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3
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1answer
588 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?
4
votes
1answer
959 views

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 ...
2
votes
1answer
206 views

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}) ...
3
votes
0answers
137 views

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 ...
2
votes
1answer
265 views

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 ...
4
votes
0answers
747 views

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 ...
3
votes
1answer
686 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?
1
vote
2answers
178 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 $\hat{x}$ ...
1
vote
1answer
100 views

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 ...
19
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5answers
2k views

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 ...
2
votes
0answers
432 views

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 ...
2
votes
1answer
190 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 ...
4
votes
1answer
284 views

Edge channels in Quantum Hall effect

Why is the value of Hall conductance directly proportional to the number of edge channels in the sample?
5
votes
1answer
214 views

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?
3
votes
0answers
166 views

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, ...
2
votes
1answer
219 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 ...
1
vote
1answer
187 views

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 ...
3
votes
1answer
188 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 ...
15
votes
4answers
2k views

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 ...
18
votes
2answers
452 views

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 ...
5
votes
1answer
231 views

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 ...
2
votes
0answers
239 views

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?
1
vote
1answer
146 views

Pair correlation function for a inhomogeneous Laughlin droplet

Pair correlation function for the usual Laughlin droplet is defined as $g(\vec{r})$: $$\rho_0 g(\vec{r})=\frac{1}{N}\langle\sum_i^N \sum_{j \neq i}^N \delta(\vec{r}-\vec{r_i}+\vec{r_j})\rangle$$, ...
2
votes
1answer
625 views

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 = ...
1
vote
1answer
298 views

“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 ...
8
votes
1answer
288 views

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 ...