All Questions
Tagged with topological-insulators quantum-hall-effect
52
questions
28
votes
5
answers
5k
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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 ...
- 5,415
23
votes
3
answers
8k
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 ...
- 1,055
18
votes
1
answer
1k
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 ...
- 271
10
votes
1
answer
8k
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Derivation of Kubo Formula for Hall Conductance
I am trying to derive the result of the TKNN formula but am experiencing difficulty in deriving the Kubo formula. The Kubo formula used in the TKNN paper is,
$$ \sigma_{xy}= \frac{ie^2}{\hbar} \sum_{E^...
- 369
10
votes
1
answer
268
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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 ...
- 1,795
7
votes
2
answers
5k
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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 ...
- 1,431
7
votes
1
answer
2k
views
How to show that Chern number gives the amount of edge states?
When talking about topological insulator and talking about bulk-edge correspondence, it seems to be widely accepted conclusion that the band Chern number (winding number) is equal to, when the ...
6
votes
3
answers
1k
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Whis is the difference between charge fractionalization in 1D and 2D?
Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations.
But as I can see, there are some differences: the ground state of Polyacetelene breaks translational ...
- 181
6
votes
2
answers
1k
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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 ...
- 3,744
5
votes
1
answer
2k
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Determining spectra of edge states numerically
Normally we write a Bloch Hamiltonian $H(\mathbf{k})$ for the bulk and determine the spectrum which gives us various bands i.e we basically obtain $E=E(\mathbf{k})$ for the bulk only.
Also in the ...
- 135
5
votes
1
answer
151
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Equivalence classes of mappings from $T^{2}$ to an arbitrary space $X$
I was reading the paper "Homotopy and quantization in condensed matter physics", by J.E Avron et al. ( http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.51.51). There they have classified the ...
5
votes
1
answer
484
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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. ...
- 508
4
votes
1
answer
391
views
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 ...
- 93
4
votes
0
answers
110
views
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 ...
- 3,701
4
votes
0
answers
878
views
Laughlin's topological argument
I have a confusion about understanding the Laughlin's topological argument on Hall conductivity quantization.
This argument states that the Hall conductivity is
$$
\sigma_{xy}=\frac{e}{h}Q,
$$
where $...
- 2,333