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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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A question regarding Coulomb sum in two dimension

The following arguments can be found in texts about Laughlin's wavefunction and theta function such as Laughlin's paper "Spin hamiltonian for which quantum hall wavefunction is exact". It is ...
fdsfsd sd's user avatar
4 votes
1 answer
111 views

Is QHE the only topological order up to 3D?

At the section II.C in this review paper about topological superconductors, the author states that The symmetry of the Hamiltonian plays a crucial role in determining the topology of the occupied ...
Guilherme Queiroz Venâncio's user avatar
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Chern-Simons theory: Connection between Thermal and Quantum Partition Function

I have been reading the Quantum Hall Effect from Prof. David Tong's notes. In the section on Chern-Simons theory, he describes the connection between the Thermal Partition Function and the Quantum ...
harshit_'s user avatar
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References for Bulk-Boundary correspondence

I have been reading the Quantum Hall Effect from Prof. David Tong's lecture notes. In the Edge Mode chapter, he talked about Bulk-Boundary correspondence where he reproduces the Laughlin wavefunctions....
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What is the meaning of the statistical gauge field in the fractional quantum Hall effect

I'm a grad student studying the fractional quantum Hall effect. To get started, I read chapter 9.5.1 of A. Altland and B. Simons' Condensed Matter Field Theory. They use the composite fermion (CF) ...
Steffen Bollmann's user avatar
4 votes
1 answer
279 views

Are the number of states available equal to the number of particles? [closed]

Let's say we have a 2d sea of electrons. The energy states of these electrons will be quantised because of some sort of boundary condition on the system, and therefore there are only an integer number ...
eli morhayim's user avatar
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35 views

Fermi Levels in the Quantum Hall Effect

What are Fermi levels in the context of 2-d electron fluids and specifically the Quantum Hall effect?
eli morhayim's user avatar
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10 views

How can we tell if we have ordinary or anomalous Hall conductivity?

Based on the Hall optical conductivity graph, how can we tell if we have ordinary or anomalous Hall conductivity?
Mohammad Mortezaei Nobahari's user avatar
1 vote
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Are hierarchal states/fractional exchange statistics equivalent in the FQHE?

There are several theories for the fractional quantum Hall effect. The last listed in the Wikipedia article are composite fermions, though these seem to be a subset of fractional exchange statistics: ...
programjames's user avatar
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What means imaginary and real parts of the optical Hall conductivity?

What is the meaning of the real and imaginary parts of the optical Hall conductivity and also the interpretation of the negative Hall conductivity?
Mohammad Mortezaei Nobahari's user avatar
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How should the charge carrier concentration be examined in the quantum Hall effect?

In the classical Hall effect, the charge carrier concentration is given by $n = \frac{1}{e R_{H}}$, where $e$ is the electron charge and $R_{H}$ the Hall coefficient, which is obtained from the slope ...
NeonGabu's user avatar
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Fractional filling of Laughlin wavefunction

I am not clear about the following argument why Laughlin wavefunctions have $1/m$ filling. The single-electron wavefunction in the zeroth Landau level is \begin{equation} \psi_{m}(z)\sim z^m e^{-|z|...
Ramal Afrose's user avatar
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Classical and quantum Hall effects

I am trying to understand the hall effects and have a few problems with them. So let's consider the classical Hall effect. We know that we consider a sample, where the electrons flow, we apply the ...
blahblah's user avatar
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Is IQHE a degenerate case of FQHE? What is the role of topological orders?

(As suggested by Tobias, I shall indicate that I will write "IQHE" for "Integer quantum Hall effect" and "FQHE" for "Fractional quantum Hall effect" below.) I ...
Yuezhao Li's user avatar
2 votes
1 answer
162 views

Why does an electric field not blur together the Landau levels?

When a crossed electric field $E$ is applied on top of a magnetic field $B$, one can show that the degeneracy of the Landau levels is lifted, such as in these David Tong notes. Intuitively it feels ...
Ghorbalchov's user avatar
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Quantum Hall effect diverges at $B=0$

In the integer quantum Hall effect, with the applied magnetic field reduced, more and more LLs get filled and one can observe higher and higher plateaus in the Hall conductivity $\sigma_H(B)$. ...
xiaohuamao's user avatar
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Why is the quantum Hall apparatus in the canonical ensemble?

Most explanations of the integer quantum Hall effect start out in the grand canonical ensemble, where the plateaus arise when the chemical potential (or equivalently the Fermi energy) is in the gaps ...
Amir Raz's user avatar
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All Chern numbers as mapping degree?

The Chern number of Haldane model can be interpreted as a mapping degree from $T^2$ (1BZ) to $S^2$ (Bloch sphere). The question is whether all the Chern numbers can be interpreted in this way. In ...
Taveren Sa's user avatar
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Plateaus in Quantum Hall Effect and its Robustness

I was studying Quantum Hall Effect and there I came out with a question that why the plateaus in the plot of Hall Resistivity are robust ? I know by solving Schrodinger equation and using Landau Gauge ...
Bishal Sarkar's user avatar
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1 answer
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Does the fractional quantum Hall effect always occur when the integer quantum Hall effect occurs?

Does the fractional quantum Hall effect always occur when the integer quantum Hall effect occurs? In other words, is there an example of a material where the IQHE can be measured without the "...
QPhysl's user avatar
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Deriving an alternating expression for Hall Conductivity

I was reading the paper (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.31.3372) in which Thouless and Wu show that the hall conductivity is a topological invariant. My question is about the ...
emir sezik's user avatar
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Deriving the non-abelian Berry connection

I'm slightly confused about a manipulation in Section 1.5.4 of Tong's notes on the Quantum Hall Effect. This concerns the derivation of the non-abelian Berry phase. Setup: We have an $N$-dimensional ...
Meths's user avatar
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Can anyons exist on a torus without any additional conditions?

While learning recently some more "advanced" stuff about path integral formalism I was introduced to the topological conditions that specify the process of construction of the propagator, i....
devoted4gainz's user avatar
2 votes
1 answer
177 views

Hofstadter butterfly patterns in different honeycomb lattice structures

Without loss of generality, we set vector potential $A=\left( -yB,0,0 \right)$. Here B is magnetic field. And due to Peierls substitution, $t_{ij}\rightarrow \exp \left( igaA_{r_j} \right) t_{ij}$, ...
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Why is a large magnetic field problematic (for topological physics)?

In papers studying or searching for topological order (intrinsic or symmetry-protected) in various condensed matter systems (e.g. Field-tuned and zero-field fractional Chern insulators in magic angle ...
mbintz's user avatar
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1 answer
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Correlators $\langle \psi(z_1) \cdots \psi(z_N) \sigma(w_1) \sigma(w_2) \rangle$ in Ising conformal field theory

Question: How one obtains $$\langle \psi(z_1) \cdots \psi(z_N) \sigma(w_1) \sigma(w_2) \rangle \sim \mathrm{Pf}\left( \frac{f(z_i,z_j; w_1, w_2)}{z_i-z_j}\right) \prod_{i=1}^N (z_i-w_1)^{-1/2} (z_i-...
Laplacian's user avatar
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2 votes
1 answer
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Can anyone clarify the origin of the radial current in this discussion on the quantum hall effect?

I am trying to understand parts of this webpage on the quantum hall effect, and I am stuck on the part where they talk about Corbino geometry. So we have a conductive 2D annulus and a changing ...
Maximal Ideal's user avatar
1 vote
0 answers
120 views

Non-unitary magnetic translation operator for Landau levels

In chapter 9 of their book [1], Altland and Simons consider the Landau Hamiltonian in the symmetric gauge, \begin{equation} H=\frac{1}{2m^*}\left[\left(-\mathrm{i}\partial_1-\frac{x_2}{2l_0^2}\right)^...
xzd209's user avatar
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Effective Theory for Matter Fields Coupled to a Chern-Simons Field

Assuming that matter fields coupled with the background Chern-Simons field (or Maxwell-Chern-Simons field), I want to obtain the effective theory in terms of matter fields only, by integrating out a ...
3 votes
0 answers
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Zero frequency limit of Hall conductivity not quantized?

The transverse conductivity $\sigma_{xy}$ at zero frequency is quantized when the chemical potential $\mu$ is within the gap for a topological system, such as quantum Hall effect and Haldane model. ...
xiaohuamao's user avatar
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Does Hall conductivity change sign with chemical potential?

The transverse conductivity $\sigma_{xy}$ at zero frequency is quantized when the chemical potential $\mu$ is within the gap for a topological system. A typical plot of $\sigma_{xy}(\mu)$ is like the ...
xiaohuamao's user avatar
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3 votes
0 answers
75 views

Infinite stacking of integer quantum Hall systems

Let us consider a (3+1)-dimensional system $\mathcal{H}$ constructed by stacking (2+1)-dimensional integer quantum Hall systems $\mathcal{H}_\text{Hall}$, e.g., $E_8$ bosonic systems (or $\sigma_H=1$ ...
Yuan Yao's user avatar
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1 answer
482 views

Why is Hall response $(\sigma_{xy}-\sigma_{yx})/2$ rather than $\sigma_{xy}$?

In this PRL paper (and other works like the review article), the Hall response is defined as the antisymmetric part $$\sigma_H=(\sigma_{xy}-\sigma_{yx})/2$$ instead of $\sigma_{xy}$ itself. What is ...
xiaohuamao's user avatar
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2 votes
1 answer
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What barriers have prevented us from using Landau levels to make qubits?

Landau levels allow us to jam all electrons into nearly identical quantum states - these states share the same quantum numbers (e.g. orbital and spin) except for the guiding center. Furthermore, the ...
BGreen's user avatar
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3 votes
0 answers
182 views

Shubnikov-de-Haas effect and Quantum Hall effect

I am wondering if these two phenomena are two names for the same thing or whether these are distinct effects and there are situation where one appears, but the other one doesn't? Both seem to produce ...
tobalt's user avatar
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1 vote
1 answer
219 views

What is a "statistical" gauge field?

In the Fractional Quantum Hall Effect (FQHE), one introduces a Chern-Simons (CS) gauge field and it is called statistical. Why? Another main question is below (*), but maybe I should state some things ...
scruby's user avatar
  • 413
2 votes
1 answer
228 views

Action for boundary term in Chern-Simons theory (David Tong's note)

This question is about obtaining the boundary action from Chern-Simons theory. While reading David Tong's chapter 6 on quantum Hall effect, I cannot derive an equation between (6.9) and (6.10) of the ...
Laplacian's user avatar
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1 vote
0 answers
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Monopoles in the fractual quantum Hall

What role do magnetic monopoles play in the fractional quantum Hall effect? Also see here. EDIT: I should add that I understand the fractual quantum Hall effect only from the perspective of minimal ...
J. H's user avatar
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2 votes
1 answer
344 views

Landau Levels degeneracy in a finite sample

According to different sources: Tong lectures on IQHE (Tong), MIT Open courses (MIT) etc, when calculating the number of states in each Landau Level all of them impose (in the Landau gauge) periodic ...
Nacho Figueruelo's user avatar
0 votes
1 answer
81 views

Gauge fixing in derivation of fractional QHE action

I'll copy the text from a relevant question: This follows the discussion in Altland and Simons Condensed Matter Field Theory -- section 9.5 on deriving the Chern-Simons action for FQHE. Starting with ...
Kouta Dagnino's user avatar
1 vote
1 answer
230 views

Prerequisites for Chern-Simons approach to the Fractional Quantum Hall Effect

I am interested in learning the Chern-Simons approach to the fractional quantum Hall effect right from the basics. I have learnt about Lie groups and Weyl quantisation and am currently learning ...
3 votes
0 answers
121 views

Quantum Hall Effect: Two-terminal resistance and thermodynamic equilibrium

In Goerbig's lecture notes on the quantum hall effect, Fig. 3.3 describes the so-called two-terminal measurement. The figure and accompanying text show us that in a two-terminal measurement, the ...
quantum rookie's user avatar
0 votes
2 answers
157 views

Fractional quantum Hall effect: is new physics required to understand it? [closed]

Is it true that some of the experimentally observed states in fractional quantum Hall effect are unexplainable by current physics? If so, does this point towards a revision of quantum mechanics, and / ...
Tejinder P. Singh's user avatar
1 vote
0 answers
110 views

Landau levels in graphene - unbounded from below spectrum

Considering the case of monolayer graphene in a perpendicular magnetic field arises LL in it. The final spectrum is given by $$ \epsilon_n=\mathrm{sign}(n)\hbar\omega\sqrt{|n|} $$ where $n\in\mathbb{Z}...
Noam Ophir's user avatar
3 votes
1 answer
157 views

Gaps in FQHE bulk spectrum

In David Tong's note on Quantum Hall Effect, Tong states on page 85 that the incompressible Laughlin wavefunction is "responsible for the gap in the bulk spectrum" of FQHE (Fractional ...
Cheng Tao's user avatar
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1 answer
352 views

Spectral flow in IQHE

I am encoutering some problems in understading the argument in David Tong's QHE lecture notes that the spectral flow of extended states give rise to currents in IQHE. First, Tong argues in page 36 ...
Cheng Tao's user avatar
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1 answer
134 views

What's the difference of flux tube and vortex in FQHE (especially in Jain wavefuntion)

In the book Composite Fermion by Jainendra K.Jain, he mentioned the motivation of Jain wavefunction: attach flux tube of 2p flux quantum to fermions to form composite fermions. Naively, this is done ...
Black Monolith's user avatar
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1 answer
136 views

Edge States in Integer Quantum Hall Effect (IQHE)

As part of an exercise we have been asked to consider a free particle in a uniform magnetic field $\vec B = (0,0,B)$, bounded by a strong confining potential: $$H = \frac {(-i\hbar\nabla^ -e \vec A)^2}...
Allod's user avatar
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0 answers
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Filling Fermions into the Lowest Landau Level and the Laughlin Wave Function

For a particle moving in the $xy$-plane in the presence of a uniform magnetic field $B$ along the $z$-direction, if one chooses the symmetric gauge of the vector potential, then one can use the ...
Zhengyuan Yue's user avatar
1 vote
0 answers
64 views

Term in Hamiltonian when electric field is turned on

In David Tong's notes on Quantum Hall Effect, in his derivation of the Kubo formula, he says that turning on the electric field has the effect of adding a $- \mathbf{J} \cdot \mathbf{A}$ to the ...
Brain Stroke Patient's user avatar

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