The tag has no usage guidance.

learn more… | top users | synonyms

6
votes
1answer
375 views

Quantum Hall Effect and Edge States

In quantum hall effect we measure the hall conductance (in transverse direction) which is quantized. My question how do they take care of the edge states that are in the longitudinal side?
3
votes
2answers
132 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 ...
5
votes
1answer
689 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|}...
12
votes
1answer
356 views

How to understand topological order at finite temperature?

I have heard that in 2+1D, there are no topological order in finite temperature. Topological entanglement entropy $\gamma$ is zero except in zero temperature. However, we still observe some features ...
3
votes
1answer
282 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 ...
0
votes
0answers
17 views

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 ...
3
votes
0answers
45 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 ...
0
votes
1answer
42 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?
12
votes
1answer
291 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. ...
4
votes
1answer
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 ...
0
votes
0answers
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 ...
1
vote
1answer
43 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: ...
3
votes
1answer
96 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 ...
17
votes
3answers
3k views

Equivalence of canonical quantization and path integral quantization

Consider the real scalar field $\phi(x,t)$ on 1+1 dimensional space-time with some action, for instance $$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t \...
0
votes
0answers
26 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 ...
0
votes
0answers
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\...
1
vote
0answers
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 ...
0
votes
0answers
11 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 ...
4
votes
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, ...
1
vote
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 ...
2
votes
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) ...
5
votes
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 ...
6
votes
2answers
612 views

A simple conjecture on the Chern number of a 2-level Hamiltonian $H(\mathbf{k})$?

For example, let's consider a quadratic fermionic Hamiltonian on a 2D lattice with translation symmetry, and assume that the Fourier transformed Hamiltonian is described by a $2\times2$ Hermitian ...
1
vote
0answers
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 ...
5
votes
1answer
102 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 ...
2
votes
0answers
85 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 ...
0
votes
0answers
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? ...
0
votes
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 ...
2
votes
0answers
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/...
2
votes
1answer
119 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-...
1
vote
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}...
0
votes
1answer
90 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+\...
0
votes
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, ...
1
vote
1answer
84 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?
5
votes
2answers
1k 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 ...
0
votes
0answers
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 ...
1
vote
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. ...
2
votes
0answers
301 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?
0
votes
1answer
64 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 ...
4
votes
1answer
2k 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 x-...
2
votes
2answers
429 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 ...
5
votes
1answer
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, ...
0
votes
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^...
5
votes
1answer
228 views

Zumino's consistent and covariant anomalies - applied to quantum hall?

What is the `physical' meaning of consistent anomalies and covariant anomalies? Perhaps a good Reference is: Consistent and covariant anomalies in gauge and gravitational theories - William A. ...
10
votes
1answer
453 views

Hall conductivity from Kubo: Bulk or edge?

Using the Kubo formula, Thouless, Kohmoto, Nightingale, and den Nijs (TKNN, PRL 49 405-408 (1982)), proved that upon summing all the contributions of the filled states of an insulator, the Hall ...
0
votes
1answer
60 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 ...
0
votes
1answer
80 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?
0
votes
2answers
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 ...
1
vote
2answers
132 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, ...
15
votes
2answers
3k views

Why are there chiral edge states in the quantum hall effect?

The most popular explanation for the existence of chiral edge states is probably the following: in a magnetic field, electrons move in cyclotron orbits, and such such cyclotron orbits ensure electrons ...