All Questions
Tagged with topological-insulators topological-phase
36
questions with no upvoted or accepted answers
6
votes
0
answers
341
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 ...
- 1,191
5
votes
0
answers
256
views
Topolgical insulators order parameter
For topological insulators
Is there any way to define order parameter for topological phase transitions?
- 331
4
votes
0
answers
204
views
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
4
votes
0
answers
1k
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Chiral symmetry vs quantized Zak phase
I've been doing some condensed matter research about the topological phases in one dimension system and have some questions.
I've heard that the chiral symmetry leads to the $\pi$-quantization of Zak ...
- 766
4
votes
0
answers
786
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About the $Z_2$ topological invariant
In Kitaev 2001 it is shown that the topological invariant $Z_2$ in a topological superconductor (Class D or BDI, one dimensional) can be defined as
$$
(-1)^\nu={\rm sign\, Pf} [ A ]={\rm sign\, Pf}[ \...
- 3,543
4
votes
0
answers
3k
views
Compute $Z_2$ Invariant of 2D Topological Insulators without Computing the Eigenstates
For 2D Time-Reversal Invariant systems ($T H(\vec{k}) T^{-1} = H(-\vec{k}) $), there is a formula by Fu-Kane-Mele in order to determine whether the system belongs to either one of distinct topological ...
- 2,024
3
votes
0
answers
75
views
Infinite stacking of integer quantum Hall systems
Let us consider a (3+1)-dimensional system $\mathcal{H}$ constructed by stacking (2+1)-dimensional integer quantum Hall systems $\mathcal{H}_\text{Hall}$, e.g., $E_8$ bosonic systems (or $\sigma_H=1$ ...
- 813
3
votes
0
answers
131
views
Berry phase from Bloch wave functions in the basis of Wannier functions
The formulate to calculate berry phase for Bloch wave functions is
$$
\gamma = i \sum_{n\in occ}\int_{\mathcal{C}} dk \langle \psi_k^n|\partial_k|\psi_k^n\rangle,
$$
where $|\psi_k^n\rangle$ is a ...
- 337
3
votes
2
answers
247
views
Homotopy classification in ten-fold way
I am trying to understand algebraic invariants in topological insulators and topological superconductors through homotopy. But I encounter kind of a conceptual question. Let's say we have a second ...
- 141
3
votes
0
answers
119
views
Polarization to define trivial and non trivial topological phases?
Polarization is well defined for particle hole symmetry systems, so can we use polarization to identify topological phases? for example polarization can have possible value
$$P=0 \quad or \quad1/2$$
...
- 143
3
votes
0
answers
164
views
What is the physical mechanism of the topological phase transition driven by temperature?
The topological property of topological insulators (TIs) is characterized by the non-trivial topological invariants of their band structures, such as $Z_{2}$ topological invariants. While it's clearly ...
- 129
2
votes
0
answers
53
views
How can we judge the topological property of a material by looking at it's band structure?
I am a beginner of studying topological insulator. I want to ask some general question in this area to clarify my understanding. May be I am asking wrong, hope you can point me out.
If certain ...
- 263
2
votes
0
answers
84
views
Must helical edge states be protected by time-reversal symmetry?
In a lattice system that exhibits quantum spin Hall effect (QSHE), like topological insulators in 2D or 3D, we call a pair of counter-propagating gapless edge states with opposite spin helical edge ...
- 71
2
votes
0
answers
79
views
Topology of Helium 3A and 3B
The question concerns the topology and dimensions of Helium 3A and 3B
A. The Helium 3A phase shows the same low energy excitations as those of a 2 spatial dimensional chiral p-wave superconductor --- ...
- 4,336
2
votes
2
answers
459
views
What does "parity eigenvalue" mean in Fu-Kane formula?
I'm studying the online course "Topology in Condensed Matter", in the QSHE section (<https://topocondmat.org/w5_qshe/fermion_parity_pump.html>), I've studied the Fu-Kane formula
$$ Q=\...
- 71