How can I calculate spin Hall conductivity for a 4*4 Hamiltonian?

[Mohammad-gl]

TL;DR Summary

Spin Hall conductivity formula

I'm trying to calculate spin Hall conductivity for a 4 × 4 Hamiltonian and I found the attached formula for spin Hall conductivity. What are Dirac matrices for 4× 4 Hamiltonian?

 

[phyro]

I have not checked it but from context I assume these are the Dirac matrices that you are familiar with from the Dirac equation in QFT, i.e. the gamma matrices that generate the Clifford algebra (as the 2x2 Pauli matrices that you are used to when talking about spin are also generators of the Clifford algebra, hence the connection)

 

[pines-demon]

Source?

 

[Mohammad-gl]

Source?

This is the reference.
DOI: 10.1103/PhysRevLett.94.226601

 

[Mohammad-gl]

I have not checked it but from context I assume these are the Dirac matrices that you are familiar with from the Dirac equation in QFT, i.e. the gamma matrices that generate the Clifford algebra (as the 2x2 Pauli matrices that you are used to when talking about spin are also generators of the Clifford algebra, hence the connection)

Thank you. I want to know metrices form.