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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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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Edge modes due to Dirac fermion with sign-flipping mass $m(y)$

I'm considering a single massive Dirac fermion in 2D with Hamiltonian $$H = p_x \sigma_x + p_y \sigma_y + m(y) \sigma_z$$ with $m(y) =\begin{cases} -1 & y\to-\infty \\ 1 & y\to \infty\end{...
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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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66 views

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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Integer Quantum Hall effect, potential due to edge states

I'm confused about the edge state formalism in the IQHE. In many literatures (for example in D.Tong lecture notes), I saw the approach that one can model the edge states by a random potential $V(x)$ ($...
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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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51 views

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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66 views

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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Projection operator (relative angular momentum) in FQHE Toy hamiltonian

I am working on Fractional Quantum Hall Effect and reading these lecture notes http://www.damtp.cam.ac.uk/user/tong/qhe/qhe.pdf. As all others sources I have found, none of them precisely define the ...
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Dynamical properties of Laughlin states

I have been studying the theory of fractional quantum Hall liquids in Xiao-Gang Wen's book "Quantum field theory of many-body systems" and at some point I came across problem 7.3.2. which goes as ...
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Anomalies on boundary and bulk physics

Few times I faced with such statements: The gravitational anomaly of the 1+1d boundary system is known to be proportional to the thermal Hall conductivity of the 2+1 dimensional bulk How ...
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Is there an AC version of the Quantum Hall Effect?

The quantum Hall effect has the well-known signature of plateaus in the Hall conductivity $\sigma_{xy}=n e^2/h$ for integer (or rational) n. This quantization is extremely precise, and can go up to ...
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How can the localization property of the edge mode in topological insulator/quantum hall system be manifested through the effective action?

To be more specific, we can write down the Chern-Simons term from coupling the system to EM to describe the 2d quantum hall system and its derivative respect to the EM field gives the current. How can ...
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What's the relation between quanutm hall effect and topological insulator state?

In a recent PRX paper(https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.011050), I see that in 45nm and 50nm-thick Cd3As2 films, they find quantum hall effect and say that this is because of ...
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Why in quantum hall effect longitudinal resistance and conductivity can be simultaneously zero?

Why in quantum hall effect longitudinal resistance and conductivity can be simultaneously zero? I am puzzled about it. What's the physics meaning of it?
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Hall conductance units and physical intuition

In the quantum hall effect state, electrons in the bulk are doing cyclotronic orbits, and electrons on the edge are going around the sample's edge. The cyclotronic electrons are all in the same ...
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Time reversal of Hall conductivity

In general, what is the time-reversal of Hall conductivity $\sigma_{xy}(q,\omega)$? Is it $\sigma_{yx}^*(-q,\omega)$? Is it possible to derive it from Kubo formula $$\sigma_{xy}(q,\omega)=\frac{1}{\...
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How to calculate $\sigma_{xx}$ in lattice model?

It is known that one can find the Hall conductivity $\sigma_{xy}$ from a lattice model (in a magnetic field, say) using the TKNN formula (PRL 49 405-408 (1982)), i.e. by summing the Chern numbers for ...
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Wavefunction phase winding numbers

Consider the quantum hall effect inside a lattice. The Hamiltonian of a single particle of mass $m$ and charge $q = -e$ in an EM field with a vector potential $\mathbf{A}$ and periodic scalar ...
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Calculating the voltage between contacts on edge of quantum Hall system

Suppose we have a two dimensional electron gas, and that the sample has an arbitrary shape. On the edge, we have four contacts, as shown in the figure. Suppose that this is a quantized Hall system, ...
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Is there SSB in IQHE?

The Wikipedia page on FQHE mentions that the discovery of FQH states is significant partly because it shows the limits of Landau's symmetry breaking theory, since different FQH states all have the ...
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Why gapped systems are called incompressible?

I study quantum Hall systems and I haven't studied Fermi liquid theory yet. But I understand the concept of having gap or being gapless. But why do we use the term incompressibility to correspond the ...
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Please explain Integer Quantum Hall effect graph

What are the green spikes in the graph? Are they the energies associated with each quantized Landau level? I am not sure I understand this properly
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I am trying to integrate the Berry curvature of Dirac Semimetal to obtain anomalous hall conductivity

$$\Omega_{ij}(k)^{\pm} = \frac{v^2cos(\theta)\left(b\pm\frac{vk_z^2}{\sqrt{k_y^2\sin^2(\theta) +k_z^2}}\right)}{4\left(v^2k_x^2+v^2k_y^2cos^2(\theta)+\left( b\pm v\sqrt{k_y^2\sin^2(\theta) +k_z^2}\...
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If I attach two leads at the edge of a quantum hall system, can I get the current without adding voltage difference between the two leads?

In a 2-dimension quantum hall system, there always exist the chiral edge state in one edge. The current of the edge state is always in one direction, e.g $v_x>0$. In this case, if I attach a ...
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Is there spatial separation between quantum hall edge channels if there are more than one?

In 2-d electron systems, for example, when a piece of graphene is tuned to N=2 quantum hall state, the hall conductance should be $6e^2/h$. So there must be more than one edge channels? My question is,...
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2D electron system: delta function impurity and principal value integral

This question refers primarily to this paper by R. Prange. The author considers a $2D$ electron system with a single impurity modeled as a $\delta$ function. The end goal is to show that when the ...
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Wiedemann-Franz law generalized to quantum Hall effects in electronic systems

Wiedemann-Franz law states a relation in a conductor between the thermal and electric conductivities by their ratio as $\kappa/\sigma=LT$ where $T$ is the temperature and $L$ is the Lorenz number ...
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Current in linear combination of landau levels

I’m working through Girvin’s Quantum Hall Effect notes (https://arxiv.org/abs/cond-mat/9907002) And I came across the following problem: It is interesting to note that the exact eigenstates in the ...
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Berry curvature from spherical polar coordinates to Cartesian coordinates

Let us consider the typical example of calculating the Berry phase: a spin in a magnetic field. We start with the Hamiltonian $H=-\textbf{B} \cdot \boldsymbol{\sigma} + B$ where $\textbf{B}$ is the ...
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How to differentiate b/w are lowest extended levels and highest extended levels in IQHE?

At low disorder there are three bands. Two side bands have one conducting state and the central band has two conducting state. I want to know that which states are lowest conducting states ?
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Where can I learn about the quantum Hall effect? [duplicate]

I am looking to learn more on the quantum Hall effect but fail to find it in any of my textbooks on statistical mechanics, quantum mechanics, or solid state physics (given I only have one of that). ...
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212 views

Plateaus in Quantum Hall effect

Why do the plateaus in the Quantum Hall Effect appear phenemenologically? Something to do with the 1D transport for the edge states?
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Good starting point for quantum Hall matrix models

I am a recent Masters in theoretical condensed matter physics and have experience in working on topological insulators and Weyl semimetals. I have also dabbled a bit in the fractional quantum Hall ...
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Degeneracy in Landau Levels

A subsection from "Landau Levels" from pg 21 from Lectures on Quantum Hall effect by David Tong. He shows and derives the energy of a charged particle in a planar surface under the action of a ...
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Projection into Lowest Landau Level and Fourier transform

I am studying Quantum Hall and therefore Laughlin wave functions and the Lowest Landau Level. States in the Lowest Landau Level have the form: $\phi_m(z,\bar{z}) \propto z^m exp( - z \bar{z} / 4 l^...
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Two definitions of current operator $J$ equivalent?

I am currently reading David Tong's lecture note on quantum Hall effect. In this note, the current operator $\mathbf J$ is defined in two ways: We define $J= -e\dot{\mathbf x}= (-e/m)(\mathbf p+e\...
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Why one can observe Quantum Hall Effect in 3D Topological Insulators in an external magnetic field when TRS is broken?

In magnetotransport experiments scientists have observed the Quantum Hall effect in 3D topolgical insulators. Using a standard hall-bar geaometry in an external magnetic field they see plateaus in the ...
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What makes a topological insulator topological?

I understand that a topological insulator is one with an insulating bulk and conducting surface but I don't understand why or how the topological part comes into it. All of the resources I've found ...

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