All Questions
Tagged with topological-insulators quantum-hall-effect
52
questions
10
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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 ...
CommunityBot
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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. ...
CommunityBot
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1
vote
0
answers
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 ...
- 1,778
0
votes
1
answer
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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 ...
- 46.1k
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 ...
- 3,701
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. ...
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3
votes
0
answers
75
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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 $\sigma_H=1$ ...
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3
votes
2
answers
800
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Questions about Berry Phase
I'm learning about the Berry Phase from the original paper, and from the TIFR Infosys Lectures The Quantum Hall Effect by David Tong (2016).
I have some questions regarding the original derivation of ...
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2
votes
1
answer
244
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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 ...
CommunityBot
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6
votes
3
answers
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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 ...
- 2,646
1
vote
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 ...
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3
votes
1
answer
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What's the relation between quantized Hall effects and topology materials?
The quantized Hall effects (ignoring fractional Hall effect) include:
Quantum Hall effect;
Quantum anomalous Hall effect;
Quantum spin Hall effect.
All these effects are just describing the ...
- 1,031
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 ...
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vote
0
answers
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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 ...
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votes
2
answers
332
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What does "continuous transformation" mean with regard to the Hamiltonian of a system?
When dealing with topological phases of matter (topological insulators, quantum hall effect, etc...) one says that the system remains in the same phase as long as any continuous transformation of the ...
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