The effect of vacancy induced localized states on the thermoelectric properties of armchair bilayer phosphorene nanoribbons

We examine an armchair bilayer phosphorene connected to two leads, one hot and one cold, on both sides, investigating the thermoelectric properties of this system with periodic vacancies along the armchair direction and at the center of the nanoribbon. Initially, we analytically demonstrate that the creation of a vacancy results in the generation of a localized state around it. Subsequently, we illustrate that the presence of periodic vacancies leads to the formation of a new energy band in the energy bandstructure. Our calculations reveal that by varying the distance between vacancies, one can tune the width of the corresponding transmission channel, the generated electric power, and the thermoelectric efficiency.