__all__ = ['atom_hsoc']
import numpy as np
[docs]def atom_hsoc(case, soc):
"""
Return atomic spin-orbit coupling matrix :math:`\\vec{l}\\cdot\\vec{s}`
in complex spherical harmonics basis.
Parameters
----------
case: str
String label indicating atomic shell,
- 'p': for :math:`p` -shell.
- 't2g': for :math:`t_{2g}` -shell.
- 'd': for :math:`d` -shell.
- 'f': for :math:`f` -shell.
soc: float
The strength of spin-orbit coupling.
Returns
-------
hsoc: 2d complex array
The spin-orbit coupling matrix.
"""
sqrt2 = np.sqrt(2.0)
sqrt6 = np.sqrt(6.0)
sqrt10 = np.sqrt(10.0)
sqrt12 = np.sqrt(12.0)
if case.strip() == 'p':
hsoc = np.zeros((6, 6), dtype=np.complex128)
hsoc[0, 0] = -1.0
hsoc[3, 0] = sqrt2
hsoc[1, 1] = 1.0
hsoc[5, 2] = sqrt2
hsoc[0, 3] = sqrt2
hsoc[4, 4] = 1.0
hsoc[2, 5] = sqrt2
hsoc[5, 5] = -1.0
return 0.5 * soc * hsoc
elif case.strip() == 't2g':
hsoc = np.zeros((6, 6), dtype=np.complex128)
hsoc[0, 0] = -1.0
hsoc[3, 0] = sqrt2
hsoc[1, 1] = 1.0
hsoc[5, 2] = sqrt2
hsoc[0, 3] = sqrt2
hsoc[4, 4] = 1.0
hsoc[2, 5] = sqrt2
hsoc[5, 5] = -1.0
return 0.5 * -soc * hsoc
elif case.strip() == 'd':
hsoc = np.zeros((10, 10), dtype=np.complex128)
hsoc[0, 0] = -2.0
hsoc[3, 0] = 2.0
hsoc[1, 1] = 2.0
hsoc[2, 2] = -1.0
hsoc[5, 2] = sqrt6
hsoc[0, 3] = 2.0
hsoc[3, 3] = 1.0
hsoc[7, 4] = sqrt6
hsoc[2, 5] = sqrt6
hsoc[6, 6] = 1.0
hsoc[9, 6] = 2.0
hsoc[4, 7] = sqrt6
hsoc[7, 7] = -1.0
hsoc[8, 8] = 2.0
hsoc[6, 9] = 2.0
hsoc[9, 9] = -2.0
return 0.5 * soc * hsoc
elif case.strip() == 'f':
hsoc = np.zeros((14, 14), dtype=np.complex128)
hsoc[0, 0] = -3.0
hsoc[3, 0] = sqrt6
hsoc[1, 1] = 3.0
hsoc[2, 2] = -2.0
hsoc[5, 2] = sqrt10
hsoc[0, 3] = sqrt6
hsoc[3, 3] = 2.0
hsoc[4, 4] = -1.0
hsoc[7, 4] = sqrt12
hsoc[2, 5] = sqrt10
hsoc[5, 5] = 1.0
hsoc[9, 6] = sqrt12
hsoc[4, 7] = sqrt12
hsoc[8, 8] = 1.0
hsoc[11, 8] = sqrt10
hsoc[6, 9] = sqrt12
hsoc[9, 9] = -1.0
hsoc[10, 10] = 2.0
hsoc[13, 10] = sqrt6
hsoc[8, 11] = sqrt10
hsoc[11, 11] = -2.0
hsoc[12, 12] = 3.0
hsoc[10, 13] = sqrt6
hsoc[13, 13] = -3.0
return 0.5 * soc * hsoc
else:
raise Exception("error in atom_hsoc: DO NOT support SOC for this case: ", case)