Controllable quantum scars induced by spin-orbit couplings in quantum dots

The spin-orbit couplings (SOCs) which are the relativistic corrections originated from the Dirac equation, offer nonlinearity in the classical limit and are capable of driving the chaotic dynamics. In a quantum dot confined by a two dimensional parabolic potential with SOCs, various quantum scar states emerge quasi-periodically in the eigenstates of the system, when the ratio of the confinement energies in the two directions are nearly commensurable. The scars, displaying both the quantum interference and the classical trajectory on the electron density, induced by the relativistic effects, indicate the bridge between the classical and quantum behaviors of the system. When the strengths of the Rashba and Dresselhaus SOCs are identical, the chaos is eliminated as the classical Hamilton's equations being linear and all the quantum scar states disappear consequently. The quantum scars induced by SOCs are found to be robust against small perturbations of the systematic parameters. As the Rashba SOC been controlled precisely by an external gate in experiments, the quantum scar here is fully predictable, controllable and accessible to detection.