Herzberg circuit and Berry's phase in chirality-based coded qubit in a triangular triple quantum dot

We present a theoretical proposal for the Herzberg circuit and controlled accumulation of Berry's phase in a chirality-based coded qubit in a triangular triple quantum dot molecule with one electron each. The qubit is encoded in the two degenerate states of a three-spin complex with total spin S = 1/2. Using a Hubbard and Heisenberg model the Herzberg circuit encircling the degeneracy point is realized by adiabatically tuning the successive on-site energies of quantum dots and tunnel couplings across a pair of neighboring dots. It is explicitly shown that encircling the degeneracy point leads to the accumulation of the geometrical Berry's phase. We show that only the triangular, not the linear, quantum dot molecule allows for the generation of Berry's phase and we discuss a protocol to detect this geometrical phase.