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3
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0answers
117 views

How are resonating valence bond (RVB) states related to fractional quantum Hall (FQH) states?

In Kalmeyer and Laughlin's paper, there is an argument made for a frustrated two-dimensional Heisenberg antiferromagnet on a triangular lattice that if one uses a FQH wavefunction for bosons to ...
2
votes
2answers
143 views

Classical Hall effect when current has neutral charge

Suppose I have a current of both negative and positive charges(I know that there is also current from only negative and only positive charges,I'm not confused) along an infinite wire of square cross-...
5
votes
1answer
102 views

Equivalence classes of mappings from $T^{2}$ to an arbitrary space $X$

I was reading the paper "Homotopy and quantization in condensed matter physics", by J.E Avron et al. ( http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.51.51). There they have classified the ...
3
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0answers
105 views

Monodromy, Holonomy and Braiding Phase

In quantum Hall effect, especially in the context of CFT description, these words come up often. I think I understand the braiding phase - as the phase gained by the wave function when a quasi ...
1
vote
1answer
538 views

How do the effects of semiconductor doping affect the Hall effect?

For instance, consider number 4 and 5 in the following sample: Using the right hand rule, B points downwards, conventional current points to the right (because of the 5V battery), and therefore, ...
2
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0answers
111 views

Explicit degeneracy in SPT phases

In the wikipedia article on symmetry protected topological phases the author states: If the boundary is a gapped degenerate state, the degeneracy may be caused by spontaneous symmetry breaking and/...
5
votes
1answer
143 views

Why can interactions be neglected for the Integer Quantum Hall effect?

Though the statement is made often, I've not seen any justification for neglecting electron-electron (Coulomb) interactions in the fully filled $\nu =1$ IQH state. I would highly appreciate if someone ...
3
votes
0answers
168 views

Relation between p+ip wave Superconductor and Moore-Read State

I am quite interested in the understanding of the relation between p_ip wave superconductor(SC) and the Moore-Read(MR) state. They share many similar properties, for example, p+ip SC has majorana as ...
3
votes
1answer
96 views

What would happen to the plateau in QHE under gradual heating ?

In quantum Hall effect (QHE), the plateau observed in $R_H$ (Hall resistance) appearing precisely at multiples of $e^2/h$ is a characteristic feature. It can be observed only at low temperatures. My ...
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0answers
81 views

Effective Theory of FQH Edge State

When I was learning Xiao-Gang Wen's paper about the edge theory of Fractional Quantum Hall(FQH) state, I had one question. The paper's link is as below:\ http://dao.mit.edu/~wen/pub/edgere.pdf As ...
2
votes
0answers
26 views

Why do I have spin splitting at 5 and 7 at the quantum hall effect?

I just learned something about the quantum hall effect, and was wondering about the spin splitting at a filling factor of 5 and 7, i.e. I have nearly equal sized plateaus for the filling factor of 2, ...
9
votes
2answers
2k views

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 ...
0
votes
1answer
227 views

Hall Effect p-type Germanium holes density

I had to do some experiments with a Hall Effect Apparatus of Leybolds with a p-doped Germanium plate, this is the datasheet (pdf). eq. (1) $U_H=R_H \frac{IB}{d}$ $U_H$ = Hall voltage $R_H$ = Hall ...
1
vote
0answers
55 views

Momentum conservation in the Fractional Quantum Hall Effect

Generically an Abelian Fractional Quantum Hall Systems is described by chiral scalar fields $\hat{\Phi}^{\ }_{i}(t,x)$ with $i=1,\ldots,N$ and a Hamiltonian of the form $ \hat{H}^{\ }_{0}:= \int\...
9
votes
1answer
2k views

What is parafermion in condensed matter physics?

Recently, parafermion becomes hot in condensed matter physics (1:Nature Communications, 4, 1348 (2013),[2]:Phys. Rev. X, 2, 041002 (2012), [3]:Phys. Rev. B, 86, 195126 (2012),[4]:Phys. Rev. B,87, ...
6
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1answer
677 views

Aharonov-Bohm Effect and Integer Quantum Hall Effect

What is the relationship between Aharonov-Bohm effect and Integer Quantum Hall effect?
1
vote
1answer
76 views

What is the quantum Hall resistance R_H as a function of magnetic field?

For the integer quantum Hall effect, the resistance $R_H = h/(ne^2)$, where $n$ is some integer. All of the graphs of $R_H$ as a function of magnetic field, $B$, that I've seen show that at $B = 0$, $...
1
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0answers
134 views

Equivalent Chern Simons Theories

This is a follow-up question to FQH Edge Theory as decoupled chiral bosons . The document that I will be refering to is http://dao.mit.edu/~wen/pub/toprev.pdf . On page 14 in Eq.(2.33) the author ...
1
vote
1answer
414 views

Significance of magnetic translation operator defined in fractional QHE's description

What is the significance of the magnetic translation operator used in describing the Fractional Quantum hall effect? I was following Anthony Leggett's lecture video in which he defines these operators ...
3
votes
1answer
181 views

Difference between Wigner crystal state and fractional quantum Hall (FQH) state

Wigner crystal and FQH effect are both due to strong electron-electron interaction under magnetic field. As we know, Landau's symmetry-breaking cannot be used to describe FQH state. But can it be used ...
3
votes
1answer
283 views

How to determine the orientation of the massive Dirac Hamiltonian?

In the calculation of the Chern number within a 2D lattice model, let's take the Haldane model for example, the Chern number$=\pm1$ has 2 contributions coming from 2 Dirac points described by $$h_1(\...
2
votes
1answer
220 views

FQH Edge Theory as decoupled chiral bosons

The action describing the edge theory of the Fractional Quantum Hall effect is given by \begin{equation} S = \frac{1}{4\pi} \int \mathrm{d}x \ \mathrm{d}t \left[ K_{IJ} \ \partial_{t}\phi_{RI} \...
6
votes
3answers
547 views

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 ...
3
votes
0answers
359 views

How is Laughlin's gauge argument explaining integer quantum hall effect(IQHE)?

It seems essential in Laughlin's gauge argument that the sample has to be cylindrical(or with similar toplogy), so that we can "thread" a thin solenoid through to control the gauge function on the ...
6
votes
1answer
356 views

Why Landau Level quantization is observed only in low temperature and strong magnetic field in real experiment?

I know that Quantum Hall Effect and Fractional Quantum Hall Effect origin from Landau Level quantization. In magnetic field, the energy of in-plane(plane perpendicular to magnetic field) degree of ...
2
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0answers
316 views

TKNN invariant changes due to continuous deformation of parameter space

Naively, I would assume that a topological invariant remains invariant under continuous deformations of whatever space the invariant belongs to. In the case of topological insulators, this space is ...
2
votes
1answer
672 views

Determining spectra of edge states numerically

Normally we write a Bloch Hamiltonian $H(\mathbf{k})$ for the bulk and determine the spectrum which gives us various bands i.e we basically obtain $E=E(\mathbf{k})$ for the bulk only. Also in the ...
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0answers
387 views

Gauge 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 ...
5
votes
1answer
223 views

What is the energy functional for $\nu=5/2$ 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 $\nu=5/2$ Moore-Read state?
1
vote
0answers
91 views

Conventions for Klein factors in bosonization of Quantum Hall edge states

I am not having much experience in the field of bosonization, hence the following question: In some papers (such as http://arxiv.org/pdf/cond-mat/9501007.pdf Eq. (6) ) a Quantum Hall edge is ...
4
votes
1answer
288 views

A naive question on the Quantum Hall Effect(QHE) and the confinement in gauge theory?

The non-interacting 2D lattice QH system is described by the Hamiltonian $H=\sum t_{ij}e^{iA_{ij}}c_i^\dagger c_j+H.c$ My confusion is: Does this imply that the $2D$ lattice QHE is described by the $...
7
votes
2answers
596 views

“Correlation energy” using the pair correlation function

In this paper on the Quantum Hall effect the authors refer to something called the correlation energy of electrons. It is defined at the top of page 5 as $E=\frac{n}{2}\int (g(r)-1)V(r)dA\ ,$ where $...
2
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0answers
52 views

What is the difference between hierarchy picture and composite Fermion in explaining FQHE

Are they equivalent? I came up this question because they both explain states beyond Loughlin state.
1
vote
1answer
146 views

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 ...
4
votes
1answer
179 views

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 ...
4
votes
1answer
187 views

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 ...
3
votes
2answers
166 views

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 ...
19
votes
2answers
3k views

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 ...
3
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0answers
177 views

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 = ...
1
vote
1answer
162 views

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 ...
4
votes
1answer
286 views

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 ...
3
votes
1answer
146 views

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 ...
3
votes
1answer
980 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
1k 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
247 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}) ~~~~~~~~\text{and}~~~~~~~~~a^{\dagger}=\frac{l_{b}}{\sqrt{2}\...
3
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0answers
196 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
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1answer
434 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 ...
3
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1answer
1k 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
207 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
110 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 ...