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revised How does bulk-boundary correspondence works for various cases of time-invariant system?
Format change for journal reference
2d
suggested suggested edit on How does bulk-boundary correspondence works for various cases of time-invariant system?
Aug
1
revised Can the current in a semiconductor be independent of mobility of charge carriers?
added 25 characters in body
Aug
1
answered Can the current in a semiconductor be independent of mobility of charge carriers?
Jun
10
comment Topolgical insulators order parameter
Yes, the order parameter is the (global) topological invariant ($\nu_{0}=0,1$) introduced by Fu, Kane, and Mele: arxiv.org/abs/cond-mat/0607699 for time-reversal symmetric free fermion systems. In (say) Bi$_{1-x}$Sb$_{x}$ alloys, the topological invariant can be defined as a function of $x$. As you increase $x$ from zero, for some $x=x_{c}$, a phase transition will occur and $\nu_{0}$ will change from 0 to 1.
Jun
5
revised $Z_2$ topological insulator: odd vs. even number of edge state pairs
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Jun
5
suggested suggested edit on $Z_2$ topological insulator: odd vs. even number of edge state pairs
Jun
5
answered $Z_2$ topological insulator: odd vs. even number of edge state pairs
Jun
1
revised Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene
Format changes
Jun
1
suggested suggested edit on Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene
Jun
1
answered Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene
May
31
comment Is edge state of topological insulator really robust?
@Mr.Gentleman: Please refer to the image in the question: physics.stackexchange.com/questions/88683/…
May
31
revised Is band-inversion a 'necessary and sufficient' condition for Topological Insulators?
Fixed broken image link
Apr
22
comment Basic questions in Majorana fermions
@user38579: I think it's best if you post a question with a much more elaborate description of what exactly it is that's bothering you in terms of the understanding of physical Majorana bound states (in condensed matter or ultracold gases). I have no problem with sticking to these comments; only problem is that this comments section is way too long already. I read the arXiv article you cited. But I'm still not sure of the best way to answer your question. Hence, once again, please elaborate. One more thing: please signal me somehow when you post the question.
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