All Questions
Tagged with topological-insulators topological-phase
98
questions
2
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0
answers
339
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About symmetry constraints in momentum space
When people study symmetry protected topological phases, certain symmetry constraints are enforced on the Hamiltonian. Specifically, for non-interacting fermionic systems, we could focus on the ...
- 171
0
votes
1
answer
321
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Meaning of complex pairing terms in Kitaev chain
I am studying some properties of the one dimensional Kitaev chain, which has the following form:
$ H = -\mu \sum_n c_n^\dagger c_n - t \sum_n (c_{n+1}^\dagger c_n + h.c.) + \Delta \sum_n (c_n c_{n+1} ...
- 171
1
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0
answers
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
7
votes
1
answer
201
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Time-reversal (explicitly) broken surface of $(3+1)$-dimensional topological insulator
Let us consider the surface of $(3+1)$-dimensional topological insulator, which is protected by the charge conservation $U(1)_Q$ and a time-reversal symmetry $\mathbb{Z}_2^T$. Such a surface, if not ...
- 813
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60
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Why are degenerate ground states interesting?
Studying the Su-Schrieffer-Heeger chain I have learned that the model has two different phases, one which is called topological and the other one trivial. In the notes it says that these phases are ...
- 1,772
2
votes
1
answer
397
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What are the applications of edge states in 1D topological systems?
In 2D, we get robust conducting edges. In 3D, we get robust conducting surfaces. These are interesting because we can possibly utilise this robustness for protected electron transport (or light ...
- 351
3
votes
1
answer
1k
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The surface states and Fermi arcs in Weyl semimetals
I'm confused about surface states in Weyl semimetals. Assume that we have a single pair of Weyl points and the Fermi level turned to this points. In this https://arxiv.org/abs/1301.0330 paper the ...
- 341
1
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1
answer
198
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Do topological transitions only occur at Dirac points?
Topological phase transitions happen when the band gap closes. It is not true that all band crossings are topological.
There are Dirac (linear) band crossings, quadratic band crossings, Dirac-like ...
- 351
4
votes
0
answers
204
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Gapless modes at the boundary between topological insulator and normal insulator
I am currently learning about topology in condensed matter physics. I think I understand most of how topological indeces come about and differences between Z and Z2 indeces and the symmetries that ...
- 93
1
vote
1
answer
426
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Is the quantum Hall state a topological insulating state?
I am confused about the quantum Hall state and topological insulating states.
Following are the points (according to my naive understanding of this field) which confuse me:
Topological insulator has ...
- 1,335
3
votes
1
answer
146
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Experimental confirmation of Majorana modes in Kitaev chain
I'm confused about majorana modes at the edge of Kitaev chain, what do we seek in experiment? When we first define this one we write the creation and annihilation operators as:
$$a^{+}=\frac{1}{2}(\...
- 341
6
votes
1
answer
236
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Topological materials and fractionalized excitations
I've been told several times that topological materials (such topological insulators) must have "fractionalized" excitations. Equivalently, if a material does not have fractionalized excitations, it ...
- 225
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
6
votes
1
answer
320
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Formula for the topological invariant for each of the symmetry classes
Is there a reference that systematically derives the topological invariant/winding number for all the ten symmetry classes in Altland and Zirnbauer's periodic table? For example, in this answer, there ...
- 61
1
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0
answers
29
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Linking phase of flux lines and excitation energy of monopole
I am reading this paper and on the left-hand side of pp.10 it states the following relation between linking phase and excitation energy of monopole:
Now the $\theta = \pi$ term in the bulk implies ...
- 351