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Dec
31
comment Edge states in the “half BHZ” model
For example, Bi$_{1-x}$Sb$_{x}$ has 4 and 5 Dirac cones in the trivial and non-trivial regime (tuned by $x$) respectively. You can destroy the 4 trivial ones by changing surface details. But the last (fifth) one is a global property and cannot be destroyed. BTW, send me an email next time (physmeso@gmail.com). Someone told me that filling up the comments section is frowned upon on this site.
Dec
31
comment Edge states in the “half BHZ” model
This is not true: “So the non-triviality […] existence of edge states isn’t.” Existence of topologically protected edge states is necessarily a property of the bulk (i.e. global property). The main point I’m trying to make is that are two types of edge/surface states: trivial and non-trivial. The trivial ones were known for decades and their existence can be seen by local Hamiltonians. The novelty of the recent breakthrough was Kane realizing that there appears a new pair of edge states, in addition to the trivial ones, when the insulator transitions to a TI phase. (continued)
Dec
30
comment Edge states in the “half BHZ” model
There is no edge state at $(0, \; \pi)$; this is in the bulk BZ. Edge states by definition have $k_{y} = 0$. Also, what I was trying to say was that local Hamiltonians don’t guarantee to give you all the information on edge states; non-triviality of TIs in a global property.
Dec
30
comment Edge states in the “half BHZ” model
The Fu & Kane formalism is an intuitive description of the same thing as the “Chern-number-like” computation; Chern number of TIs is zero. Evaluating the topological invariant (or Chern-number-like quantity), by integrating over the entire BZ, is overkill compared to the Fu & Kane formalism. I referred to it (as opposed to other tricks) because it makes sense to talk about annihilation of parities in this context, not edge states. It doesn’t make sense to say “edge states at $(0, \; \pi)$ and $(0, \; 0)$ annihilate each other.” (continued)
Dec
30
answered Edge states in the “half BHZ” model
Dec
28
revised Do Cooper pairs act like Cheshire cats?
grammar fix
Dec
28
revised Do Cooper pairs act like Cheshire cats?
grammar fix
Dec
28
revised Do Cooper pairs act like Cheshire cats?
Additional comments
Dec
28
answered Do Cooper pairs act like Cheshire cats?
Dec
18
revised Topological Insulators: is HgX a special case?
corrected spelling, grammar, content
Dec
18
revised Topological Insulators: is HgX a special case?
fixed grammar
Dec
18
suggested suggested edit on Topological Insulators: is HgX a special case?
Dec
18
answered Topological Insulators: is HgX a special case?
Dec
11
answered Is band-inversion a 'necessary and sufficient' condition for Topological Insulators?
Nov
27
awarded  Revival
Nov
26
revised Experimental signature of topological superconductor
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Nov
23
revised Determining spectra of edge states numerically
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Nov
23
suggested suggested edit on Determining spectra of edge states numerically
Nov
23
answered Determining spectra of edge states numerically
Oct
21
comment Bloch's theorem and Bloch's state
Equation (28) is valid. The $e^{i\mathbf{k}\cdot\mathbf{r}}$ is simply a phase factor; two kets can, in general, be related in that fashion. To make better sense of it, take a $\langle\mathbf{r}|$ on both sides. You'll get $\langle\mathbf{r}|\psi_{n\mathbf{k}}\rangle = e^{i \mathbf{k} \cdot\mathbf{r}} \langle \mathbf{r}|u_{n\mathbf{k}}\rangle\Rightarrow\psi_{n\mathbf{k}}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}}u_{n\mathbf{k}}(\mathbf{r})$, which is our familiar Bloch wavefunction