconductor rings, which visualize the spatial discreteness of the Landau orbits in high magnetic fields (typically B > 2 T). We will show that these oscillations are caused by the fluxquantized, discrete electronic size of the ring leading to a corresponding modulation of its two-point conductance. The oscillation period is given by the number of flux quanta penetrating the conducting area of the structure. These high-field oscillations are distinctively different from the well-known Aharonov-Bohm effect 1 , where, most generally, the penetration of individual flux quanta h/e through a nanostructure causes periodic crossings of field-dependent energy levels, which give rise to magneto-quantum oscillations in its conductance 2-4. Conductance oscillations in mesoscopic structures subjected to a magnetic field are generally assigned to periodic modifications of the electron phase with the magnetic flux penetrating the system. When a charged particle moves phase-coherently through a quantum ring (QR), it accumulates a phase, which changes periodically with the number of magnetic flux quanta, φ 0 = h/e, enclosed by the ring (Fig. 1b). This results in magnetic-fieldperiodic oscillations of its conductance 1-4. Such traditional Aharonov-Bohm (AB) oscillations are also observed in high magnetic fields in QRs (refs 5, 6) and quantum dots 7-9. They are due to quantum Hall edge channels propagating along the outer rim and their period is given by the area encompassed by this edge. This means that changing a quantum dot to a QR by removing its centre does not affect the period of the AB oscillations. However, in narrow rings, where inner and outer edge channels are no longer separated, phase coherence is destroyed and the AB oscillations disappear in strong magnetic fields. Generally, any field dependence of the single-particle energies in a magnetic field can lead to a redistribution of electrons and will cause field-dependent oscillations in the physical properties of the system. Specifically in quantum dots 10,11 , oscillations arising from crossings of different Landau levels are observed. They are periodic only when just the two lowest Landau levels are occupied, and these oscillations disappear in the quantum limit when only one Landau level is filled.

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confidence: 67%

Correlation-induced single-flux-quantum penetration in quantum rings

et al. 2010

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“…Figure 10 in [13]. However, signs of the anomalous oscillations can be observed in different geometries [62,63]. Because of the excellent agreement of the simplified model (24) and the Green's function calculations, see figure 7, we can use this simplified model to study larger stripes, for which NEGF calculations are demanding.…”

Section: Experimental Observabilitymentioning

confidence: 89%

Edge magnetotransport in graphene: A combined analytical and numerical study

Stegmann

Lorke

2015

Annalen der Physik

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The current flow along the boundary of graphene stripes in a perpendicular magnetic field is studied theoretically by the nonequilibrium Green's function method. In the case of specular reflections at the boundary, the Hall resistance shows equidistant peaks, which are due to classical cyclotron motion. When the strength of the magnetic field is increased, anomalous resistance oscillations are observed, similar to those found in a nonrelativistic 2D electron gas [New. J. Phys. 15:113047 (2013)]. Using a simplified model, which allows to solve the Dirac equation analytically, the oscillations are explained by the interference between the occupied edge states causing beatings in the Hall resistance. A rule of thumb is given for the experimental observability. Furthermore, the local current flow in graphene is affected significantly by the boundary geometry. A finite edge current flows on armchair edges, while the current on zigzag edges vanishes completely. The quantum Hall staircase can be observed in the case of diffusive boundary scattering. The number of spatially separated edge channels in the local current equals the number of occupied Landau levels. The edge channels in the local density of states are smeared out but can be made visible if only a subset of the carbon atoms is taken into account.

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“…This may be a consequence of a reduced screening and rougher potential closer to the antidot due to a lower local carrier density [15]. There is evidence from experiments on single dots [16] and antidots [5] that tunneling is strongly enhanced by equivalent geometrical factors such as curvature in the edge-state path. In this scenario the behavior of dots and antidots might be expected to differ since for dots (antidots) the spatially closest mode to the current carrying edge states originates from the lower (higher) Landau level at lower (higher) densities.…”

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confidence: 99%

“Spectator” Modes and Antidot Molecules

et al. 1996

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The interaction of edge states via localized states leads to the "generic" breakdown of the quantum Hall effect. Using a versatile two-antidot structure we study the magnetoconductance oscillations of coupled antidot systems in regimes where "atomic" modes exist around individual antidots in addition to "molecular" modes encompassing both antidots. We find and discuss an apparent passivity of the molecular modes during both resonant transmission and reflection processes.

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Resonant suppression of the quantized Hall effect in ballistic junctions

Cited by 44 publications

References 23 publications

Correlation-induced single-flux-quantum penetration in quantum rings

Correlation-induced single-flux-quantum penetration in quantum rings

Edge magnetotransport in graphene: A combined analytical and numerical study

“Spectator” Modes and Antidot Molecules

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