Questions tagged [spin-orbit]
Use this tag for questions relating to the "spin-orbit" effect/interaction/coupling/torque. This tag is often discussed in quantum mechanics and condensed matter physics. It is a relativistic effect that describes a single particle whose (linear or angular) momentum is coupled to the spin degree of freedom in the presence of a potential well.
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Why does mirror/inversion symmetry exclude nearest-neighbor spin-orbit coupling in the Kane-Mele model?
I've been reading about the Kane-Mele model and noticed that it does not include nearest-neighbor spin-orbit coupling, with explanations often pointing to mirror symmetry as the reason. Could someone ...
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The origins of the SOC in silicene
I read that silicene has a stronger SOC than graphene. As far as I know the SOC ~ $Z^4$. Thus, since silicon lies further in the periodic table, it explains why it has a stronger SOC than graphene. ...
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Rotation of spin orbit coupling matrix
In first-principle calculation, we could get different solutions for different directions of magnetization for ferromagnetic system.
I want to know the details about whether or when does the SOC ...
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Origin of anisotropic interaction in magnetic Hamiltonian in the absence of SOC
The general second-order interactions between two spins can be decomposed into three parts: isotropic Heisenberg interaction, antisymmetric DMI and anisotropic $\Gamma$ interaction.
\begin{equation}
\...
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Can a Foldy–Wouthuysen transformation of Dirac equation in an EM field highlight Thomas interaction?
Based on a previous question Is the Thomas precession a correction to a Lorentz transformation or an interaction? , Thomas precession can be seen as an additional weakly relativistic interaction to ...
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Is the Thomas precession a correction to a Lorentz transformation or an interaction?
In the heuristic derivations I have seen for the fine structure of hydrogen includes three terms spin-orbit coupling, Darwin term and corrections to the kinetic energy. For the spin-orbit coupling the ...
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Why spin orbit coupling leads to band splitting?
For a crystal with time-reversal symmetry, its band structure is double degenerate. When we turn on SOC, the band splits except for special points where Kramers' theorem applies.
How should I ...
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Empirical tight-binding sp$^3$s* band structure of semiconductors
I'm simulating on code the tight-binding sp3s* bandstructure of certain semiconductors, such as GaAs, AlP, InP, ZnSe, etc. with spin-orbit coupling at a temperature of $T = 0$ K but I'm having trouble ...
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How could spin-orbit coupling works?
I am not able to understand how does spin and orbital angular momentum interacts with each other, the spin magnetic field interacts with its own angular momentum magnetic field but how that can happen?...
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Can Zeeman effect be observed around black holes?
I'm trying to study the motion of charged-spinning test particles around a black hole immersed in the magnetic field. There will be spin-orbit coupling due to the spin of the particle, and external ...
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Magnetic field arising due to electron's orbital motion around the nucleus
My book writes -
The magnetic field in a reference frame fixed with the electron, arising from the orbital motion of the electron with velocity $\vec{v}$ in the electric field $\vec{E}$ (due to the ...
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Sodium spectrum and doublet: the 18 T field origin
The sodium spectrum is dominated by the bright doublet known as the Sodium D-lines at 588.9950 and 589.5924 nanometers. Their origin, as far as we know, is explained by quantum mechanics. The spin ...
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How spin orbit coupling breaks mirror symmetry?
I have been studying in several research papers with statement that spin orbit coupling breaks the all three mirror symmetry in cubic crystals when the magnetization direction is along the (110) ...
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What's the relationship between Term Symbol and Wave Functions?
I'm trying to represent the Term Symbols in terms of wavefunctions and/or arrows for the excited state of hydrogen atom $2p^1$: $^2P_{3/2}$ and $^2P_{1/2}$.
Ideas I have:
The sum of $2J+1=4$ and $2J+1=...
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Confusion of spin-orbit coupling in Hydrogen atom
I'm learning the fine structure of hydrogen and feel a little confused about the spin-orbit coupling term in the hamiltonian.
The corrected hamiltonian is:
$$H = \frac{\vec{P}^2}{2m}+ V(R)-\frac{\vec{...
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What is a p-wave superconductor in 1-dimension often referred in the Kitaev model? What term in the hamiltonian makes it P wave?
I am currently reading papers related to Majorana zero modes observation in 1D nanowire systems. I am very new to the field and I read everywhere that the presence of spin-orbit interaction, magnetic ...
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Why does the illustration below just show $J = 1/2$ and $J = 3/2$ for $n = 2$?
for example $p^4$ on $n = 2$, $l = 1$ would have $J = 2$ as $S = 1$ and $L = 1$. However there are just two not 4 levels for $J$ depicted here
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Spin orbit coupling in transitional metal dichalcogenides (TMDC)
I am doing studies on 2D materials, especially graphene and transitional metal dichalcogenides (TMDC). But I always have a question on the spin-orbit coupling (SOC) in TMDC: why does the spin-orbit ...
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Thomas Precession on Neutron Stars
We know that Thomas Precession is a relativistic correction that is applied to a particle spin that adds an angular velocity to the spin of the particle that moves along a curvilinear orbit linked to ...
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Spin-orbit and internal magnetic field
I'm currently studying the fine structure of the hydrogen atom but there is something about spin-orbit interaction that I can't understand.
The spin-orbit interaction adds a new term to the ...
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Time Reserval Symmetry Operator on Spin Orbit Coupling
Suppose the spin orbit coupling term is written below.
$$H_{soc} = \xi L\cdot\sigma$$
where, $\xi$ is the strength of the spin orbit coupling, $L$ and $\sigma$ are angular momentum and pauli matrix ...
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Finding the first-order perturbation of the energy of a hydrogen atom due to Spin Orbit coupling
I am given an exercise on perturbation theory involving an electron in a hydrogen atom in the presence of a constant magnetic field $\vec{B} = B_z \hat{z}$. Due to Zeeman effect and Spin-Orbit ...
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Book Recommendation for spin-orbit coupling
I am wondering if there were any recommendations for any books that are around graduate level in regards to the discussion of spin-orbit coupling and the Rashba spin-orbit coupling
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Rashba spin orbit Hamiltonian
I am studying the rashba spin orbit interaction in graphene
I know the effective Hamiltonian for RSOI in the presence of a perpendicular electric field ($E_z$) is
$$
H_{RSO}=\frac{\alpha}{\hbar}(P_x\...
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Calculating the magnetic field of the Proton in Spin-orbit Coupling in Hydrogen Atom
I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-independent Perturbation Theory, Section: Spin -Orbit Coupling. I understood that the spin–orbit ...
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Origin of spin-orbit interaction
The spin-orbit interaction in a hydrogen atom is often explained as arising from an interaction energy $U=-\mathbf{m}\cdot\mathbf{B}$ where $\mathbf{m}$ is a magnetic moment due to the electron’s spin ...
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Strong spin-orbit coupling allowing for fast qubit manipulation in Ge based heterostructures
I have been reading about Ge/SiGe hole qubit resaerch and noticed that the strong intrinsic spin orbit coupling (SOC) replaces on-chip micromagnet often found on Si/SiGe based spin qubits.
The ...
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Spin-orbit interaction in the frame of the nucleus
When I derived the spin orbit interaction, I switched to the electron's reference frame, so it feels a magnetic field $B$.
after calculations I get the spin orbit interaction in the electron's frame ...
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Why does spin-orbit coupling lead to a nonzero Berry curvature?
Many theories consider spin orbit coupling to be a prerequisite for a nonzero Berry curvature, and therefore, for the classical anomalous Hall effect. Here, the spin orbit coupling is defined as:
$$
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Why do you need weak spin-orbit interaction for $LS$ coupling?
From my lecture notes, the residual electrostatic perturbation causes the orbital angular momentum to couple and also spin $L=l_1+l_2 \ ,\ S=s_1+s_2$ (and it's not clear how residual electrostatic ...
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Spin Orbit Coupling Hamiltonians
I am really struggling with something fundamental.
I keep coming across two versions of the hamiltonian for spin orbit coupling:
$H_{soc}=\frac{\mu_B}{2c^2}(v \times E) \cdot \sigma $
$\mu_B =$ ...
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What is "spin-orbit torque?"
I am trying really hard to understand the concept of spin-orbit torque. It is a new-ish discovery in the field of spintronics and has many applications for magnetic devices. The information that has ...
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Spin Orbit ($LS$) interaction energy
Well, I am currently using a pretty old book by H.E White "Atomic Spectra", and he defined spin orbit interaction energy as the product of the resultant frequency and the projection of spin ...
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Spin-orbit coupling constant for rubidium
I have come across the following question in my course notes:
The $5s\to 5p$ transition in rubidium is split into two components with wavelengths of 780nm and 795nm respectively. For the $5p$ state, ...
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How Fundamental is Spin-Orbit Coupling to Topological Insulators?
I'm well aware this is a very active area of research so the best answer one can give to this question may be incomplete.
Topological states in condensed matter are well-known, even if not always ...
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