Supersymmetric analysis of the Dirac-Weyl operator within $\mathcal{PT}$PT symmetry

Abstract

Two dimensional effective Hamiltonian for a massless Dirac electron interacting with a hyperbolic magnetic field is discussed within PT symmetry. Factorization method and polynomial procedures are used to solve Dirac equation for the constant Fermi velocity and the effective potential which is complex Scarf II potential. The more general effective Scarf II potential models are also obtained within pseudo-supersymmetry. Finally, an extension of Panella and Roy's work [12] to the both PT symmetric and real Scarf II partner potentials are given using the position dependent Fermi velocity. keyword: pt symmetry, Dirac electron PACS: 03.65.w, 03.65.Fd, 03.65.Ge.

Form-preserving Darboux transformations for $4\times 4$ Dirac equations

“…In the first approach, Darboux transformation is not applied directly on the Dirac Hamiltonian, but rather on the Schrödinger-like operator that corresponds to the square of Dirac Hamiltonian, see e.g. [22][23][24][25][26][27][28]. In the second case, Darboux transformation is used directly to modify Dirac energy operators.…”

The massless Dirac–Weyl equation with deformed extended complex potentials

“…Also, graphene with the zero energy states is searched and scalar potentials are generated within the exactly solvable models [9]. On the other hand, pseudo-particles have a Fermi velocity 10 6 m/s and they can be replaced with the position dependent one as given in [10], [11], [12] and [13]. And, rationally extended potentials have been attracted too much attention in the literature [14], [15], [16], [17].…”