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Rashba spin texture plot

Posted 5 months ago

Dear Experts,
I need your help visualizing the spin texture.
I want to plot spin texture in kx-ky plane after solving Rashba Hamiltonian as provided in the attached file. Kindly help.

consider m= hbar = 1, alpha= 0.2
Range of kx and ky = [-1.5,1.5] or [-3,3]
Clear[k, m, \[Alpha], \[HBar], \[Sigma]0, \[Sigma]x, \[Sigma]y, \
\[Sigma]z]

(*Define symbolic variables*)
\[HBar] = \[HBar]; (*The reduced Planck constant*)
k = Sqrt[kx^2 + ky^2]; (*Magnitude of the wavevector*)
m = m; (*Effective mass of electrons*)
\[Alpha] = \[Alpha] ; (*Rashba spin-orbit coupling strength*)

(*Define Pauli matrices*)
\[Sigma]0 = PauliMatrix[0];
\[Sigma]x = PauliMatrix[1];
\[Sigma]y = PauliMatrix[2];
\[Sigma]z = PauliMatrix[3];

(*Define the Rashba Hamiltonian*)
hamiltonian = (\[HBar]^2 k^2)/(2 m) \[Sigma]0 + \[Alpha] (\[Sigma]x \
ky - \[Sigma]y kx);

(*Diagonalize the Hamiltonian*)
{eigenvalues, eigenvectors} = Eigensystem[hamiltonian];

enter image description here enter image description here

POSTED BY: Manish Kumar
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