scholarly journals Quantum Hall edge states in topological insulator nanoribbons

2016 ◽  
Vol 94 (12) ◽  
Author(s):  
A. Pertsova ◽  
C. M. Canali ◽  
A. H. MacDonald
Keyword(s):  
Topological Insulator ◽  
Quantum Hall ◽  
Edge States

scholarly journals Topological gaps by twisting

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.

scholarly journals Controllable quantum point junction on the surface of an antiferromagnetic topological insulator

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Nicodemos Varnava ◽  
Justin H. Wilson ◽  
J. H. Pixley ◽  
David Vanderbilt
Keyword(s):  
Topological Insulator ◽  
Information Science ◽  
Domain Walls ◽  
Quantum Hall ◽  
Edge State ◽  
Wave Functions ◽  
Quantum Hall Systems ◽  
Electron Quantum ◽  
Quantum Point ◽  
Higher Temperature

AbstractEngineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.

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

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.

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

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

scholarly journals Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator Sn−Bi1.1Sb0.9Te2S devices

2019 ◽  
Vol 99 (8) ◽  
Author(s):  
Faji Xie ◽  
Shuai Zhang ◽  
Qianqian Liu ◽  
Chuanying Xi ◽  
Ting-Ting Kang ◽  
...  
Keyword(s):  
Phase Transition ◽  
Topological Insulator ◽  
Quantum Hall ◽  
Anomalous Scaling

Magnetocapacitance Investigation of Quantum Hall Effect and Edge States

1997 ◽  
Vol 11 (22) ◽  
pp. 2593-2619 ◽  
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.

Universality test of the quantum Hall effect on topological insulator

2016 ◽  
Author(s):  
Tetsuro Misawa ◽  
Yasuhiro Fukuyama ◽  
Yuma Okazaki ◽  
Shuji Nakamura ◽  
Nariaki Nasaka ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Topological Insulator ◽  
Quantum Hall

VERTEX OPERATORS IN THE QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (03) ◽  
pp. 509-527 ◽  
Author(s):  
MICHAEL STONE
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Group Action ◽  
Quantum Hall ◽  
Vertex Operators ◽  
Edge States ◽  
Many Body ◽  
Level I ◽  
The Many

The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.

scholarly journals THE EDGE STATES OF THE BF SYSTEM AND THE LONDON EQUATIONS

1993 ◽  
Vol 08 (04) ◽  
pp. 723-752 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
P. TEOTONIO-SOBRINHO
Keyword(s):  
Scalar Field ◽  
Scaling Limit ◽  
Quantum Hall ◽  
Simons Theory ◽  
Massless Scalar ◽  
Electromagnetic Current ◽  
Massless Scalar Field ◽  
Edge States ◽  
Chern Simons ◽  
London Equations

It is known that the 3D Chern–Simons interaction describes the scaling limit of a quantum Hall system and predicts edge currents in a sample with boundary, the currents generating a chiral U(1) Kac-Moody algebra. It is no doubt also recognized that, in a somewhat similar way, the 4D BF interaction (with B a two-form, dB the dual *j of the electromagnetic current, and F the electromagnetic field form) describes the scaling limit of a superconductor. We show in this paper that there are edge excitations in this model as well for manifolds with boundaries. They are the modes of a scalar field with invariance under the group of diffeomorphisms (diffeos) of the bounding spatial two-manifold. Not all diffeos of this group seem implementable by operators in quantum theory, the implementable group being a subgroup of volume-preserving diffeos. The BF system in this manner can lead to the w1+∞ algebra and its variants. Lagrangians for fields on the bounding manifold which account for the edge observables on quantization are also presented. They are the analogs of the (1+1)-dimensional massless scalar field Lagrangian describing the edge modes of an Abelian Chern-Simons theory with a disk as the spatial manifold. We argue that the addition of “Maxwell” terms constructed from F∧*F and dB∧*dB does not affect the edge states, and that the augmented Lagrangian has an infinite number of conserved charges—the aforementioned scalar field modes—localized at the edges. This Lagrangian is known to describe London equations and a massive vector field. A (3+1)-dimensional generalization of the Hall effect involving vortices coupled to B is also proposed.

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