All Questions
9
questions
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Topological Insulator [closed]
What effect on the Brillouin zone (torus) after applying the magnetic field? As in real space, pressure deforms the torus and up to a certain pressure, this remains invariant topologically. Similar to ...
5
votes
2
answers
280
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How to see that the trivial insulator is trivial?
I have been trying to better understand gapped phases of matter — which may be "topological" or "trivial" — and I have run into the problem that I don't really understand the ...
- 8,343
1
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1
answer
910
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What is a bulk state and bulk bands?
I am a bachelor student and I started studying topology and I came across two terms I have never seen before: Bulk band structure and bulk states.
Can someone explain these two terms or provide me a ...
- 155
1
vote
1
answer
102
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Why does particle-hole symmetry in 1D lead to a $Z_2$ topological invariant?
From the well-known AZ Tenfold Classification Table, a 1D system with square-positive particle-hole symmetry belong to class D and hence is characterized by a $Z_2$ topological invariant. I suppose ...
- 66
2
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0
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53
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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
924
views
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
1
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0
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81
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Algebra of Time Reversal and Particle Hole Symmetry in 10-fold Classification of Topological Insulator/superconductor
In the ten fold classification of TI/TSC, when time reversal symmetry $\mathcal{T}$ and particle hole symmetry $\mathcal{P}$ are both present, i.e., in the symmetry classes BDI, DIII, CII, CI, for all ...
- 407
6
votes
1
answer
387
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Is topological surface state always tangential to bulk bands?
Think of a topologically nontrivial $D$-dimensional system. Its bulk bands form a $D+1$-dimensional manifold ($+1$ from energy). Its surface/edge bands form a $D$-dimensional one. Is the latter always ...
- 3,701
2
votes
2
answers
420
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 ...
- 366