Tunnel transport problem for open multilayer nitride nanostructures with an applied constant magnetic field and time-dependent potential: An exact solution

A quantum mechanical theory for description of electronic quasistationary states in two-dimensional (2D) layered semiconductor nanostructure was developed. A constant external magnetic field <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>B</a:mi></a:math> was directed along semiconductor layers. The presence of internal electric fields <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>F</b:mi></b:math> originated from the potential barriers and wells in semiconductor layers was taken into account. The vector of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>F</c:mi></c:math> was directed perpendicularly to semiconductor layers. The interaction of tunneled electrons with a time-dependent electromagnetic fields was analyzed in detail. An approach to obtain an exact solution to the problem based on a combination of the Lewis-Riesenfeld method for complete Schrödinger equation and scattering theory was developed. Application of the scattering theory in combination with the -matrix and transfer-matrix methods allowed us to calculate the electron quasistationary spectra. Effects of magnetic field on the resonant energy and width of electronic quasistationary states as well as on the electronic conductivity were also discussed.