  A non-Hermitian version of Rashba Hamiltonian has been introduced motivated
from the Levy-leblond type linearisation of Schrodinger equation in a Galilean
invariant frame-work. The said Hamiltonian is found to be pseudo-Hermitian
under fermionic time-reversal and its eigen-spinors show bi-orthogonality. The
whole discussion has been cast in a Clifford algebraic frame-work and the said
biorthogonality has been variously understood in terms of time-reversal
operator and Clifford involutions. The possibility of an equivalent version of
Kramers' degeneracy theorem has been explored and the super-symmetric and
pseudo-super-symmetric structures relating to the present system are also
discussed.
