Bi-orthogonal quantum mechanics related to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> -pseudo-Hermitian Rashba Hamiltonian

Abstract A non-Hermitian version of Rashba Hamiltonian has been introduced. The said Hamiltonian is found to be pseudo-Hermitian under fermionic time-reversal and its eigen-states show a kind of two-parameter-bi-orthogonality. The possibility of an equivalent version of Kramers’ degeneracy theorem has been explored and the supersymmetric and pseudo-supersymmetric structures relating to the present system are also discussed.