All Questions
Tagged with topological-insulators topological-phase
98
questions
0
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424
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Winding number of SSH model 3
SSH model can be written as
$$H=-\sum_n\big[Jc_n^\dagger d_n + J'd_n^\dagger c_{n+1}\big]+h.c.$$
in Fourier space
$$H(k)=
\begin{bmatrix}
c_k^\dagger && d_{k}^\dagger
\end{bmatrix}
\begin{...
- 1,335
28
votes
3
answers
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What does the Chern number physically represent?
In 2D the Chern number can be written as
$$C_m=\frac 1{2\pi}\int_{BZ}\Omega_m(\mathbf k)\cdot d^2 \mathbf k$$
where we are integrating over the Brillouin zone.
In 2D this is equivalent to finding ...
- 1,189
3
votes
1
answer
241
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Why is the flux quantized in 4D quantum Hall effect?
I am reading "Topological Field Theory of Time-Reversal Invariant Insulators" by Qi, Hughes, and Zhang (https://arxiv.org/abs/0802.3537). It argues that time reversal invariant (TRI) insulators in 2+1 ...
- 464
4
votes
0
answers
1k
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Chiral symmetry vs quantized Zak phase
I've been doing some condensed matter research about the topological phases in one dimension system and have some questions.
I've heard that the chiral symmetry leads to the $\pi$-quantization of Zak ...
- 766
2
votes
1
answer
228
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Units related to chemical potential and orbital magnetization
I am studying this paper: Physical Review B 74, 024408 (2006) (arxiv)
Abstract
We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the ...
- 486
6
votes
1
answer
340
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Is this a topological $\mathbb Z_2$ (Majorana-)invariant in *any* dimension?
Consider a non-interacting superconducting Hamiltonian in an arbitrary dimension. This is most conveniently expressed in terms of Majorana modes, which are defined as $$\gamma_{2n-1} = c_n + c_n^\...
- 9,081
0
votes
2
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868
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Chern number for the systems with open boundary conditions
For two-dimensional materials with periodic boundary conditions, we can solve the Bloch states and substitute them into the definition of Chern number, as shown in the picture:
In the case of open ...
3
votes
1
answer
2k
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Chern number in one-dimensional system
As the title, could we define Chern number for condensed matter systems with one spatial dimension? E.g. the 1D Su-Schrieffer–Heeger (SSH) model.
2
votes
1
answer
332
views
Transfer matrix approach to the topological phases
The transfer matrix contains all the information. i.e., information about the edges and bulk. What new insight does the transfer matrix approach provide in the study of the topological phases of ...
- 177
1
vote
0
answers
117
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Is the 'Chern number' of a topological Kondo insulator an integer?
If you calculate the anomalous Hall conductance $\sigma_{xy}/\sigma_0$ for a simple complex hopping model at a whole band filling, this will equal an integer Chern number (given e=h=1).
I would like ...
- 167
9
votes
1
answer
559
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AKLT state and Nobel physics prize 2016
The AKLT Hamiltonian and the chain is described in Wikipedia, and also the page 17 of this year Nobel Prize advanced information
I have questions concerning the info released by nobelprize.org, and ...
user32229
6
votes
1
answer
1k
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Homotopy Theory for Topological Insulators
I'm trying to understand topological insulators in terms of homotopy invariants. I understand that in 2 spatial dimensions, we have Chern insulators since $$\pi_2(S^2) = \mathbb{Z}$$
One subtlety that ...
- 483
2
votes
1
answer
4k
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Berry phase in 1D materials
The Berry phase $\phi_B$ is the phase that an eigenstate acquires after its momentum vector goes around a circle at constant energy around the Dirac point.
It is defined as $\phi_B = -i \int \langle\...
- 359
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
2
votes
0
answers
228
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About Weyl superconductors and fractionalized Weyl semimetals
Recently, the experimental observations of Weyl fermion semi-metal have been made. Weyl fermion becomes very hot in condensed matter physics. I am confused about the Weyl superconductors and ...
- 291