Questions tagged [skyrmion]
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Helicity vs vorticity in skyrmion lattice
I am interested in clarifying the difference between the helicity and vorticity of a skyrmion.
There has been interest in centrosymmetric skyrmion hosting materials due to centrosymmetry giving a ...
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Concise formula for Skyrmion number of a four-band Hamiltonian
The Haldane model on the honeycomb lattice is often written as
$H=\sum_{i=0}^3 \vec{d}_i\cdot \vec{\sigma}_i$
where $\vec{\sigma}$ is the vector of Pauli matrices and $\vec{d}$ is a vector of ...
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Hopfion with only in-plane vortex rather than skyrmion along the torus?
A simple torus-like hopfion with hopf charge $Q_H=1$ will typically exhibit a skyrmion at each slice cutting the toroidal circle. What if the skyrmion is replaced by an in-plane 2D vortex, i.e., we ...
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How can I see the Calculation process of the skyrmion number?
I'm having a problem calculating a skyrmion number.
below equations are from Wikipedia - Magnetic skyrmion
I know that I should use the chain rule with the polar, spherical coordinate system.
But I ...
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What is the modern status on the Skyrmion theory of baryons?
It was noticed in the 1960s that chiral perturbation theory, describing the goldstone-bosons (pions) of the breaking $SU(N_f)_L \times SU(N_f)_R \to SU(N_f)_V$ of the chiral symmetry, has solitonic ...
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Circular symmetry argument in integration
I'm working through a book on magnetic skyrmions and in some calculations the integral
$\int d^2 \vec{r}\, \left(\partial_x \vec{S}\right)\cdot\left(\partial_y \vec{S}\right)$
pops up, where we ...
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What is the difference between a skyrmion and a magnetic vortex?
Skyrmions and magnetic vortices are spin structures occurring in magnets.
What are the differences between them? More specifically, I would like to understand their origin and how to distinguish them.
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A primer on topological solitons in scalar field theories
As the title suggests I want to learn more about topological solitons in scalar field theories. I am searching for a resource which is self-contained, in the sense that it also explains the ...
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How does the Mermin-Ho theorem handle singularities arising from the hairy ball theorem?
I am reading about the derivation of the Mermin-Ho relation in chapter III. B of (Kamien, 2002) and trying to understand how it fits with the hairy ball theorem.
Assuming you have a unit vector $\hat{...
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What is physical significance of $k$-space topology?
I am working with topological materials and I do understand what topology is. While reading papers, I am not able to understand the "nontrivial k-space topology". How skyrmions are mostly ...
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How "hedgehog" or instanton event changes the configuration of neel vector in 2D antiferromagnet?
The definition of "hedgehog" or instanton event here is "a space-time event where the skyrmion number Q changes by $\pm1$ is called a hedgehog" (ref.1 & 2).
A nice figure ...
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Skyrmion number
The skyrmion number is defined as
$$n=\frac{1}{4\pi}\int\mathbf{M}\cdot\left(\frac{\partial\mathbf{M}}{\partial x}\times\frac{\partial\mathbf{M}}{\partial y}\right)dxdy$$
where $n$ is the topological ...
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What are Skyrmion bubbles?
what exactly is the difference between a skyrmion and a skyrmion bubble? Thanks.
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How to derive the Einstein-Skyrme equations?
I would like to derive the Einstein-Skyrme equations. The action can be read as
\begin{equation}
S[g,U] = \int d^{4}x\sqrt{-g}\biggl[R + \frac{K}{4}Tr\bigg(A^{\mu}A_{\mu} + \frac{\lambda}{8}F_{\mu\...
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What does topologically stable mean?
I am working on an article about skyrmion manipulation and it is written that those particles are "topologically stable particle-like spin configurations that carry a characteristic topological charge ...
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No global monopoles in QCD
If a global symmetry gets both spontaneously and explicitly broken, the explicit symmetry breaking pattern is crucial for understanding the formation of topological defects.
For example, in the axion ...
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Number of baryons in the Skyrme model
In QCD, the Eightfold Way organizes the number of baryons with respect to their flavor and color quantum numbers: for three light $(u,d,s)$ quark constituents, a spin-(1/2) baryon octet and a spin-(3/...
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Skyrmion of pseudo-scalar mesons and vector mesons
I had heard statements that Skyrmion of pions (pseudo-scalar mesons) cannot be an object like baryon, however, Skyrmion of vectors mesons may indeed form an object like baryon. For example, see this ...
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Non-chiral skyrmion v.s. Left/Right chiral skyrmion
A skyrmion in a 3-dimensional space (or a 3-dimensional spacetime) is detected by a topological index
$$n= {\tfrac{1}{4\pi}}\int\mathbf{M}\cdot\left(\frac{\partial \mathbf{M}}{\partial x}\times\frac{...
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half Skyrmion vs Meron
Is there a difference between a half skyrmion and a meron? I'm asking this in regard to half skyrmion theories of High Tc Superconductors. It would be interresting to know if the proposed half ...
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