Questions tagged [quantum-hall-effect]

Questions related to the quantum Hall effect (the quantisation of resistivity observed when a 2-dimensional electron gas system is subjected to a strong perpendicular magnetic field), as well as formulations of states, topological properties, and applications.

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39 views

Energy-Momentum Tensor for lagrangian with Chern Simons term

I am trying to find the energy-momentum tensor for the effective field theory that is used to describe the fractional quantum hall effect(Ref: [Zhang 1992][1]). The effective Lagrangian is \begin{...
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How does the generalized Haldane statistics give rise to the admissible configurations of fractional quantum Hall ground states?

It's often stated in fractional quantum Hall and fractional Chern insulator literature (see for example, https://journals.aps.org/prx/abstract/10.1103/PhysRevX.1.021014 and https://arxiv.org/pdf/1308....
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Can the word “doping” refer to controlling the Fermi energy via a gate field?

In the Integer Quantum Hall Effect with a fixed value of the perpendicular magnetic field, I believe that the filling factor $\nu$ which determines the Hall conductivity is experimentally controlled ...
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Calculating the Hall Conductance using the torus shape for the Magnetic Brillouin zone

Komoto's paper (ANNALS OF PHYSICS 160, 343-354 (1985)) on the calculation of the Hall conductance provides a clear discussion about how calculate the conductance using the torus shaped magnetic ...
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Which one is the correct representation of the Landau levels?

Sometimes the Landau levels in a finite 2D sample drawn as in the figure below: where the energy $E$ is graphed against the width $x$ of the sample in real space where $x=0$ and $x=W$ are the two ...
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What are Landau bands as opposed to Landau levels?

I think, I understand what Landau levels are. They are quantized harmonic oscillator levels that arise when a bunch on noninteracting electrons are subjected to an external magnetic field. Can ...
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Laughlin's Gauge Argument and Quantum Spin Hall Effect

I'm reading C.L. Kane and E.J. Mele's original paper of QSHE(DOI:https://doi.org/10.1103/PhysRevLett.95.226801). When proving the existence of edge state, they use the Laughlin's gauge argument which ...
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Cohesive energy of mixed phase of electron bubble phase in higher Landau levels

I am trying to understand the mixed-phase formed between 1-electron and 2-electron bubbles in the higher Landau levels by following this paper; https://arxiv.org/abs/cond-mat/0310383. To find the ...
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Boundary term for Chern-Simons action

As discussed in David Tong's lecture series on the edge modes in the quantum Hall effect (http://www.damtp.cam.ac.uk/user/tong/qhe.html) (page 203), varying the 2+1D Chern-Simons action yields: $$\...
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Current flow in incompressible electron fluid

So I understand that in the quantum Hall effect there are incompressible and compressible strips that form and the incompressible strips have an energy gap. Therefore incompressible strips can be ...
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How to prove the non-communtative relation of magnetic translation operator?

Consider the boson with charge +1 hopping in a square lattice in the xy plane with an uniform magnetic field B perpendicular to the xy plane. The magnetic field effect in hopping process can be ...
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Adiabatic charge transport in quantum mechanics

I am reading an article on adiabatic charge pumping. However, I am not completely certain of the origin of the first line of eq. (2.11) in this paper. Eq. (2.11) is \begin{equation} C = \frac{\rho}{L}...
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Is the angular momentum operator changed under electromagnetic field?

We know that the momentum operator is changed to canonical momentum $p-iq A(r)$ in the electromagnetic field, and this leads to the change of translation momentum operator in the lattice also. The ...
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Do I correctly understand the reason why the Hall resistivity in Quantum Hall Effect becomes larger as magnetic field increases?

I'm wondering whether I correctly understand the increase of the Hall resistivity rho_xy in Quantum Hall effect. As you can see the graph, As magnetic field becomes much larger, the quantization of ...
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Haldane pseudopotential

When reading Prof. David Tong's notes on FQHE, I got a question regarding the Haldane pseudopotential. We have the unique analytic solution of the lowest Landau level of two particles with a potential ...
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Quantum spin Hall effect, spin accumulation and Time reversal breaking

Looking at the quantum spin Hall effect as two copies of the Haldane model for spin-less particles with opposite magnetic field, we can understand the spin transport in the same manner as in the ...
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A half-quantum vortex for spinful fermions is equivalent to a single-quantum vortex of spinless fermions? in a $p$-wave superconductor

Reference: "Non-abelian statistics of half-quantum vortices in p-wave superconductors" D. A. Ivanov Phys. Rev. Lett. 86, 268 (2001) https://doi.org/10.1103/PhysRevLett.86.268, journal ...
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About the $\sigma_{xy}$ in the integer quantum Hall effect (or quantum anomalous Hall effect)

We know that $\sigma_{xy}$ in the integer quantum Hall effect (or quantum anomalous Hall effect) can be calculated by the Berry curvature, but we also know that $\sigma_{xy}$ is calculated by the ...
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What affect longitudinal conductance but not hall conductance in semiconductors

Hi as a general question, what mechanisms (e.g. impurities) affect σxx but not as much σxy in a semiconductor system at low temperature with impurities. I know with electric field scattering induced ...
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Where do interactions enter the composite fermion theory in the fractional quantum Hall effect?

The question is, in short, where in the composite fermion argument are electron-electron interactions used? I know that interactions, namely Coulomb repulsion, between electrons are crucial in ...
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Anyon statistics in a lattice Moore-Read state

I'm trying to understand this paper1, in particular the remark after Eq. 26. Let me rephrase the problem. According to the paper, one can write the Berry phase as $$ \theta_B=i\oint_\Gamma\frac{1}{C}\...
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Quantum Hall effects with an additional uniform unit flux on a compact manifold

I have two questions: Let us imagine that we have an integer quantum Hall system with electric Hall conductance as $\sigma_\text{H}$ on a two-dimensional (spatial) torus with size $L_1\times L_2$. If ...
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References on what kind of order does the integer quantum Hall effect exhibit

I'm looking for references to understand how exactly does the integer quantum Hall effect (IQHE) escapes Landau's symmetry breaking description. Any recommendations would be appreciated, thanks!
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Anomalous Hall Effect Saturation Field with Berry Curvature

Whenever you see anomalous Hall effect resistivity/conductivity vs. external magnetic field curves, there is always some low-field part with a greater slope that changes to a lesser slope at some ...
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Why is the Quantum Hall Effect insulating when the localized states below the extended states are populated?

In Tong's notes about the Quantum Hall effect (http://www.damtp.cam.ac.uk/user/tong/qhe/qhe.pdf), he talks on page 50 about localized and extended states, and that the disorder is what makes the QHE ...
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Difference between “ordinary” quantum Hall effect and quantum anomalous Hall effect

I am reading a review article on Weyl semimetal by Burkov where he writes, top of page 5: A 3D quantum anomalous Hall insulator may be obtained by making a stack of 2D quantum Hall insulators [Ref. ...
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Integer Quantum Hall Effect: Corbino Ring Derivation

Why are we allowed to consider adding extra flux to the system? When we measure the hall resistance, we don't add such a flux. Why is this not considered a different system? I will go through the ...
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Transverse current in a 2D topological pump?

Topological pumps (Thouless pumps) and Chern insulators are often brought up in the same context, as they both result in quantized transport, and feature a certain robustness (they are 'topologically ...
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Factor of half in the braiding statistics of Chern-Simons theory

My question is about the factor of $1/2$ discrepancy in the braiding phase of quasiparticles, from what one would naively expect. Why should it be that there is a certain flux at the location of each ...
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35 views

What is the fractal dimension of the Cantor sets appearing in the Hofstadter butterfly

It is well known that the spectrum of Bloch electrons in a magnetic field is given by the Hofstadter butterfly. Since Hofstadter's own 1976 paper it is believed that, when the flux per plaquette (in ...
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Why harmonic oscillator levels for noninteracting electrons in 2D in an applied magnetic field?

Classically, a system of noninteracting electrons restricted to move in 2D will execute circular motion in an external magnetic field $\perp$ to the plane. But in quantum analysis, the same ...
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Noninteracting electrons in 2D in presence of a magnetic field and a periodic potential?

Equally spaced discrete harmonic oscillator levels, called Landau levels, are obtained for noninteracting electrons in 2D in presence of a magnetic field applied perpendicular to the plane. The Landau ...
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Intuition on why quantum hall effect?

I think I can understand hall effect using the right hand rule, the electrons experience lorentz force in the presence of a magnetic field but I don't get why quantum? I saw the resistivity looks ...
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Calculating the Hamiltonain kernel of a Haldane model in zigzag graphene

Currently I'm learning how to calculate the edge effect of a material. I try to calculate edge state of a Haldane model in a zigzag graphene. Since Im writing in a second quantisation basis, each ...
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Chern-Simons theory for FQHE

Recently I have read something about describing FQHE within chern simons field theories. According to Atland's text book,Condensed matter field theory, one can map interacting fermions to composite ...
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Intuitive Understanding of Mathematical Proof of Quantum Hall

I'm curious about the proof of the existence of a quantum Hall effect, which has recently come up because of the 40$^{\mathrm{th}}$ anniversary of the QHE problem. In particular, the paper says [The ...
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Two-band system with Hall effect formalism

Suppose we have a two level system \begin{equation} \label{HGE2D+EFirstorder} H=H_{0} \left( \vec{k}-\dfrac{e}{2} \vec{A} \right) \simeq H_{0} (\vec{k})+\frac{e}{h} \sum_{j=x,y,z} \left( \nabla d_{j}\...
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The Quantum Hall Effect

In the integral quantum Hall effect, one has that in regions where $R_{xy}$ (the Hall resistance) is a constant, $R_{xx}$ surprisingly goes to zero. Why does that happen? Do impurities in the material ...
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Interacting helical edge state and scattering process

Imagine if you have a 2D topological insulator system where you can bring together the helical edge states from the opposite boundaries to interact (say, by a voltage gate or by a narrow constriction)....
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How to know a semiconductor is p type or n type from hall effect calculations? [closed]

Using the hall effect calculations how can we determine a semiconductor is p type or n type
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What is Hall Conductance?

What is Hall Conductance in the Quantum Anomalous Hall Effect? I can't seem to find anything online about what it actually is, although there is a lot about what to do with it.
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Difference between thermal hall and phonon hall effect

I know of thermal hall effect which refers to a charge-neutral excitations exhibit hall effect that transport heat: for example, a heat current along x-direction generates a temperature gradient along ...
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Question about the proof of different contractions for the effective Brillouin zone differing by an even Chern number

I am reading Moore and Balents'paper (DOI: 10.1103/PhysRevB.75.121306) which proves the Z2 invariant is the parity of the Chern number for the effective Brillouin zone. I am confused about some ...
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The quantum hall effect and Hofstadter's butterfly spectrum

What is the connection between the quantum Hall effect and the Hofstadter's butterfly spectrum? I mean, can I understand something about the quantum Hall effect in the Hofstadter's butterfly spectrum?
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Are charged excitation excited states ? - FQHE

I have been reading tong's lectures notes, as well as Prange / Girvin book and Laughlin nobel's lecture. I still can't figure it out. What is the laughlin ground state off ? I understand there are ...
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Integer Quantum Hall effect, scattering

I'm confused about the scattering mechanism in the Integer Quantum Hall effect. I often read the statement, that at a hall plateaux, the particles can't scatter, since an integer number of Hall ...
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Integer Quantum Hall effect, conductivity & edge states

I'm confused about the conductivity and the edge states in the IQHE. On the plateaux, we zero the longitudinal conductivity and resistivity, right? So is it really true, that on the plateaux, there is ...
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Is there any heat loss in chiral edge channels of topological insulators?

If we are working with nontrivial topological insulator with broken time reversal symmetry then we can expect that we have some chiral edge states. Chiral states have the property that the current can ...
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Chern-Simons term in Coulomb or radiation gauge

In some of the literature (for example, below Eq. (A3) of this paper), the following is claimed to be the Chern-Simons term in the Coulomb gauge: \begin{equation} 2a_0(\partial_1a_2-\partial_2a_1) \...
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One-form current in 3d QED

3d QED in IR can be described in terms of dual scalar field $\varphi$ have trivially conserved current with two indices, associated with U(1) one-form symmetry: $$ J_{\mu\nu} = \epsilon_{\mu\nu\rho}\...

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