Questions tagged [topological-insulators]
Topological insulator are materials formed by an insulator bulk and metallic surfaces with topological origin. These materials may be important for developments in Quantum Computing and Spintronics.
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Why surface and bulk states of topological insulators (TI) have different topological invariants and how it leads to conductive states?
I am trying to understand how TIs work. Right now, the main thing I understand is that the surface states and bulk states have different topological invariants. This leads to spin orbit coupling being ...
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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 "...
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Role of particle number conservation for SPT order
It is shown in https://arxiv.org/abs/1111.6341, that non interacting SPT phases of fermions are at least protected by U(1) symmetry (a.k.a. particle number conservation). I wondered if this result ...
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Why do the edge states of a topological insulator always have zero energy?
Recently, I am learning the topological insulator, I learned about SSH model, and found out that the edge states of topological insulator always have zero energy, but on the other side,we define edge ...
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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}
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Is there a topological invariance/winding number for non-translation invariance system?
My question is: Is there a topological invariance/winding number for non-translation invariance system? For example, if we modify the interacting parameter in SSH model, such that it depends on the ...
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Weyl crystal with broken time reversal symmetry (TRS) and spin-momentum locking
We know that the stability of Weyl points crucially requires that the bands involved are non-degenerate. Otherwise, there can be terms that cause band hybridization within the degenerate subspaces and ...
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Meaning of wavevector in SSH model [closed]
If we solve the hamiltonian of the following form in the SSH model,
You will get an eigen vector of the following form.
I am having difficulty interpreting this eigen vector.
According to this eigen ...
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Can topologically non-trivial edge states exist without an energy gap?
I am relatively new to the field of topological materials, and I came across a paper that claims that they found topologically non-trivial states in a material. Basically, the authors found a type-I ...
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Can the hybridization of edge states in the 1D SSH model be observed numerically?
So I was reading the lecture notes by Asboth on topological insulators . In the first chapter the SSH model is discussed :
$H_{SSH} = \sum_{i = 1}^N v|i,A\rangle \langle i,B | + h.c. + \sum_{i = 1}^{N-...
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Plotting edge modes for a tight binding Hamiltonian with superconducting pairing
I would like to obtain a plot such as the one in the first picture for the eigenstates of the Hamiltonian reported in the second picture. The problem here is that we have superconducting pairing and I ...
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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 ...
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How do I find the matrix for the Su-Schrieffer-Heeger model's Hamiltonian?
I will not bother to write down the tensor product in the joint basis of A and B here in this post, where A and B are atoms/electrons and m denotes a unit cell.
The Hamiltonian for this model is given ...
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How can a Soliton be neutral in the Su-Schrieffer-Heeger (SSH) model when it carries an electron?
I apologize if this is a trivial question. I am currently studying Girvin and Yang's book where they try to explain Spin-charge separation for the Solitons in the SSH model.
To my understanding, a ...
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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 ...
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