All Questions
Tagged with topological-insulators topological-phase
98
questions
3
votes
2
answers
247
views
Homotopy classification in ten-fold way
I am trying to understand algebraic invariants in topological insulators and topological superconductors through homotopy. But I encounter kind of a conceptual question. Let's say we have a second ...
- 141
1
vote
1
answer
466
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Argument for number of edge states as topological invariant for SSH model
I am currently reading the book "A short introduction to Topological insulators" by Asboth etal.
In the first chapter on SSH model, they argue (see sec 1.5.3) that number of edge states is a ...
- 43
2
votes
0
answers
53
views
How can we judge the topological property of a material by looking at it's band structure?
I am a beginner of studying topological insulator. I want to ask some general question in this area to clarify my understanding. May be I am asking wrong, hope you can point me out.
If certain ...
- 263
5
votes
1
answer
473
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About Chern insulator
I know when we talk about Insulator, U(1)charge symmetry naturally exists.
But in this article:Quantum phase transitions of topological insulators without gap closing, the author claims that:
"...
- 61
2
votes
0
answers
84
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Must helical edge states be protected by time-reversal symmetry?
In a lattice system that exhibits quantum spin Hall effect (QSHE), like topological insulators in 2D or 3D, we call a pair of counter-propagating gapless edge states with opposite spin helical edge ...
- 71
2
votes
0
answers
79
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Topology of Helium 3A and 3B
The question concerns the topology and dimensions of Helium 3A and 3B
A. The Helium 3A phase shows the same low energy excitations as those of a 2 spatial dimensional chiral p-wave superconductor --- ...
- 4,336
1
vote
1
answer
82
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Why topologically non-trivial materials are robust againist any external perturbations or defects?
Topologically non-trivial materials are insensitive to perturbations or defects. How can I prove it mathematically?
I thought of making the first-order perturbation term zero.
$$\left< \psi \right|...
- 1,348
5
votes
1
answer
484
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Difference between "ordinary" quantum Hall effect and quantum anomalous Hall effect
I am reading a review article on Weyl semimetal by Burkov where he writes, top of page 5:
A 3D quantum anomalous Hall insulator may be obtained by making a stack of 2D quantum Hall insulators [Ref. ...
- 508
1
vote
1
answer
259
views
Chern number for nonintracing hamiltonian while bands crossing
Is it possible to define and calculate chern number for two bands while they're crossing each other?
- 13
5
votes
1
answer
924
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Why does an energy band crossing the Fermi energy mean the gap closes?
This online course on topology in condensed matter states the following:
We say that two gapped quantum systems are topologically equivalent if their Hamiltonians can be continuously deformed into ...
- 3,986
4
votes
1
answer
200
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Bosonic SPT phases with time reversal and a $Z_2$ symmetry
Consider a bosonic system with time reversal symmetry $\mathcal{T}$ and a unitary on-site $\mathbb{Z}_2$ symmetry. Suppose the symmetry is realized in a special way such that $$\mathcal{T}^2= (-1)^B$$ ...
- 407
2
votes
2
answers
459
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What does "parity eigenvalue" mean in Fu-Kane formula?
I'm studying the online course "Topology in Condensed Matter", in the QSHE section (<https://topocondmat.org/w5_qshe/fermion_parity_pump.html>), I've studied the Fu-Kane formula
$$ Q=\...
- 71
2
votes
0
answers
71
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Mutual statistics between dyons (charge-monopole composite)
I am asking for some intuitive understanding between two dyons with $(e,m)$ in 3-dimensional space. Here the magnetic charge $m$ is normalized as
\begin{eqnarray}
m=\int_{S^2}\frac{B}{2\pi}\in\mathbb{...
- 813
1
vote
1
answer
232
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Alternatives for calculating topological invariants in topological materials
My questing is regarding the different alternatives for calculating topological invariants in topological materials protected by symmetry, specially time-reversal invariant topological insulators, ...
2
votes
0
answers
141
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Does flat band imply localization?
Consider the Kitaev chain, whose Hamiltonian is as follows:
$$ H = -\mu \sum_n c_n^\dagger c_n -t\sum_n (c_n^\dagger c_{n+1} + \mathrm{h.c.}) +\Delta \sum_n (c_n c_{n+1} + \mathrm{h.c.}) $$
I have ...
- 171