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.

learn more… | top users | synonyms

1
vote
0answers
32 views

Topological Theta Term as a Topological Quantum Field Theory?

It is well known that the theta term $\int d^4x\frac{\theta}{4\pi}Tr[F\wedge F]=\int d^4x\frac{\theta}{4\pi}\epsilon_{\mu\nu\sigma\lambda}Tr[F^{\mu\nu}F^{\sigma\lambda}]$ is a topological term, ...
2
votes
2answers
124 views

What makes a superconductor topological?

I have read a fair bit about topological insulators and proximity induced Majorana bound states when placing a superconductor in proximity to a topological insulator. I've also read a bit about ...
2
votes
0answers
27 views

does Hall plateus require the existence of impurity in the sample?

While studying Hall conductivity with The Qantum Hall effect written by S.M.Girvin, I read a sentence "We have shown that the random impurity potential(and by implication Anderson localization) ...
5
votes
1answer
62 views

Equivalence classes of mappings from $T^{2}$ to an arbitrary space $X$

I was reading the paper "Homotopy and quantization in condensed matter physics", by J.E Avron et al. ( http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.51.51). There they have classified the ...
1
vote
0answers
34 views

Problems and applications of Topoligcal Insulators today [closed]

I am learning about topological insulators in my applications of quantum mechanics class and i was wondering why exactly are they important? Who cares if the material only conducts on the surface? ...
0
votes
0answers
19 views

Bloch Hamiltonian of low energy edge mode of a 2D topological insulator

First time to pose a question here. It's a Hamiltonian appears in this paper https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.87.137 The equation (71) $$ h_0(q) = v q\sigma^y+m\sigma^x-\mu ...
2
votes
0answers
36 views

$\mathbb{Z}_2$ topological insulators which obey inversion symmetry as well

According to Fu & Kane (2006), systems with simultaneous time-reversal invariance and inversion symmetry have their $\mathbb{Z}_2$ topological invariant given by the product of the parity ...
1
vote
0answers
51 views

Compute $Z_2$ Invariant of 2D Topological Insulators without Computing the Eigenstates

For 2D Time-Reversal Invariant systems ($T H(\vec{k}) T^{-1} = H(-\vec{k}) $), there is a formula by Fu-Kane-Mele in order to determine whether the system belongs to either one of distinct topological ...
2
votes
0answers
56 views

How are topological invariants constructed?

I've seen several different definitions for what are called topological invariants, for instance in the context of Majorana unpaired modes, by Kitaev: http://arxiv.org/abs/cond-mat/0010440 ...
2
votes
0answers
52 views

What is the physical mechanism of the topological phase transition driven by temperature?

The topological property of topological insulators (TIs) is characterized by the non-trivial topological invariants of their band structures, such as $Z_{2}$ topological invariants. While it's clearly ...
1
vote
1answer
102 views

Questions on gapless edge excitations in symmetry-protected topological state

I am studying a one-dimensional bosonic system with $ U(1) \rtimes Z_2^T$ symmetry numerically, which might has a symmetry-proteced toplogical(SPT) phase. I have several questions about the ...
1
vote
0answers
54 views

How to find dispersion relation for 1 d topological insulator?

Is it correct to write the dispersion relation for following Hamiltonian where $\sigma_{x}$ act in spin space and $\tau_{x}$ acts in pseudo spin particle hole spin $H_{BdG} (k)=(\xi_{k}+B\sigma_{x}+u ...
1
vote
0answers
31 views

What is the different between topological order and Landau's order in a system

I have thought about topological order for a long time, but I am still confused it. Roughly speaking in my understanding, the topological state is the eigen-state of some special symmetry such time ...
1
vote
0answers
56 views

Berry phase integration [closed]

In the calculation of Berry phase for Dirac fermions one comes across the integral $$\gamma = \oint_c d\mathbf{k}\cdot i \langle u_{\pm}(\mathbf{k})|\nabla u_{\pm}(\mathbf{k})\rangle = \pi.$$ Can ...
2
votes
2answers
74 views

Which Symmetry class and what kind of topological invariant for $2D -p+ip$?

What kind of topological invariants are there for $2D-p+ip$ topological superconductor and to which symmetry class it belongs to?
2
votes
0answers
79 views

Interacting Chiral topological invariants using Green function

We can calculate the topological invariants for 1D interacting topological insulators as $n=\frac{\text{Tr}}{2\pi i}\oint_cG\partial_kG^{-1} $ where as for interacting chiral topological ...
1
vote
1answer
123 views

Does time reversal symmetry hold for (kitaev model) 1D spinless $p-$ wave superconductor?

The hamiltonian 1D spinlesss p wave superconductor can be written as $$ H=\sum_k \phi_k^\dagger \begin{pmatrix} \xi(k) & 2i\Delta \sin(k)\\ -2i\Delta \sin(k ) & -\xi(k)\end{pmatrix}\phi_k $$ ...
3
votes
2answers
157 views

What symmetry class does 1D spinless $p$-wave superconductor belongs to?

$Z_{2}$ topological invariant exist for Kitaev model. What symmetries does it conserve? And to what symmetry class it belongs to? The hamiltonian for kitaev model can be written as $$ H=\sum_k ...
0
votes
0answers
52 views

What is meant by time reversal invariant momenta (TRIM) point of the Brillouin zone (BZ) and how to determine them in 3D reciprocal space?

In literatures related to topological insulators, I have frequently encountered the term "time reversal invariant momenta" or TRIM points in the Brillouin zone of the crystal. In many literatures, I ...
0
votes
2answers
56 views

What can we learn from a band structure diagram?

Other than the band gap and its magnitude, what are the things that we can immediately learn about the properties of the material just by glancing at its band structure? Can we say something about ...
0
votes
0answers
42 views

Question about the argument for robust edge state in topological insulator

As a time reversal protected insulator ($Z_2$ insulator), we can argue that edge states are stable when there exists disorder because time revesal symmetry makes some dynamical matrix elements vanish. ...
0
votes
1answer
37 views

What is “trivial” about the trivial topological superconducting phase?

Once more I am stuck on my favorite word: "trivial". I am reading a bunch of stuff about topological superconductors at the moment and people keep talking about having to distinguish between the ...
1
vote
1answer
91 views

Does the surface topological order on the boundary of 3D topological insulator also have topological ground state degeneracy?

The boundary of a 3D topological insulator can be fully gapped (under strong interaction) by the surface topological order without breaking the symmetry (see Fidkowski-Chen-Vishwanath, ...
2
votes
1answer
88 views

How to distinguish between a topological state from from a non-topological one?

How to distinguish between a topological state from from a non-topological one? Is there any standard procedure for identifying the topological features of a given hamiltonian? In general what are the ...
5
votes
1answer
202 views

“Topological” notions in physics

I've been trying to make sense recently of the usage of 'topological' in various fields of physics, and get sort of an intuition for what this means in context. This all boils down to my main question ...
0
votes
0answers
37 views

Intuitive way to explain why the edge states of topological insulators are dissipationless?

I was just wondering if there was an intuitive way to see why the edge states of topological insulators are dissipationless. More mathematically, is there a quick proof for why the edge states are ...
2
votes
0answers
97 views

Pedagogical introduction to vertex, domain wall, and kink

Recently, Majorana fermion becomes hot in condensed matter physics. The concepts: vertex, domain wall, and kink often appear in these articles about Majorana fermion. I have no idea about the ...
3
votes
1answer
147 views

What's the difference between insulators and topological insulators?

What's the difference between insulators and topological insulators? When I asked some people about this, they told me that "because the topological insulators have gapless edge states,...", but what ...
3
votes
2answers
216 views

Topological insulator vs. topological superconductors in any dimension

My question today is simple. What is the difference between a topological insulator and a topological superconductor? How that difference depends on the dimensionality of space(time)? What is the ...
2
votes
1answer
116 views

Particle-hole symmetry and the sign of the superconducting gap

Time-reversal (TR) symmetry leads to topological insulator property. As expected, the topological invariant depends on TR (Pfaffian) operator. TR+particle-hole symmetry leads to topological ...
2
votes
1answer
67 views

How does bulk-boundary correspondence works for various cases of time-invariant system?

I was pondering this question after I read this review: M. Zahid Hasan and Charles L. Kane. “Colloquium: topological insulators.” Reviews of Modern Physics 82, no. 4 (2010): 3045. (arXiv) How do ...
1
vote
0answers
98 views

Dirac fermion in curved space

What is the connection between Dirac equation in curved space-time and effective Hamiltonian for Dirac fermion in curved space (topological insulators)? I am trying to find this connection but I am ...
2
votes
2answers
193 views

Who proposed the bulk-edge correspondence principle?

Who proposed the bulk-edge correspondence principle? The principle is often quoted in counting the number of zero energy states localized on the interface between two insulators with distinct band ...
0
votes
1answer
87 views

Regimes of Josephson junction

There are several formulas to describe critical current in Josepshon S-N-S junction mainly based on Eilenberger and Usadel equations for quasi-classical Green's functions. The starting point is the ...
1
vote
2answers
123 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
87 views

Topolgical insulators order parameter

For topological insulators Is there any way to define order parameter for topological phase transitions?
0
votes
1answer
158 views

Is phosphorene a topological insulator?

All of the other "-ene" materials (silicene, germanene, stanene, and even graphene) are topological insulators. Phosphorene and these other materials all have honeycomb lattices and would appear to ...
3
votes
1answer
281 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 ...
5
votes
0answers
146 views

What are the prerequisites to study topological quantum computation/topological phases of the matter? [closed]

I am an undergraduate student and I would like to approach the subject of topological order with focus on topological quantum computation, I know (very) little QFT and basic algebraic topology (if ...
2
votes
1answer
299 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
31 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 ...
8
votes
0answers
430 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 ...
3
votes
0answers
236 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
71 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 ...
0
votes
1answer
232 views

Phase factor for nearest neighbor hopping in the Haldane Model

In Haldane's model, he imagines a staggered magnetic field in graphene where the net flux through a unit cell is zero. To model this, he has a phase factor in next nearest neighbor hopping on the ...
9
votes
1answer
671 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
152 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 ...
0
votes
1answer
456 views

How to derive the spin-orbit term in Kane Mele model?

The Kane mele model is a famous quantum spin hall model on honeycomb lattice (C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)). The Hamiltonian is $$H = - t\sum\limits_{\left\langle ...
3
votes
1answer
194 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 ...
1
vote
2answers
166 views

Which of these two different forms of spin-orbit interaction is correct?

I am seeing the spin-orbit interaction in two different ways: $\lambda [\mathbf{p} \times \nabla V]\cdot \sigma$ $\lambda [\nabla V \times \mathbf{p}]\cdot \sigma$ I don't see how these two ...