All Questions
12
questions
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}
...
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
1
vote
2
answers
282
views
Edge state protection in Chern insulator
I have a confusion about the nature of topologically protected boundary states in the Chern insulator. Since the Chern insulator does not require any symmetries to be present in the system, what is ...
- 11
1
vote
1
answer
256
views
How to describe SSH chain with odd number of sites?
Usually when we discuss SSH(Su-Schrieffer–Heeger) chain, we discuss a chain with 2N atoms, with v the intra-cell coupling and w the inter-cell coupling. When N is infinite, the system becomes bulk, ...
- 442
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
0
votes
2
answers
332
views
What does "continuous transformation" mean with regard to the Hamiltonian of a system?
When dealing with topological phases of matter (topological insulators, quantum hall effect, etc...) one says that the system remains in the same phase as long as any continuous transformation of the ...
- 423
5
votes
1
answer
473
views
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
1
vote
1
answer
232
views
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, ...
1
vote
1
answer
426
views
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
28
votes
3
answers
23k
views
What does the Chern number physically represent?
In 2D the Chern number can be written as
$$C_m=\frac 1{2\pi}\int_{BZ}\Omega_m(\mathbf k)\cdot d^2 \mathbf k$$
where we are integrating over the Brillouin zone.
In 2D this is equivalent to finding ...
- 1,189
4
votes
0
answers
1k
views
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
views
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