All Questions
58
questions
1
vote
1
answer
113
views
What is the Haldane gap?
The Haldane Phase is a topological phase of matter in which a Haldane gap opens due to the breaking of either time-reversal symmetry or inversion symmetry. Physically speaking, what is the "...
- 43
1
vote
0
answers
37
views
How to numerically calculate Zak phase for SSH3 model?
The k-space hamiltonian of SSH3 model with nearest neighbour hopping is given by H(k)= \begin{bmatrix}
0 & u & w e^{-ika} \\
u & 0 & v \\
w e^{ika} & v & 0
\end{bmatrix}
...
0
votes
1
answer
69
views
Sublattice symmetry and the Fermi level
I am a math student who is learning topological phases from this website.
Let's assume the fermi level is zero. For the graphene, the sublattice symmetry $\sigma_z H \sigma_z = -H$ makes the ...
- 125
1
vote
0
answers
75
views
Topological properties of twisted TMD homobilayers
I'm reading this article about twisted TMD homobilayers (https://arxiv.org/abs/1807.03311) and there are certain topological properties that I don't understand:
On page 3, in the paragraph next to Fig ...
- 41
0
votes
0
answers
68
views
Absence of topology in semi-dirac materials
Good morning everybody, I am facing a problem when calculating the topological invariant in a semi-dirac system, whose Hamiltonian is:
$$
H=k_x^2\sigma_x+k_y\sigma_y
$$
My question is that this ...
4
votes
2
answers
267
views
Why are topological materials/phases "exotic"?
From what I understand, when a system has topological order, any local perturbation doesn't change the phases and thus its properties. This would suggest that it should be really easy to find ...
- 423
1
vote
0
answers
57
views
The $\rm SO(8)$ invariant interaction piece in Fidkowski and Kitaev's model
In this paper (arXiv link), the authors demonstrate the existence of a quartic interaction $W$ involving the 8 majorana operators $c_1 \ldots c_8$ (eq. 8) which is invariant under an $\rm SO(7)$ ...
- 151
0
votes
2
answers
111
views
What is the physical meaning of adiabatically varying the wavevector $k$ as a parameter to calculate the Chern number for topological effects?
Could it mean something like applying a weak electric field and perturbing the band structure? Or some other weak perturbation? Or is that the wrong idea?
- 107
5
votes
2
answers
280
views
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
15
votes
4
answers
989
views
What is the topological space in “topological materials/phases of matter”?
I’m embarrassed to admit that after sitting in on several “topological physics” seminars, I still don’t understand the basic ideas of the area. In particular, when physicists talk about the “topology” ...
- 3,407
2
votes
1
answer
694
views
Calculation of Bulk and edge states in SSH model
I am reading “A Short Course on Topological Insulators” by János K. Asbóth. et.all., and want to calculate the Bulk and edge state of the SSH model (Chapter 1) to drive the energy spectrum in Fig. 1....
- 303
1
vote
1
answer
910
views
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
views
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
1
vote
0
answers
32
views
Phase freedom of the edge states in topological insulator
Suppose that we consider the BHZ-like Hamiltonian of the form
$$
H_{bulk}=\left(M-B k^{2}\right) \tau_{z}-A k_{x} \tau_{y}+A k_{y} \sigma_{z} \otimes \tau_{x}
$$
where $\tau_i $ acts on the orbital ...
- 503
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