All Questions
Tagged with topological-insulators topological-phase
98
questions
28
votes
3
answers
23k
views
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
views
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
17
votes
1
answer
977
views
Are there topological non-trivial states in zero dimension?
The periodic table of topological insulators and superconductors suggests that there can be topological non-trivial phases in zero dimension in non-interacting system with certain symmetries.
A 0D ...
- 3,543
15
votes
4
answers
989
views
What is the topological space in “topological materials/phases of matter”?
I’m embarrassed to admit that after sitting in on several “topological physics” seminars, I still don’t understand the basic ideas of the area. In particular, when physicists talk about the “topology” ...
- 3,407
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 ...
9
votes
1
answer
2k
views
Jordan Wigner Transformation in 1d Majorana chain
So, I was reading the paper by Fidkowski and Kitaev on 1d fermionic phase http://arxiv.org/abs/1008.4138. It explains the classification of 1d fermionic SPT phases with $\mathbb{Z}_2^T$ symmetry for ...
- 733
9
votes
1
answer
559
views
AKLT state and Nobel physics prize 2016
The AKLT Hamiltonian and the chain is described in Wikipedia, and also the page 17 of this year Nobel Prize advanced information
I have questions concerning the info released by nobelprize.org, and ...
user32229
7
votes
1
answer
201
views
Time-reversal (explicitly) broken surface of $(3+1)$-dimensional topological insulator
Let us consider the surface of $(3+1)$-dimensional topological insulator, which is protected by the charge conservation $U(1)_Q$ and a time-reversal symmetry $\mathbb{Z}_2^T$. Such a surface, if not ...
- 813
6
votes
2
answers
2k
views
Topological insulator vs. topological superconductors in any dimension
My question today is simple. What is the difference between a topological insulator and a topological superconductor? How that difference depends on the dimensionality of space(time)? What is the ...
- 6,611
6
votes
1
answer
2k
views
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
6
votes
1
answer
387
views
Is topological surface state always tangential to bulk bands?
Think of a topologically nontrivial $D$-dimensional system. Its bulk bands form a $D+1$-dimensional manifold ($+1$ from energy). Its surface/edge bands form a $D$-dimensional one. Is the latter always ...
- 3,701
6
votes
1
answer
236
views
Topological materials and fractionalized excitations
I've been told several times that topological materials (such topological insulators) must have "fractionalized" excitations. Equivalently, if a material does not have fractionalized excitations, it ...
- 225
6
votes
1
answer
2k
views
Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene
Borrowing from Laughlin's argument on quantum Hall effect, Kane and Mele argued why there must be edge states in graphene with spin-orbit coupling in one paragraph, which is above the one with ...
- 1,566
6
votes
1
answer
1k
views
Homotopy Theory for Topological Insulators
I'm trying to understand topological insulators in terms of homotopy invariants. I understand that in 2 spatial dimensions, we have Chern insulators since $$\pi_2(S^2) = \mathbb{Z}$$
One subtlety that ...
- 483
6
votes
1
answer
340
views
Is this a topological $\mathbb Z_2$ (Majorana-)invariant in *any* dimension?
Consider a non-interacting superconducting Hamiltonian in an arbitrary dimension. This is most conveniently expressed in terms of Majorana modes, which are defined as $$\gamma_{2n-1} = c_n + c_n^\...
- 9,081