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.
Questions tagged [quantum-hall-effect]
343 questions
44
votes
2 answers
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
$$ S[\phi] = \frac{1}{4\pi\nu} \int dx\,dt\, (v(\partial_x \phi)^2 - \partial_x\phi\partial_t \phi), $$
where $v$ is some constant and $1/\nu\in…
Greg Graviton
- 5,397
33
votes
2 answers
Topological Charge. What is it Physically?
I have seen the term topological charge defined in an abstract mathematical way as a essentially a labeling scheme for particles which follows certain rules. However I am left guessing when trying to explain what physical properties of a system lead…
Mangler
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29
votes
5 answers
Simple models that exhibit topological phase transitions
There are a number of physical systems with phases described by topologically protected invariants (fractional quantum Hall, topological insulators) but what are the simplest mathematical models that exhibit topological phases? Is the toric code as…
wsc
- 5,615
28
votes
4 answers
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 of topological order in fractional quantum Hall…
Shenghan Jiang
- 556
23
votes
4 answers
Quantum Hall effect for dummies
In the past few days I've become increasingly intrigued by the QHE, mainly thanks to very interesting questions and answers that have appeared here. Unfortunately, I am as of yet very confused by all the (seemingly disparate) stuff I learned.
First,…
Marek
- 23,981
23
votes
3 answers
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 to move in a single direction at the edge. That…
Brioschi
- 1,055
22
votes
1 answer
What is parafermion in condensed matter physics?
Recently, parafermion becomes hot in condensed matter physics (1:Nature Communications, 4, 1348 (2013),[2]:Phys. Rev. X, 2, 041002 (2012), [3]:Phys. Rev. B, 86, 195126 (2012),[4]:Phys. Rev. B,87, 035132, (2013)).
But I have little knowledge about…
ZuoYou
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21
votes
2 answers
Edge theory of FQHE - Unable to produce Green's function from anticommutation relations and equation of motion?
I'm studying the edge theory of the fractional quantum Hall effect (FQHE) and I've stumbled on a peculiar contradiction concerning the bosonization procedure which I am unable to resolve. Help!
In particular, consider the first few pages of X.G.…
Greg Graviton
- 5,397
19
votes
1 answer
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 conductivity must be an integer (the Chern number)…
user21859
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17
votes
3 answers
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:
$$t_{ij}c_i^{\dagger}c_j \to t_{ij}e^{iqA|i-j|}c_i^{\dagger}c_j$$
when transformed to Bloch basis,…
Tim
- 625
15
votes
4 answers
Questions about Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper
I am reading the famous and concise Thouless-Kohmoto-Nightingale-den Nijs (TKNN) paper Quantized Hall Conductance in a Two-Dimensional Periodic Potential, Phys. Rev. Lett. 49, 405–408 (1982), where I have several subtle questions about the details.…
Machine
- 2,015
14
votes
1 answer
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. This is the case for integer and some fractional…
SM Kravec
- 881
13
votes
1 answer
Physical Interpretation of Relationship Between Hall Conductivity and Berry Curvature?
Why is the Hall conductivity in a 2D material
$$\tag{1} \sigma_{xy}=\frac{e^2}{2\pi h} \int dk_x dk_y F_{xy}(k)$$
where the integral is taken over the Brillouin Zone and $F_{xy}(k)$ is the Berry curvature of the filled bands?
What is the physical…
ChickenGod
- 2,255
12
votes
0 answers
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 $\sigma_{xy}=n e^2/h$ that occur at integer values of $n$. This quantization is extremely precise, up to one part in $10^{-9}$. SI units uses this…
KF Gauss
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11
votes
3 answers
Quantum Hall Effect: Why the spikes of the longitudinal resistance appear every time when Hall conductance jumps?
[
Let's focus on the longitudinal resistance, I have two confusions:
Why it shows spike like feature every time the hall conductance jumps?
Why its amplitude grows when the magnetic field grows?
I find some literature says when the Landau level…
an offer can't refuse
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