CPT-conserving Hamiltonians and their nonlinear supersymmetrization   using differential charge-operators C
  A brief overview is given of recent developments and fresh ideas at the intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric quantum mechanics (SUSY QM). We study the consequences of the assumption that the "charge" operator C is represented in a differential-operator form. Besides the freedom allowed by the Hermiticity constraint for the operator CP, encouraging results are obtained in the second-order case. The integrability of intertwining relations proves to match the closure of nonlinear SUSY algebra. In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial oscillators with real spectrum which turn out to be PT-asymmetric. 
B. Bagchi, A. Banerjee, E. Caliceti, F. Cannata, H. B. Geyer, C.   Quesne and M. Znojil