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How to confirm experimentally the effect of momentum space Berry curvature in solids?

I'm studying spin-orbit coupling and Berry curvature effects, especially on the spin Hall effect. However, Table 3 in a review paper http://journals.aps.org/rmp/abstract/10.1103/RevModPhys.87.1213 ...
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42 views

Is integer quantum hall state long range entangled state or short range entangled?

I am reading about short range and long range entanglement. I know that topological insulator is short range entangled (SRE), STP state as we can disentangle it by breaking the symmetry using magnetic ...
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1answer
41 views

Connection between fractional charge and Schrodinger's cat

In the FQHE, it is said that one electron splits into three 1/3-charged entities. Is it like the Schrodinger cat?
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73 views

Finding explicit unimodular transformations for Chern-Simons K-matrices

An invertible, symmetric matrix with integer entries, $K$, that encodes the braiding and statistics of an Abelian topologically ordered state, is equivalent to another such matrix, $K'$, if there ...
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14 views

Measurement of Quantum Hall Effect

I'm somewhat confused about the original measurement of the QHE in a Si-MOSFET, which might stem from my not understanding MOSFETs very well. In their measurement, von Klitzing et al. measure the ...
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1answer
40 views

What is the Single Mode Approximation?

When Girvin and co-workers solved the excited collective modes called magneto-rotons in Fractional Quantum Hall liquids, they used something called the Single Mode Approximation (SMA). My question is: ...
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25 views

Quantum Hall effect in a Corbino disk

I'm a little bit confused about the Quantum Hall effect. I follow a course in condensed matter physics and the Quantum Hall effect is seen as the mother of all effects in condensed matter physics ...
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33 views

Simplify $K$-matrix

2+1D Abelian topologically ordered states are believed to be described by multicomponent $U(1)$ Chern-Simons theories, with Lagrangian \begin{equation} \mathcal{L}=\frac{K_{IJ}}{4\pi}\epsilon^{\mu\nu\...
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42 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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10 views

Temperature dependence of phase transition in Quantum Hall Effect

Most phase transitions have a distinct critical temperature, depending on the parameters of the system. For example, the critical temperature of Bose-Einstein condensation depends on the particle ...
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1answer
94 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 ...
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1answer
57 views

Relation between a change in the topological invariant and the closure of the gap

I would like to understand the relation between a change of the topological invariant (e.g. when the Chern number changes from 1 to 2) and the closure of the gap of a condensed matter system. I know ...
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1answer
57 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 ...
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24 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
95 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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93 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
64 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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50 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 (http://arxiv.org/abs/...
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1answer
115 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 hand-...
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1answer
37 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} \frac{e^2}{|\vec{r}...
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1answer
83 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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70 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
89 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} H=\frac{k_x^2-k_y^2}{m}\sigma_x+\...
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1answer
52 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
63 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
132 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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83 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
419 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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1answer
129 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
138 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{ ie^...
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1answer
59 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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1answer
79 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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83 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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99 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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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 ...
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2answers
131 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
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-...
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1answer
62 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
100 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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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 ...
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1answer
681 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 t_{ij}e^{iqA|i-j|}...
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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/...
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163 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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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 ...
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1answer
95 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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288 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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25 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
223 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
277 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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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\...