The quantum-hall-effect tag has no wiki summary.
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Why is planar geometry preferred to observe ordinary Hall effect?
In the Physics Today article by Avron et.al. "A Topological Look at the Quantum Hall Effect" Physics Today (2003) it is suggested that to observe ordinary Hall effect, planar geometry is preferred to ...
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How to understand topological order at finite temperature?
I have heard that in 2+1D, there are no topological order in finite temperature. Topological entanglement entropy $\gamma$ is zero except in zero temperature. However, we still observe some features ...
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Whis is the difference between charge fractionalization in 1D and 2D?
Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations.
But as I can see, there are some differences: the ground state of Polyacetelene breaks translational ...
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Laughlin state unique ground state?
In the FQHE, one typically encounters the statement that the $\nu = 1/3$ Laughlin state is a unique exact ground state of a model Hamiltonian where the Haldane pseudopotentials $V_1 \neq 0$ and $V_m = ...
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Simple uncertaintly calculation of the center coordinates of a Landau Level
I am reading the following review paper on the Quantum Hall Effect. I am sorry for the extremely stupid question, but I have been stuck on this very easy equation for long.
In equation 2.39, the ...
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Calculation of the quantized Hall coefficient in the Integral Quantum Hall Effect
I have been reading about the QHE over the past couple of days. I am facing difficulty understanding a calculation in this review.
www.nimt.or.th/nimt/upload/linkfile/sys-metrology-248-434.pdf
In ...
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Why FQHE need a lower energy state?
There are a lot papers explaining why Laughlin's wavefunction are energetically favorable, but seldom explain why a lower energy state could explain the plateau at $\nu=1/3$. I met at several places ...
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Topological Charge. What is it Physically?
I have seen the term topological charge defined in an abstract mathematical way as a essentially a labeling scheme for particles which follows certain rules. However I am left guessing when trying to ...
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1answer
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Rewriting Creation and Annihilation Operators
I am playing with the Landau Level problem and Algebraic solutions to it. I am given
$$a=\frac{l_{b}}{\sqrt{2}\hbar}(\pi_{x}-i\pi_{y}) ...
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161 views
Zero Resistance in Quantum Hall Effect and Superconductivity
What is the difference between the zero resistance of $R_{xx}$ in integer quantum Hall effect and the zero resistance in superconductivity?
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Why quantum hall effect has chiral edge state?
The most popular explaination may be the following: in magnetic field, electrons move in cycolotron orbits, such cycolotron orbits ensure electrons to move in one direction at the edge. That is why ...
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First Chern number, monoples and quantum Hall states
The first Chern number $\cal C$ is known to be related to various physical objects.
Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to ...
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Questions about Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper
I am reading the famous and concise Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405–408 (1982), where I ...
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Equivilence of One Flux Quantum and Zero Flux
In Ady Stern's review of the Quantum Hall effect, he says of a quantum hall system "The spectrum at $\Phi = \Phi_0$ is the same as the spectrum at $\Phi = 0$..." Can someone explain why this is? It ...
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Flux quantization and AB effect and Laughlin's argument of IQHE
I have a question essentially the same with this one "Aharonov-Bohm Effect and Flux Quantization in superconductors" which is why we can say the flux is quantized in superconducting disk but not in AB ...
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guage invariance in Laughlin's argument
In Laughlin's gedanken experiment which aims to explain quantization of Hall conductance, one takes the adiabatic derivative of the Hamiltonian with respect to vector potential. Now it seems that it ...
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What is the Laughlin argument?
The fundamental question is
Why is Hall conductance quantized?
Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the ...
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Are Hall edge currents truly dissipationless?
Integer quantum Hall states has integer number of chiral edge current channels flowing around like supercurrent in a superconductor.
Are they truly dissipationless?
If so, what is the mechanism that ...
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1answer
318 views
Chern number in condensed matter physics
In mathematics, the Chern number is defined in terms of the Chern class of a manifold. What is the exact definition of Chern number in condensed matter physics, i.e. quantum hall system?
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Simple model of edge states for a two-dimensional topological insulator
Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features?
See e.g. the ...
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Isn't it incorrect for the minimal gauge coupling and related calculations in Prof. Ezawa's book on quantum Hall effect?
He is CORRECT. I use $\mathbf{B}=\left(0,0,B_{\perp}\right)$ and he use $\mathbf{B}=\left(0,0,-B_{\perp}\right)$. $B_{\perp}>0$.
Nov.28.2012
Basically I got mad with conventions.
1.Here is the ...
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1answer
110 views
What is the operator for the edge current of a fracional quantum Hall state?
The edge of a fractional quantum Hall state is a chiral conformal field theory. In the Laughlin case it corresponds to the chiral boson,
$$ S = \frac{1}{4\pi} \int dt dx ...
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Aharonov-Bohm Effect and Integer Quantum Hall Effect
What is the relationship between Aharonov-Bohm effect and Integer Quantum Hall effect?
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What is nonlocal resistance?
We are first taught to calculate local resistance, where current and voltage are on the same part of the material.
But many experiments measure nonlocal resistance, where current and voltage are ...
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1answer
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Edge channels in Quantum Hall effect
Why is the value of Hall conductance directly proportional to the number of edge channels in the sample?
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Curvature and edge state
If the boundary of quantum hall fluid has non-constant curvature, how will it affect the edge state which is usually described in chiral Luttinger fluid?
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Are the electrons in a quantum hall edge state entangled?
I am reading the paper on Quantum Energy Teleportation by Yusa, Izumida and Hotta(This article), and it seems that they are assuming that the quantum hall edge state is a quantum correlated state, ...
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177 views
Is Fractional quantum Hall effect proof that leptons are composite particles?
The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values. Should this be considered ...
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Is quantum Hall current density local? (${\bf j}({\bf r}) = \sigma_H {\bf \hat n \times E}({\bf r}) $)
The good old Ohm's law $${\bf j}({\bf r}) = \sigma_O {\bf E}({\bf r})$$
if translated into words would be "the local current density is proportional to a local electric field."
In a quantum Hall ...
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What is the mass of the emergent magnetic monopoles in spin ice and how is the mass of an emergent particle determined?
In solid state physics emergent particles are very common.
How one determines if they are gap-less excitations?
Do the defects in spin ice called magnetic monopoles have mass?
What is the mass of ...
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151 views
Laplacian of a delta function as an interaction potential for Laughlin state
I am reading Xiao-Gang Wen's paper "Pattern-of-zeros approach to Fractional quantum Hall states and a classification of symmetric polynomial of infinite variables", on page 8, he gives three ...
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2answers
128 views
Hall conductivity and edge response
The hall conductivity $\sigma_{xy}$ seems to reflect to some extent the response of a system in direction $\hat{y}$ to certain perturbation (electric field for example) restricted in $\hat{x}$ ...
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Is this a possible scenario for the teleportation of energy?
Ok, so I've been reading a paper (Here's the paper) published by a physicist named M. Hotta et al. recently and as far as I can tell with my limited understanding, the protocol for the teleportation ...
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The bijective correspondence between a symmetric polynomial and edge excitation of the fractional quantum hall droplet
I am recently reading Xiao-Gang Wen's paper (http://dao.mit.edu/~wen/pub/edgere.pdf) on edge excitation for fractional quantum hall effect. On page 25, he claimed that it is easy to show that there ...
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Analytic form of the normalization constant for Laughlin wavefunction
Is there any analytic form of the normalization constant for Laughlin wavefunction
$$\prod_{i < j} (z_i-z_j)^{1/\nu} e^{-\sum_i |z_i|^2/4}$$
where $\nu$ is the filling factor?
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1answer
115 views
Pair correlation function for a inhomogeneous Laughlin droplet
Pair correlation function for the usual Laughlin droplet is defined as $g(\vec{r})$:
$$\rho_0 g(\vec{r})=\frac{1}{N}\langle\sum_i^N \sum_{j \neq i}^N \delta(\vec{r}-\vec{r_i}+\vec{r_j})\rangle$$, ...
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type of Hall sensor conductor
For example, if I have Hall sensor, have can I determine type of Hall conductor material? I want to know is it an electron or is it just a hole.
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Edge theory of FQHE - Unable to produce Green's function from anticommutation relations and equation of motion?
I'm studying the edge theory of the fractional quantum Hall effect (FQHE) and I've stumbled on a peculiar contradiction concerning the bosonization procedure which I am unable to resolve. Help!
In ...
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How do you obtain the commutation relations at non-equal times (for the edge of a fractional quantum Hall state)?
The edge of a fractional quantum Hall state is an example of a chiral Luttinger liquid. Take, for the sake of simplicity, the edge of the Laughlin state. The Hamiltonian is:
$$H = ...
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“Classical” limit of Quantum Hall Effect
Imagine a partially filled $\nu=1$ state of the integer quantum Hall effect (IQHE). One way to think about it is to imagine a gas of electrons where each particle is locked to the lowest quantum state ...
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What is the energy functional for v=5/2 Moore-Read state?
I am trying to do some Monte Carlo simulations for Pfaffian state from Fractional Quantum Hall effect. I am wondering what is the energy functional for v=5/2 Moore-Read state?
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Quantum Hall effect for dummies
In the past few days I've become increasingly intrigued by the QHE, mainly thanks to very interesting questions and answers that have appeared here. Unfortunately, I am as of yet very confused by all ...
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Resistance of a two-dimensional sample
In this review of the QHE, Steve Girvin makes the following statement (bottom of pg. 6, beginning of Sec. 1.1.1):
As one learns in the study of scaling in the localization transition, resistivity ...
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Simple models that exhibit topological phase transitions
There are a number of physical systems with phases described by topologically protected invariants (fractional quantum Hall, topological insulators) but what are the simplest mathematical models that ...
