All Questions
Tagged with topological-insulators topological-phase
99
questions
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103
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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
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0
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33
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
1
answer
163
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Is there a Majorana representation for toric code
Kitaev's toric code is known to be the Z2 gauge field theory, which suggests that there might exists a Majorana representation for the toric code, e.g., Majorana + Z2 gauge field. Hence, I wonder if ...
- 81
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41
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Dealing with discontinuous phase issue in computing winding number numerically
Consider a 1D SSH model with winding number given by
$$\nu = \frac{1}{2\pi i}\int_{-\pi}^\pi d\phi,$$
where $d\phi$ is the change in phase of the eigenvectors between nearby $k$ points. The phase is ...
- 101
1
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115
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Time reversal in a two-band system
Suppose I have a 3D system of spinless fermions described by the following two-band model Hamiltonian:
$$
H(\vec{k})=\vec{d}(\vec{k}) \cdot \vec{\sigma}
$$
where $\vec{d}=\left(-\sin k_{x},-\sin k_{y},...
- 43
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0
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65
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Relation between Displacement Operator and Winding number
I am trying to implement a paper [https://arxiv.org/abs/2003.06086] using quantum computing techniques. In the supplementary material[SM] with the main paper, they introduce a displacement operator ...
- 53
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1
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69
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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
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63
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Topological Insulators with different spin band
To obtain a topological band insulator, we usually start with two bands with either spin up or down. If these bands now get 'inverted', they will cross. When there is coupling of these two bands such ...
- 137
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29
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Topological Insulator [closed]
What effect on the Brillouin zone (torus) after applying the magnetic field? As in real space, pressure deforms the torus and up to a certain pressure, this remains invariant topologically. Similar to ...
3
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73
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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
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238
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Topological phase and Chern number
the relation between topological phase and Chern numbers is unclear to me.
For Haldane model if the Chern numbers of its two bands go from (+1,-1) to (0,0), we say that it goes from topological phase ...
- 41
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130
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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
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2
answers
275
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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
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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
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68
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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 ...
