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A non-Hermitian version of Rashba Hamiltonian has been introduced motivatedfrom the Levy-leblond type linearisation of Schrodinger equation in a Galileaninvariant frame-work. The said Hamiltonian is found to be pseudo-Hermitianunder fermionic time-reversal and its eigen-spinors show bi-orthogonality. Thewhole discussion has been cast in a Clifford algebraic frame-work and the saidbiorthogonality has been variously understood in terms of time-reversaloperator and Clifford involutions. The possibility of an equivalent version ofKramers' degeneracy theorem has been explored and the super-symmetric andpseudo-super-symmetric structures relating to the present system are alsodiscussed.

Bi-orthogonal spinors associated to T -pseudo-Hermitian Rashba Hamiltonian : Time reversal in Clifford Algebra Cl3(R) and Pseudo-Supersymmetry