About the rotation matrices, especially the SU(2) spin rotation matrix used by vasp.

[hszhao.cn@gmail.com]

Some time ago, I've conducted some discussion with Dr. Gui-Bin Liu on topological materials here. The following are the comments related to the discussion:

The format of trace.txt file is only a necessary condition to be used by getBandRep.
Another issue is that the rotation matrices used, especially the SU(2) spin rotation matrix, have to be the same with vasp and vasp2trace.

OTOH, as for SU(2) representation, there are two popular gauges: Pauli and Cartan, as commented here. So, I want to know/confirm the precise forms of these matrices used by vasp. Any tips would be greatly appreciated.

Regards,
HZ

[marie-therese.huebsch]

Hi HZ,

You can have a look in spinsym.F to figure out the exact way the SU(2) symmetry has been implemented.

Best regards,
Marie-Therese

[hszhao.cn@gmail.com]

Then, what about the rotation matrices?

Regards,
HZ

[hszhao.cn@gmail.com]

See here for more detailed discussion.

[marie-therese.huebsch]

I am glad people helped you find the relevant comments in the code.

Code: Select all

! Define Pauli-matrices
sig=zero
sig(1,2,1)=cmplx( 1.0_q, 0.0_q,kind=q)
sig(2,1,1)=cmplx( 1.0_q, 0.0_q,kind=q)
sig(1,2,2)=cmplx( 0.0_q,-1.0_q,kind=q)
sig(2,1,2)=cmplx( 0.0_q, 1.0_q,kind=q)
sig(1,1,3)=cmplx( 1.0_q, 0.0_q,kind=q)
sig(2,2,3)=cmplx(-1.0_q, 0.0_q,kind=q)

and

Code: Select all

!The two rotations are the same as the EULER routine:
! 1. rotation around y-axis of beta
! R_s(beta,y) = [ cos(beta/2)   -sin(beta/2) ]
!               [ sin(beta/2     cos(beta/2) ]
!
! 2. rotation around z-axis of alpha
! R_s(alpha,z) = [ exp(-I*alpha/2)              0 ]
!                [               0 exp(I*alpha/2) ]
!
! The spin rotation is given by
! R = R_s(alpha,z)*R_s(beta,y)

Closing this issue now.
Kind regards,
Marie-Therese