Quantum scattering in two-dimensional nanostructures using a novel method of sources and absorbers

There have been several attempts in the literature to provide a variational approach to solve quantum scattering problems. However, the asymptotic boundary conditions (BCs) used in such methods do not take crucial evanescent modes into account, making them unsuitable for applications in meso- and nano-scale devices. Further, widely used atomistic models are computationally expensive for any device scale applications. We develop a method based on sources and absorbers to study quantum scattering in two-dimensional systems. The Cauchy BCs that are essential in the action integral formulation of scattering are reduced to simpler Dirichlet BCs by introducing totally absorbing “stealth regions.” Solutions decay within the stealth regions, thereby vanishing at the finite boundaries. A Green’s function source is constructed to provide incident plane waves in the active scattering regime. This method overcomes the limitations of the currently prevalent approaches to provide a complete non-asymptotic variational description for scattering in confined as well as open domain quantum systems. We also discuss the applications of our method in simulating nanoscale rectifiers and enhancement of the thermoelectric power in quantum waveguides with embedded defects.