Bound States in the Continuum in Two-Dimensional Serial Structures

We investigate the occurrence of bound states in the continuum (BIC's) in serial structures of quantum dots coupled to an external waveguide, when some characteristic length of the system is changed. By resorting to a multichannel scattering-matrix approach, we show that BIC's do actually occur in two--dimensional serial structures, and that they are a robust effect. When a BIC is produced in a two--dot system, it also occurs for several coupled dots. We also show that the complex dependence of the conductance upon the geometry of the device allows for a simple picture in terms of the resonance pole motion in the multi--sheeted Riemann energy surface. Finally, we show that in correspondence to a zero--width state for the open system one has a multiplet of degenerate eigenenergies for the associated closed serial system, thereby generalizing results previously obtained for single dots and two-dot devices.