Scattering states of a particle, with position-dependent mass, in a ${\cal{PT}}$ symmetric heterojunction

TL;DR

This paper investigates the quantum scattering states of a particle with position-dependent mass in a ${ m PT}$ symmetric heterojunction, revealing preserved non-Hermitian features and discussing charge conservation.

Contribution

It extends the analysis of ${ m PT}$ symmetric systems to include position-dependent mass within heterojunctions, providing exact solutions and exploring unique scattering properties.

Findings

Reflection and transmission coefficients are calculated and analyzed.

Left/right asymmetry and spectral singularities are observed.

Charge conservation possibilities are discussed.

Abstract

The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian ${\cal{PT}}$ symmetric systems --- viz., left / right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed.