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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 ...
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16 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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47 views

Difference between $\nu=5/2$ quantum Hall state, chiral p-wave superconductor, He 3

I am interested in the relation between the following three phases of matter (in 2D): chiral $p$-wave superconductor (spineless $p_x + i p_y$ pairing) $\nu=5/2$ fractional quantum Hall state A-phase ...
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76 views

why Hall conductance quantized

When I am studying quantum Hall effect, the quantum Hall conductance can be represented by Green function $\left(\text{up to}\ \frac{e^2}{h}\large \right)$: I cannot understand why it is an integer? ...
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1answer
48 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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43 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 ...
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1answer
80 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 ...
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34 views

The exact derivation of spin current conductivity?

I'm reading the Universal Intrinsic Spin Hall effct(http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.92.126603).For the formula(9), I wonder how it comes from the original kubo formula. As[26] ...
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1answer
30 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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1answer
65 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?
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45 views

How do the compressible strips carry current in Quantum Hall effect?

I would be very grateful if anyone can answer this question on Quantum Hall effect According to most papers I have gone through, states at the fermi energy actually carry the current. The width of the ...
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1answer
57 views

Landau level for quadratic band touching in Dirac Hamiltonian

I wonder if there is anyone or any references that have solved the Landau level spectrum and eigenstates with respect to the following Hamiltonian: \begin{equation} ...
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1answer
43 views

incompressibility of fully filled Landau level

Suppose Landau level degeneracy is $10^9$, if we force to put ($10^9+1$) particles on the level, what extra energy will we gain? (ignore particles interactions) Like electron degeneracy pressure, ...
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1answer
55 views

Why is there longitudinal conductance in a partially-filled Landau level?

Suppose I consider an infinite, non-interacting (so no FQHE should happen) 2DEG in the magnetic field $\vec B=B\hat z$ with a non-integer filling factor, say 0.13 or whatever. Suppose I apply an ...
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1answer
117 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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54 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 ...
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2answers
188 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 ...
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92 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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1answer
114 views

Prove that Laughlin's 3-electron states are a complete set of states

In R. B. Laughlin's 1983 Physical Review B article, Quantized motion of three two-dimensional electrons in a strong magnetic field, Laughlin separates out the center of mass motion of the electrons, ...
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1answer
105 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{ ...
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1answer
42 views

How to implement the form of current density in a Hall Effect related calculation?

Please consider the following; Question. A rectangular plate of semiconducting material has dimensions 10mm x 4mm x 1mm. A current of 3 mA flows along the length and a Hall Voltage of 13.6 mV is ...
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2answers
69 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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75 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, ...
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2answers
82 views

Is the Hall coefficient a resistance?

The Hall coefficient is defined as this: $$R_H=\frac{E_y}{j_xB_z}.$$ Always as $R_H$. I am currious as to how to use this coefficient? Is it the y-direction resistance/resistivity (it is very close ...
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104 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 ...
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2answers
111 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, ...
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2answers
128 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 ...
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77 views

Can a conformal field theory with chiral central charge be gapped out?

Consider a 2-dimensional conformal field theory with nonzero chiral central charge (that is, the central charges of the holomorphic and antiholomorphic sectors are different.) I think that ...
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51 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) ...
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1answer
92 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 ...
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95 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 ...
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1answer
559 views

Peierls substitution vs minimal coupling

In the presence of vector potential (let's assume it's uniform), a tight-binding Hamiltonian will be changed according to the Peierls substitution: $$t_{ij}c_i^{\dagger}c_j \to ...
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104 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 ...
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133 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 ...
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72 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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1answer
93 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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226 views

Has anyone experimentally shown the quantized thermal hall conductivity in Quantum Hall systems?

For background: In a $D=2+1$ state with edge modes described by a chiral $( c_L \neq c_R )$ CFT there is a predicted thermal Hall conductance associated with the gravitational anomaly at the edge. ...
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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, ...
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1answer
190 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 ...
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1answer
229 views

Quasi-particle and quasi-hole excitations of Laughlin states and generalization of Laughlin states

The Laughlin wave function at filling fraction $\nu=\frac{1}{m}$ is \begin{equation} \Psi_m=\prod_{i<j}(z_i-z_j)^m e^{-\sum|z_i|^2/4l_B^2} \end{equation} It is claimed in section 7.2.3 of Wen's ...
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51 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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2answers
908 views

Why does the n=0 Landau level in graphene have half the degeneracy of the other levels?

I've looked through several papers that talk about the anomalous integer quantum Hall effect of graphene (such as http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.95.146801), and they all state ...
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2answers
114 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 ...
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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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123 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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1answer
310 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
256 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 ...
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1answer
194 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} ...
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333 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 ...
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331 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 ...