GROUP THEORY SYMBOL

GTTbSpinMatrix

GTTbSpinMatrix[angular momentum,s1,s2]
gives elementary spin matrices for tight-binding Hamiltonians.

DetailsDetails

  • If the tight-binding Hamiltonian is constructed without spin-orbit coupling atomic-like wave functions characterised by the quantum numbers are used.
  • Wave functions, including the spin quantum number , i.e. characterised by are not eigenfunctions if spin-orbit coupling is included. The transformation of the correct eigenfunctions to quantum numbers to the basis leads to four matrices of dimension . Those matrices describe the on-site spin-orbit interaction to angular momentum and depend on the spin direction.
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.4.3

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package.

In[1]:=
Click for copyable input

Spin matrices for d electrons (l=2) will be constructed.

spin up - spin up

In[2]:=
Click for copyable input
Out[2]//MatrixForm=

spin down - spin down

In[3]:=
Click for copyable input
Out[3]//MatrixForm=

spin up - spin down

In[4]:=
Click for copyable input
Out[4]//MatrixForm=
Top