  This work presents theoretical demonstration of a carrier trap unit formed by
dual topological insulator constrictions (TIC) on the HgTe/CdTe quantum well
(QW) with inverted band structures. The sample of HgTe/CdTe QW is patterned
into a Hall bar device and a topological quantum dot is created by adding split
gate electrodes closely on the QW. In sharp contrast to conventional
semiconductor quantum dots, the presence or absence of topological edge states
in the proposed quantum hall bar system leads to distinct
propagating/insulating state of the TICs with large on/off ratio. This
topological quantum dot functions as a carrier trap memory element with near
perfect program/erase efficiency by proper adjusting the voltages applied to
the split gates. For completeness, we also demonstrate that the Rashba spin
orbit interaction in the quantum dot does not destroy the topological edge
states and have negligible impact on the conductance of the quantum hall bar.
The rapid oscillations in conductance can be suppressed when applying a
perpendicular magnetic field in the quantum dot.
