TRANSMISSION RESONANCES AND ZEROS IN MULTIBAND MODELS

We report on an efficient numerical technique for directly locating tr ansmission resonances and zeros in semiconductor heterostructures usin g tight-binding multiband models. The quantum transmitting boundary me thod is employed to generate the inverse of the retarded Green's funct ion G(R)(E) in the tight-binding representation. The poles of G(R)(E) are located by solving a nonlinear non-Hermitian eigenvalue problem. T he eigenvalues are calculated using a shift and invert nonsymmetric La nczos algorithm followed by Newton refinement. We demonstrate that res onance line shapes are accurately characterized by the location of the poles and zeros of G(R)(E) in the complex energy plane. The real part of the pole energy corresponds to the resonance peak and the imaginar y part corresponds to the resonance width. A Fano resonance is charact erized by a zero-pole pair in the complex energy plane. In the case of an isolated Fano resonance, the zero always occurs on the real energy axis. However, we demonstrate that for overlapping Fano resonances th e zeros can move off of the real axis in complex conjugate pairs. This behavior is examined using a simple analytic model for multichannel s cattering.