Wigner molecules in phosphorene quantum dots

Abstract

We study Wigner crystallization of electron systems in phosphorene quantum dots with confinement of an electrostatic origin with both circular and elongated geometry. The large effective masses in phosphorene promote the separation of the electron charges already for quantum dots of relatively small size. The anisotropy of the effective mass allows for the formation of Wigner molecules in the laboratory frame with a confined charge density that has lower symmetry than the confinement potential. We find that in circular quantum dots separate single-electron islands are formed for two and four confined electrons but not for three trapped carriers. The spectral signatures of the Wigner crystallization to be resolved by transport spectroscopy are discussed. Systems with Wigner molecule states are characterized by a nearly degenerate ground state at B = 0 and are easily spin-polarized by the external magnetic field. In electron systems for which the single-electron islands are not formed, a more even distribution of excited states at B = 0 is observed, and the confined system undergoes ground state symmetry transitions at magnetic fields of the order of 1 Tesla. The system of five electrons in a circular quantum dot is indicated as a special case with two charge configurations that appear in the ground-state as the magnetic field is changed: one with the single electron islands formed in the laboratory frame and the other where only the pair-correlation function in the inner coordinates of the system has a molecular form as for three electrons. The formation of Wigner molecules of quasi-1D form is easier for orientation of elongated quantum dots along the zigzag direction with heavier electron mass. The smaller electron effective mass along the armchair direction allows for freezing out the transverse degree of freedom in the electron motion. Calculations are performed with a version of the configuration interaction approach that uses a single-electron basis that is pre-optimized to account for the relatively large area occupied by strongly interacting electrons allowing for convergence speed-up.