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.

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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 ...
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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, ...
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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 ...
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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 ...
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215 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 ...
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861 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 ...
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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 ...
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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, ...
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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 ...
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183 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?
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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 ...
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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1answer
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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 ...
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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 ...
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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 ...