scholarly journals Edge States and Entanglement Entropy

1997 ◽  
Vol 12 (03) ◽  
pp. 625-641 ◽  
Author(s):  
A. P. Balachandran ◽  
Arshad Momen ◽  
L. Chandar
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Coarse Graining ◽  
Gauge Fields ◽  
Edge States ◽  
Area Law

It is known that gauge fields defined on manifolds with spatial boundaries support states localized at the boundaries. In this paper, we demonstrate how coarse-graining over these states can lead to an entanglement entropy. In particular, we show that the entanglement entropy of the ground state for the quantum Hall effect on a disk exhibits an approximate "area" law.

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.

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 A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Ajit Coimbatore Balram
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Topological Structure ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=2+3/8, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.

scholarly journals Quantum parity Hall effect in Bernal-stacked trilayer graphene

2019 ◽  
Vol 116 (21) ◽  
pp. 10286-10290 ◽  
Author(s):  
Petr Stepanov ◽  
Yafis Barlas ◽  
Shi Che ◽  
Kevin Myhro ◽  
Greyson Voigt ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Exchange Interactions ◽  
Mirror Reflection ◽  
Edge States ◽  
State Variables ◽  
Coulomb Interactions ◽  
Spin Polarized ◽  
Trilayer Graphene

The quantum Hall effect has recently been generalized from transport of conserved charges to include transport of other approximately conserved-state variables, including spin and valley, via spin- or valley-polarized boundary states with different chiralities. Here, we report a class of quantum Hall effect in Bernal- or ABA-stacked trilayer graphene (TLG), the quantum parity Hall (QPH) effect, in which boundary channels are distinguished by even or odd parity under the system’s mirror reflection symmetry. At the charge neutrality point, the longitudinal conductance σxx is first quantized to 4e2/h at a small perpendicular magnetic field B⊥, establishing the presence of four edge channels. As B⊥ increases, σxx first decreases to 2e2/h, indicating spin-polarized counterpropagating edge states, and then, to approximately zero. These behaviors arise from level crossings between even- and odd-parity bulk Landau levels driven by exchange interactions with the underlying Fermi sea, which favor an ordinary insulator ground state in the strong B⊥ limit and a spin-polarized state at intermediate fields. The transitions between spin-polarized and -unpolarized states can be tuned by varying Zeeman energy. Our findings demonstrate a topological phase that is protected by a gate-controllable symmetry and sensitive to Coulomb interactions.

scholarly journals Separately contacted edge states: A spectroscopic tool for the investigation of the quantum Hall effect

2002 ◽  
Vol 65 (7) ◽  
Author(s):  
A. Würtz ◽  
R. Wildfeuer ◽  
A. Lorke ◽  
E. V. Deviatov ◽  
V. T. Dolgopolov
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Edge States ◽  
Spectroscopic Tool

scholarly journals INTERACTING QUANTUM TOPOLOGIES AND THE QUANTUM HALL EFFECT

2008 ◽  
Vol 23 (09) ◽  
pp. 1327-1336 ◽  
Author(s):  
A. P. BALACHANDRAN ◽  
KUMAR S. GUPTA ◽  
SEÇKIN KÜRKÇÜOǦLU
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Wave Functions ◽  
Gauge Fields ◽  
Representation Space ◽  
Covariant Formulation ◽  
Integer Quantum Hall Effect ◽  
Background Magnetic Field ◽  
Integer Quantum

The algebra of observables of planar electrons subject to a constant background magnetic field B is given by [Formula: see text], the product of two mutually commuting Moyal algebras. It describes the free Hamiltonian and the guiding center coordinates. We argue that [Formula: see text] itself furnishes a representation space for the actions of these two Moyal algebras, and suggest physical arguments for this choice of the representation space. We give the proper setup to couple the matter fields based on [Formula: see text] to electromagnetic fields which are described by the Abelian commutative gauge group [Formula: see text], i.e. gauge fields based on [Formula: see text]. This enables us to give a manifestly gauge covariant formulation of integer quantum Hall effect (IQHE). Thus, we can view IQHE as an elementary example of interacting quantum topologies, where matter and gauge fields based on algebras [Formula: see text] with different θ′ appear. Two-particle wave functions in this approach are based on [Formula: see text]. We find that the full symmetry group in IQHE, which is the semidirect product [Formula: see text] acts on this tensor product using the twisted coproduct Δθ. Consequently, as we show, many particle sectors of each Landau level have twisted statistics. As an example, we find the twisted two particle Laughlin wave functions.

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