Designing quantum resonant scatterers at subwavelength scale

For an isotropic quantum resonant scatterer, such as a quantum dot embedded in host semiconductors, we propose a method to achieve resonant electron scattering by taking physical quantities into account through the second-order expansion. All needed physical information for spherical harmonic channels in anomalous quantum resonant scattering is revealed in a parameter space as the size of quantum scatterer is comparable to the de Broglie wavelength of incoming matter wave. Our results provide the guideline to realize quantum resonant scatterers with state-of-the-art semiconductor heterostructure technology.