Non-Hermitian fermions with effective mass

In this work, we readdress the Dirac equation in the position-dependent mass (PDM) scenario. Here, one investigates the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming (1 + 1)-dimension flat spacetime. In seeking a Schrodinger-like theory with PT symmetry is appropriate to assume a complex potential. This imaginary interaction produces an effective potential purely dependent on mass distribution. Furthermore, we study the non-relativistic limit by adopting the Foldy-Wouthuysen transformation. As a result, that limit leads to an ordering equivalent to the ordering that describes abrupt heterojunctions. Posteriorly, particular cases of mass distribution also were analyzed. Thus, interesting results arise for the case of a linear PDM, which produces an effective harmonic oscillator and induces the emergence of bound states. For a hyperbolic PDM, an effective potential barrier emerges. However, in this case, the fermions behave as free particles with positive-defined energy.

Automated summary

In this work, we study the Dirac equation in the position-dependent mass (PDM) scenario, investigating the quantum dynamics of non-Hermitian fermionic particles with effective mass assuming flat spacetime. We introduce a complex potential to achieve PT symmetry and explore the resulting effective potential purely dependent on mass distribution. The non-relativistic limit and specific cases of mass distribution are also examined, revealing intriguing phenomena such as the emergence of bound states and the behavior of fermions as free particles with positive-defined energy.