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192 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 ...
3
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0answers
601 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 ...
3
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0answers
191 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, ...
3
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2answers
123 views

Numerical Tools to find Braiding Statistics of Quasiparticles

While certain classes of systems that exhibit topological order can be solved exactly (such as the Toric Code, Abelian FQH Edges, etc.) there also exist systems (think of perturbed versions of the ...
2
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1answer
238 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 ...
2
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2answers
138 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 ...
2
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2answers
321 views

Why bulk states in quantum hall effect do not contribute to electric conductivity

Most reviews and textbooks explain quantum hall effect as insulating bulk states and conducting edge states, as is shown in the following picture. My question is: why bulk states are insulating in ...
2
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1answer
242 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}) ...
2
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1answer
102 views

Why Integer Quantum Hall Effect (IQHE) can only happen in even dimensions?

I read that Integer Quantum Hall Effect (IQHE) can only exist in even dimensions, while Quantum Spin Hall Effect (QSHE) can be generalized to 3D (or rather any dimensions?). Does anyone have a ...
2
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1answer
213 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} ...
2
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1answer
641 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 ...
2
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1answer
416 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 ...
2
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1answer
751 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 = ...
2
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1answer
76 views

Entanglement between the electrons in the Laughlin wave function

Consider the $1/3$-Laughlin wave function $$ \Psi \propto \exp \left(-\sum_i |z_i|^2 \right) \prod_{1\leq i<j\leq N} (z_i-z_j)^3 . $$ It cannot be written in the form of a Slater determinant, ...
2
votes
1answer
227 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 ...
2
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0answers
46 views

Relation between Berry phase and degeneracies, the example of Hall effect in graphene

In principle, the Berry-curvature can be related to the degeneracy of some underlying energy levels, using the adiabatic picture and expanding the Berry's expression in the language of instantaneous ...
2
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0answers
48 views

Pair correlation function of the QHE “plasma”

I am trying to teach myself the theory of quantum Hall effect, and realized that I can not reproduce a basic textbook result. Let me closely follow Girvin's Les Houches lectures ...
2
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0answers
70 views

properties of p-wave superconductors in a self consistent calculation

2D p+ip superconductors have zero energy mid-gap modes localized at the boundaries as well as in the vortex cores as pointed out in several places such as Read, Green and Ivanov. The modes result in ...
2
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1answer
58 views

does Hall plateus require the existence of impurity in the sample?

While studying Hall conductivity with The Qantum Hall effect written by S.M.Girvin, I read a sentence "We have shown that the random impurity potential(and by implication Anderson localization) ...
2
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0answers
105 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 ...
2
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0answers
24 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, ...
2
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0answers
297 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
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0answers
50 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.
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0answers
293 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?
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2answers
122 views

Anyonic braiding statistics from density matrix renormalization group (DMRG) simulations

How does the ground state energy of the system change when we braid two anyons? Can the braiding of anyons be simulated with a computational method such as the density matrix renormalization group, ...
1
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1answer
371 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 ...
1
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1answer
47 views

Elementary question about the quantization of Hall conductivity

In the literature I read that the Hall conductivity is quantized because the Hall conductivity is actually the winding number associated with the mapping from the brillouin zone (a torus) to the space ...
1
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1answer
145 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 ...
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1answer
75 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 $B = 0$, ...
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1answer
109 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 ...
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1answer
77 views

Wavefunction for Anti-Pfaffian state

What is the most general form of a wavefunction for anti-Pfaffian in variables $\{z_i\}$ which represent the positions of electrons on a two dimensional plane?
1
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1answer
127 views

why does Laughlin wave function have a relative angular momentum no less than n

The textbooks say, the relative angular momentum of any two particles i and j should be no less than n, n is the power of (zi-zj)^n in the equation below I don't see this is an obvious argument. ...
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1answer
401 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 ...
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1answer
511 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, ...
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1answer
159 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 ...
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1answer
231 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 ...
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2answers
206 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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1answer
171 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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0answers
35 views

How to write Fractional Quantum Hall States with Symmetric Polynomials?

Is there a link between Fractional Quantum Hall States and Symmetric Polynomials. In papers of Xiao Gang Wen [1], [2] work out a few examples: $ \Phi_{1/2} = \prod_{i < j} (z_i - z_j)^2$ is the ...
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0answers
23 views

Intersection of $\rho_{xx}$ and $\rho_{xy}$ in Drude magnetotransport

Okay, so I've recently been working through the rather elementary derivation of the Hall effect in a 2 dimensional electron gas, using the Drude model. The idea is that with an E field in the x ...
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1answer
35 views

Neutralizing Background and Fractional Quantum Hall ground state

The idealized many-body Hamiltonian describing FQH is given by $$ H = \sum_i \left\{\frac{[\vec{p}_i -e/c \vec{A}(\vec{r}_i)]^2}{2m}+V(\vec{r}_i)\right\} + \frac{1}{2}\sum_{i\neq j} ...
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0answers
111 views

Quadratic Casimir Operator of $SO(5)$ [closed]

In the article A Four Dimensional Generalization of the Quantum Hall Effect, arXiv:cond-mat/0110572, by Zhang and Hu Quadratic Casimir operator for $SO(5)$ is given as $$p^2/2+q^2/2+2p+q .$$ When ...
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0answers
79 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 ...
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0answers
54 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}:= ...
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0answers
130 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 ...
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0answers
90 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 ...
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0answers
377 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 ...
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1answer
75 views

Fractional quantum Hall effect [duplicate]

Can someone explain the fractional quantum Hall effect in layman's terms, I'm having some difficulty understanding it?
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1answer
58 views

Elementary introduction to (quantum) hall effect

Where can I find an elementary introduction to classical and quantum hall effect? Only physics I know is some basic quantum mechanics, EM and statistical physics. My goal eventually is to understand ...
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1answer
135 views

Problem with quantum Hall effect and Berry curvature

I am having trouble proving that the Hall conductivity is equal to the integral over the Berry curvature in momentum space. In the TKNN (1982) paper, using the Kubo formula $$ \sigma_{xy} = \frac{ ...