All Questions
Tagged with topological-insulators topological-phase
98
questions
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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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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
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166
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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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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
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118
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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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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 ...
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75
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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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242
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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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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
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2
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282
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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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0
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75
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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 ...
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2
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267
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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
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279
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Detection of topological phases
In the book A Short Course on Topological Insulators (https://arxiv.org/abs/1509.02295) the authors start with a simple toy model, the SSH-Chain, which is a bipartite one-dimensional lattice with ...
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Why number of left-moving and right-moving edge states on a finite lattice system is equal?
I read an arguments about number of left-movers and right-mover in finite system in paper titled as
Antichiral Edge States in a Modified Haldane Nanoribbon. In second paragraph of introduction, it ...
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57
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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
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2
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111
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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
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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, ...
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280
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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 ...
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4
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989
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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
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Inversion Symmetry in Periodic Lattices
I am studying Short Course On Topological Insulator by J. K. Asboth, et.al.
In the context of inversion symmetry in section 3.2, the effect of inversion symmetry, $\Pi$, on the external degree of ...
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694
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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
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910
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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
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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 ...
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2
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332
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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
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Homotopy group for spin-1 BEC
Homotopy group can be used to classify topological defects. The procedure is
Find the Lie group $G$ that leaves the free-energy functional invariant when transforming $\psi$, where $\psi$ is the ...
- 169
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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
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2
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377
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Topological phases of matter
So according to this, scientists have discovered more than 5 states of matter we usually had that is the solid, liquid, gases, and Bose-Einstein-Condensate, and plasma. So how many topological phases ...
- 11