All Questions
8
questions
1
vote
0
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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 ...
- 123
0
votes
2
answers
332
views
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 ...
- 423
0
votes
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 ...
- 61
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 ...
- 1
1
vote
1
answer
426
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Is the quantum Hall state a topological insulating state?
I am confused about the quantum Hall state and topological insulating states.
Following are the points (according to my naive understanding of this field) which confuse me:
Topological insulator has ...
- 1,335
0
votes
0
answers
65
views
Visualizing k-space tori in 3D
In many introductions to topological insulators (in the exposition of Haldane’s model, for example), we represent the parameter space, a torus, on a plane with axes running from $0$ to $2\pi$.
In an ...
- 591
2
votes
0
answers
541
views
Hall Conductance and Chern Number Sign Convention
I have a simple question regarding sign conventions pertaining to the Chern number and Hall conductance (and what seems to be inconsistencies in the literature).
In a 2D band insulator, the Chern ...
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