1
vote
1answer
33 views

Why does proximity to a superconductor open a gap in the surface states of topological insulators

I have read in many places that the gapless surface states of 3D topological insulators are robust to perturbations which do not break time-reversal symmetry. I have recently also seen many papers ...
3
votes
0answers
63 views

Topolgical insulators order parameter

For topological insulators Is there any way to define order parameter for topological phase transitions?
3
votes
1answer
104 views

$Z_2$ 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 ...
2
votes
1answer
108 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 ...
2
votes
0answers
23 views

In k$\cdot$p theory, how does one calculate the bulk inversion asymmetry coefficients given in table 6.3 in Winkler?

In k$\cdot$p theory, how does one calculate the bulk inversion asymmetry coefficients given in table 6.3 in Winkler? Winkler's book on spin-orbit coupling effects is available free online. In ...
6
votes
0answers
266 views

When can we take the Brillouin zone to be a sphere?

When reading some literatures on topological insulators, I've seen authors taking Brillouin zone(BZ) to be a sphere sometimes, especially when it comes to strong topological insulators. Also I've seen ...
2
votes
0answers
83 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 ...
2
votes
0answers
52 views

Why p-wave superconductors are rare in nature?

I have the basic question that why so many superconducting materials are s-wave and d-wave pairing, but the p-wave superconductors are so rare in nature? An equivalent question may be that why ...
7
votes
1answer
338 views

Topological insulators: why K-theory classification rather than homotopy classification?

I am reading a 2009 paper by Kitaev on K-theory classification of topological insulators. In the 4th page, 1st paragraph in the section "Classification principles", he says, Continuous ...
2
votes
0answers
98 views

How much merit is there in the heuristic argument of bulk-edge relation for topological insulators?

Take 2D quantum hall insulator for example. The typical argument goes like this: We have a Hamiltonian that has translation symmetry in both directions on a infinite lattice, and we assign a integer ...
3
votes
1answer
145 views

How to determine the orientation of the massive Dirac Hamiltonian?

In the calculation of the Chern number within a 2D lattice model, let's take the Haldane model for example, the Chern number$=\pm1$ has 2 contributions coming from 2 Dirac points described by ...
2
votes
1answer
153 views

Edge states in the “half BHZ” model

Consider the "half BHZ" Hamiltonian $${\cal H}=\sum_{\mathbf{k}}\left(A\sin(k_{x})\sigma_{x}+A\sin(k_{y})\sigma_{y}+{\cal M}(\mathbf{k})\sigma_{z}\right)c_{\mathbf{k}}^{\dagger}c_{\mathbf{k}}$$ where ...
4
votes
1answer
102 views

Topological Insulators: is HgX a special case?

I got confused by reading this article: Francois Virot, Roland Hayn, Manuel Richter, and Jeroen van den Brink. “Engineering topological surface-states: HgS, HgSe and HgTe.” arXiv preprint ...
1
vote
1answer
175 views

Determining spectra of edge states numerically

Normally we write a Bloch Hamiltonian $H(\mathbf{k})$ for the bulk and determine the spectrum which gives us various bands i.e we basically obtain $E=E(\mathbf{k})$ for the bulk only. Also in the ...
0
votes
0answers
295 views

how to determine the parity eigenvalues of time-reversal invariant momenta point from first principle calculation when we judge topological insulator?

This is a question of topological insulator. Liang Fu and C. L. Kane proposed a method to judge whether an inversion symmetric insulator is a topological insulator or not in their article(L. Fu and ...
4
votes
1answer
1k views

About Dirac cones

This nice image of Dirac cones (from this article), in a ($E,\vec k$ graph) will be an introduction for several questions, in the realm of topological insulators. 1) Does the Dirac cone appears ...
11
votes
3answers
1k views

Reconciling topological insulators and topological order

We make an important distinction between the topological insulators (which are essentially uncorrelated band insulators, "with a twist") and topological order (which covers a variety of exotic ...
1
vote
1answer
62 views

Hexagonal Warping

Hexagonal warping had observed in $Bi_2Te_3$. Is it related somehow with the topological insulator type? Is it a characteristic of weak topological insulator or are there other reasons for this ...
7
votes
1answer
691 views

Trivial and Non-trivial topology of band structure

I don't understand the meaning of the expression "trivial topology" or "non-trivial topology" for an electronic band structure. Does anybody have a good explanation?
7
votes
1answer
547 views

Topological band structure, difference between a sphere and a donut

Kohmoto from TKNN(Thouless-Kohmoto-Nightingale-deNijs) who described the topology of the integer quantum hall effect always stressed the importance of the 2D Brillouin zone being a donut due to ...
1
vote
0answers
214 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 ...
3
votes
1answer
466 views

How to define the mirror symmetry operator for Kane-Mele model?

Let us take the famous Kane-Mele(KM) model as our starting point. Due to the time-reversal(TR), 2-fold rotational(or 2D space inversion), 3-fold rotational and mirror symmetries of the honeycomb ...
2
votes
2answers
721 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 ...
9
votes
2answers
892 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
297 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 ...
3
votes
1answer
207 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 ...
7
votes
1answer
813 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 ...
5
votes
2answers
418 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
1k 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 ...
5
votes
1answer
177 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?
6
votes
2answers
2k 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
371 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 ...
6
votes
2answers
767 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
159 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
504 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 ...
6
votes
1answer
489 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 ...
5
votes
0answers
232 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. ...
6
votes
0answers
420 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
2k 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 ...
12
votes
2answers
363 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
345 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 ...
7
votes
0answers
276 views

Descent equation and anomaly polynomial

I am just reading Ryu, Moore and Ludwig's paper on classifications of topological insulators and quantum anomaly. They are trying to relate the quantum anomaly as a signal of the presence of a ...
4
votes
1answer
1k 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 ...
19
votes
5answers
2k 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 ...