Topological insulator are materials formed by a insulator bulk and metallic surfaces with topological origin. These materials may be important for developments in Quantum Computing and Spintronics.
0
votes
0answers
32 views
Some questions about the edge states for time-reversal invariant topological superconductors?
Stimulated by my some recent calculations on edge states(ES) for time-reversal invariant(TRI) topological superconductors(TS) as well as many questions concerning the "edge states" in Physics ...
2
votes
0answers
75 views
Topological band theory [closed]
Why topological insulators were discovered so late? While the band theory was known long time ago! I mean why the topological properties of electronic bands were not noticed in the past?
4
votes
2answers
109 views
Whis is the difference between charge fractionalization in 1D and 2D?
Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations.
But as I can see, there are some differences: the ground state of Polyacetelene breaks translational ...
2
votes
0answers
89 views
How to define the mirror symmetry operator for Kane-Mele model?
Let us take the famous Kane-Mele(KM) model(http://prl.aps.org/abstract/PRL/v95/i22/e226801 and http://prl.aps.org/abstract/PRL/v95/i14/e146802) as our starting point.
Due to the time-reversal(TR), ...
2
votes
2answers
130 views
Would HgTe be a topological insulator?
In "Quantum Spin Hall Insulator State in HgTe Quantum Wells", researchers observed a 2D topological insulator by sandwiching HgTe between CdTe. Is the CdTe really necessary? Would Vacuum/HgTe/Vacuum ...
8
votes
2answers
390 views
What is the mathematical reason for topological edge states?
There are many free fermion systems that possess topological edge/boundary states. Examples include quantum Hall insulators and topological insulators. No matter chiral or non-chiral, 2D or 3D, ...
5
votes
1answer
143 views
A question on the doped Kitaev-Heisenberg model?
Recently, some groups have studied the effects of doping the Kitaev model on honeycomb lattice(e.g.,http://arxiv.org/abs/1109.6681 and http://arxiv.org/abs/1109.4155) and their calculations show the ...
0
votes
0answers
94 views
Wave function ansatz for disclinated graphene with spin
I am currently investigating spin dynamics in disclinated graphene. More information about my approach can be found in my other post. I would like to know if my approach is somewhat correct to find ...
4
votes
0answers
100 views
Intuition on topologically nontrivial 2D-band structures?
I want to get more intuition on topologically nontrivial band structures.
There's this popular 2D two-band model for a topological insulator
where $H=\sum_{k}h(\boldsymbol{k})$ (see Qi, Hughes, and ...
3
votes
1answer
105 views
Graphene with a disclination and the spin-orbit coupling
I am trying to follow the methods used in this paper (http://arxiv.org/pdf/1208.3023.pdf) to construct the Hamiltonian of a graphene cone, but taking into account the spin-orbit coupling.
The paper ...
4
votes
1answer
200 views
Is edge state of topological insulator really robust？
I am a little confused! Some people are arguing that the gapless edge state of Topological insulator is robust as long as the time reversal symmetry is not broken，while other people say that it is ...
1
vote
2answers
146 views
Time-reversal symmery and topological insulators
I have a very naive question about the notion of time-reversal symmetry applied to topological insulators that are studied in experiments. If I understand correctly, the exsistance of time-reversal ...
4
votes
1answer
181 views
Chiral edge state as topological properity of bulk state
As far as I know, quantum hall effect and quantum spin hall effect has chiral edge state. Chiral edge state is usually closely related with delocalization, since back scattering is forbidden. However, ...
10
votes
2answers
337 views
Why quantum hall effect has chiral edge state?
The most popular explaination may be the following: in magnetic field, electrons move in cycolotron orbits, such cycolotron orbits ensure electrons to move in one direction at the edge. That is why ...
3
votes
1answer
102 views
Measurement of topological spin
How do you measure the topological spin of an anyon? So how could an experimental setup look like? Is topological spin an observable at all?
3
votes
0answers
152 views
Hamiltonian of the surface states of a 3D topological insulator
The surface states of a 3D topological insulator (let's say in the (x-y) plane) are sometimes described by the following Hamiltonian :
$$H(k)=\hbar v_F (p_x \sigma_x + p_y \sigma_y)$$
or sometimes by ...
7
votes
0answers
164 views
What is the precise definition or list of prerequisites for an anyonic system?
I have been reading some reviews and looked into books on anyons and topological quantum computation and I found it a little difficult to make out a short list of parameters and a clear and short list ...
5
votes
2answers
418 views
How is the topological $Z_2$ invariant related to the Chern number? (e.g. for a topological insulator)
This question relates to the $Z_2$ invariant defined e.g. for topological insulators:
Is it correct to relate $Z_2$ = 1 to an odd Chern number and $Z_2$ = 0 to an even Chern number?
If yes, is it ...
2
votes
0answers
173 views
Simple model of edge states for a two-dimensional topological insulator
Quantum spin Hall states or, topological insulators are novel states of matter that have insulating bulk and gapless edge states. Are there any simple models that show these features?
See e.g. the ...
2
votes
1answer
110 views
What is the operator for the edge current of a fracional quantum Hall state?
The edge of a fractional quantum Hall state is a chiral conformal field theory. In the Laughlin case it corresponds to the chiral boson,
$$ S = \frac{1}{4\pi} \int dt dx ...
5
votes
2answers
432 views
Why are Topological Superconductors hard to make?
Topological insulators (TI) have already been made in lab. Topological superconductors (TSC), being close cousins of TI, seem harder to make.
Why is that?
It seems that materials in connection with ...
3
votes
1answer
90 views
Nonlocal Transport in the Quantum Spin Hall State
It has been reported that nonlocal Transport in the can be realized in topological insulator. Why non-local transport through edge channels has the potential application for low-power information ...
4
votes
2answers
325 views
What happens when a bare 3d topological insulator is subject to a magnetic field?
Effective field theory of 3d topological insulators (TI) predict some novel electromagnetic effects. Unfortunately it require a gapped surface which is hard to achieve experimentally. Then I have two ...
4
votes
1answer
223 views
Counterexamples to the bulk-boundary correspondence (topological insulators)
In the literature on topological insulators and superconductors the 'bulk-boundary correspondence' features quite heavily. One version of this conjecture says roughly: "At an interface between two ...
4
votes
0answers
152 views
Significance of Dirac cones in condensed matter physics
In condensed matter physics, Dirac cones can be found in graphene, topological insulators, cuprates, and iron-pnictides. This means that electrons behave as massless particles near the Dirac points.
...
4
votes
0answers
67 views
Defects in 3+1 TFTs/2+1 CFTs
I would like to know of good pedagogic references to learn about the notion of "defects" in TFTs and CFTs. I am specially interested in 3+1 TFTs (.and probably about their relation to 2+1 CFTs..)
In ...
5
votes
1answer
351 views
How can one localize the massless fermions in Dirac materials?
I noticed that finite electric potential cannot localize the low energy excitations in a graphene sheet. Is it possible to localize the massless fermions in the surface band of topological insulators ...
18
votes
1answer
774 views
How Fundamental is Spin-Orbit Coupling to Topological Insulators?
I'm well aware this is a very active area of research so the best answer one can give to this question may be incomplete.
Topological states in condensed matter are well-known, even if not always ...
10
votes
2answers
261 views
Is there a way to directly observe the spin texture of the surface states of topological insulators?
Is there a way to directly, here I means in real space, observe the interaction of the surface states of 3D topological insulators with defects (dopings and adatoms)? How to observe the spin texture ...
1
vote
0answers
268 views
1D Topological insulator with PT symmetry
Assume I have the Hamiltonian for a 1D topological insulators as:
$H=sin(P_x) \sigma_x+i \Delta \sigma_{y}+(1-m-cos(P_x)) \sigma_z $ where $m$ is the mass term, $P_x$ is the momentum and $\Delta$ is ...
4
votes
1answer
766 views
1D topological insulator
This question is inspired by another one about the simplest model of topological insulator, where 4tnemele showed a nice two band model in the answer.
I read that and am wondering if we and push that ...
11
votes
1answer
878 views
Graphene and Klein bottle?
I am trying to understand graphene as a topological insulator.
The spin orbital interaction in graphene is very small (~10mK?). But if we consider that, then graphene should be a topological ...
8
votes
1answer
316 views
How metallic surfaces states can emerge in topological insulators?
Topological insulators are materials known to have bulk insulator and metallic surface states. But, what is the origin of these metallic surface states? And how the topology of band could help the ...
15
votes
5answers
1k views
Simple models that exhibit topological phase transitions
There are a number of physical systems with phases described by topologically protected invariants (fractional quantum Hall, topological insulators) but what are the simplest mathematical models that ...
