Electrically tunable spin filtering for electron tunneling between spin-resolved quantum Hall edge states and a quantum dot

Edge states have been a backbone of our understanding of the experimental basis of the quantum Hall effect for quite some time. Interestingly, this comprises a quantum system with well defined currents and particle trajectories. The role of trajectories in quantum mechanics has been a problematic question of interpretation for quite some time, and the open quantum dot is a natural system in which to probe this question. Contrary to early speculation, a set of well defined quantum states survives in the open quantum dot. These states are the pointer states and provide a transition into the classical states that can be found in these structures. These states provide resonances, which are observable as oscillatory behavior in the magnetoconductance of the dots. But, they have well defined current directions within the dots. Consequently, one expects trajectories to be a property of these states as well. As one crosses from the low to the high field regime, quite steady trajectories and consequent wave functions can easily be identified and examined. In this talk, we review the current understanding and the support for the decoherence theory.

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Topological gaps by twisting

Communications Physics ◽

10.1038/s42005-021-00630-3 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Matheus I. N. Rosa ◽

Massimo Ruzzene ◽

Emil Prodan

Keyword(s):

Magnetic Field ◽

Quantum Hall Effect ◽

Twist Angle ◽

Quantum Hall ◽

Topological Phases ◽

Edge States ◽

Layered Systems ◽

Virtual Laboratories ◽

Higher Dimensional ◽

Chern Numbers

AbstractTwisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twisted n-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.

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Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy

Nature Communications ◽

10.1038/s41467-021-22886-7 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Sungmin Kim ◽

Johannes Schwenk ◽

Daniel Walkup ◽

Yihang Zeng ◽

Fereshte Ghahari ◽

...

Keyword(s):

Atomic Force Microscopy ◽

Chemical Potential ◽

Quantum Hall ◽

Broken Symmetry ◽

Topological Order ◽

Edge States ◽

Force Microscopy ◽

Atomic Force ◽

Intimate Relation ◽

Boundary Measurements

AbstractThe quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the “bulk” topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements. In this article, we spatially map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $${{\nu }}={{0}},\pm {{1}}$$ ν = 0 , ± 1 across the quantum Hall edge boundary using high-resolution atomic force microscopy (AFM) and show a gapped ground state proceeding from the bulk through to the QH edge boundary. Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moiré superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

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“Can quantum dot in form of molecular ground be implied in IETS to measure the voltage effectively by sudden potential rise due to phonon assisted electron tunneling as Klein paradox?”

Materials Today Proceedings ◽

10.1016/j.matpr.2020.10.602 ◽

2020 ◽

Author(s):

Amitabh Sharma ◽

Umesh Prasad Verma

Keyword(s):

Quantum Dot ◽

Electron Tunneling ◽

Klein Paradox

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Equilibration and filtering of quantum Hall edge states in few-layer black phosphorus

Physical Review Materials ◽

10.1103/physrevmaterials.4.114008 ◽

2020 ◽

Vol 4 (11) ◽

Author(s):

Jiawei Yang ◽

Kangyu Wang ◽

Shi Che ◽

Zachary J. Tuchfeld ◽

Kenji Watanabe ◽

...

Keyword(s):

Quantum Hall ◽

Black Phosphorus ◽

Edge States

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Magnetocapacitance Investigation of Quantum Hall Effect and Edge States

International Journal of Modern Physics B ◽

10.1142/s0217979297001295 ◽

1997 ◽

Vol 11 (22) ◽

pp. 2593-2619 ◽

Cited By ~ 7

Author(s):

Sadao Takaoka ◽

Kenichi Oto ◽

Kazuo Murase

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Electron System ◽

Edge Length ◽

Capacitance Measurement ◽

Edge States ◽

Bulk Conductivity ◽

Cyclotron Radius ◽

Bulk State

The quantum Hall effect for the GaAs/AlGaAs heterostrcture is investigated by an ac capacitance measurement between the two-dimensional electron system (2DES) and the gate on GaAs/AlGaAs. The capacitance minima at the quantum Hall plateaus are mainly determined not by the 2DES area under the gate but by the edge length of 2DES. There exists the high conductive region due to the edge states along the 2DES boundary, when the bulk conductivity σxx is small enough at low temperatures and high magnetic fields. From the temperature and frequency dependence of the capacitance minima, it is found that the measured capacitance consists of the contribution from the edge states and that of the bulk state, which is treated as a distributed circuit of a resistive plate with the conductivity σxx. The evaluated width of edge states from the capacitance is much larger than the magnetic length and the cyclotron radius expected from the one-electron picture. This wide width of edge states can be explained by the compressible-incompressible strip model, in which the screening effect is taken into account. Further the bulk conductivity of less than 10-12 S (S=1/Ω) is measured by the capacitance of the Corbino geometry sample, where the edge states are absent and the capacitance is determined by only σxx in this geometry. The localization of the bulk state is investigated by the obtained σxx.

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