All Questions
31
questions
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42
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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 ...
0
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1
answer
187
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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 ...
3
votes
0
answers
78
views
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. ...
4
votes
0
answers
110
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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 ...
1
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0
answers
99
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The flat-band basis, Green's function projectors, and TKNN
Bernevig & Hughes' book "Topological Insulators and Topological Superconductors" have a derivation of the TKNN invariant in terms of the finite-temperature Green's function. From the ...
3
votes
1
answer
228
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Is the Integer Quantum Hall Effect a distinct phase of matter?
In the Landau classification scheme, phases of matter differ in terms of symmetry. However, we know of many instances where this classification scheme does not apply. I have often heard topological ...
1
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0
answers
43
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Noncontractable loops in the 2D Brilluoin zone and the Chern number
I'm getting quite twisted around trying to figure out what all is quantized exactly in IQH looking at it from the Chern number perspective.
Let's suppose quantum hall on a torus -- I can apply a large ...
1
vote
0
answers
70
views
Is Hall conductivity time-reversal-odd at finite frequency in a topological system?
In some topological materials, e.g., the quantum (anomalous) Hall state and some related variants, the Hall conductivity $\sigma_{xy}$ is quantized and directly related to the Chern number, which ...
0
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0
answers
133
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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 ...
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. ...
10
votes
1
answer
268
views
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
vote
0
answers
34
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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 ...
2
votes
1
answer
244
views
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 ...
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 ...
0
votes
0
answers
227
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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 ...