Effects of breaking current conservation on the phase properties of two-terminal quantum systems

We study the reflection and transmission phase properties of two-terminal quantum structures coupled to a third lead. The systems are effectively three-terminal and current conservation is broken with regard to the original two-terminal systems. Two structures, a waveguide with an attached stub quantum dot and a waveguide with an inline, double-barrier confined quantum dot, are considered. The transmission and reflection phase properties are calculated for these systems with different couplings to the third lead. The results show that the discontinuous phase shifts seen in the current-conserved two-terminal systems are removed when the third lead is attached. However, as long as the coupling between the quantum systems and the additional lead is weak, sharp but continuous phase drops within narrow energy ranges can still be clearly identified.