All Questions
Tagged with topological-insulators topological-phase
8
questions
11
votes
2
answers
6k
views
Is band-inversion a 'necessary and sufficient' condition for Topological Insulators?
According to my naive understanding of topological insulators, an inverted band strucure in the bulk (inverted with respect to the vaccum/trivial insulator surrounding it) implies the existence of a ...
28
votes
3
answers
23k
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What does the Chern number physically represent?
In 2D the Chern number can be written as
$$C_m=\frac 1{2\pi}\int_{BZ}\Omega_m(\mathbf k)\cdot d^2 \mathbf k$$
where we are integrating over the Brillouin zone.
In 2D this is equivalent to finding ...
- 1,189
24
votes
4
answers
19k
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Chern insulator vs topological insulator
What is the basic distinction between a Chern Insulator and a Topological Insulator? Right now I know that a Chern Insulator has "topologically non-trivial band structure" and that a Topological ...
- 411
6
votes
1
answer
2k
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$Z_2$ topological insulator: odd vs. even number of edge state pairs
I am having trouble in understanding why in $Z_2$ topological insulators odd number of Kramers' pairs on one edge are protected by time reversal symmetry against elastic backscattering while even ...
- 1,566
6
votes
1
answer
2k
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Chiral anomaly in Weyl semimetal
In the presence of electromagnetic fields $E$ and $B$, four current is not conserved in a Weyl semimetal i.e. $\partial_{\mu} j^{\mu}\propto E\cdot B \neq 0$. There are some proofs in the literature ...
- 135
4
votes
1
answer
421
views
How to distinguish between a topological state from from a non-topological one?
How to distinguish between a topological state from from a non-topological one? Is there any standard procedure for identifying the topological features of a given hamiltonian? In general what are the ...
- 115
2
votes
1
answer
4k
views
Berry phase in 1D materials
The Berry phase $\phi_B$ is the phase that an eigenstate acquires after its momentum vector goes around a circle at constant energy around the Dirac point.
It is defined as $\phi_B = -i \int \langle\...
- 359
2
votes
3
answers
862
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Can a symmetry-preserving unitary transformation that goes from a trivial SPT to a non-trivial SPT be local?
This question concerns the very interesting paper: ''Symmetry protected topological (SPT) orders
and the group cohomology of their symmetry group'' by Chen et al., http://arxiv.org/abs/1106.4772
In ...
- 21