Bound states in the continuum in two-dimensional serial structures

We investigate the occurrence of bound states in the continuum (BICs) 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 BICs 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, BICs also occur for several coupled dots. We also show that the complex dependence of the conductance upon the geometry of the multi--dot system 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 zero--width states 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 structures.