Effects of Parity and Symmetry on the Aharonov-Bohm Phase of a Quantum Ring.

We experimentally investigate the properties of one-dimensional quantum rings that form near the surface of nanowire quantum dots. In agreement with theoretical predictions, we observe the appearance of forbidden gaps in the evolution of states in a magnetic field as the symmetry of a quantum ring is reduced. For a twofold symmetry, our experiments confirm that orbital states are grouped pairwise. Here, a π-phase shift can be introduced in the Aharonov-Bohm relation by controlling the relative orbital parity using an electric field. Studying rings with higher symmetry, we note exceptionally large orbital contributions to the effective g-factor (up to 300), which are many times higher than those previously reported. These findings show that the properties of a phase-coherent system can be significantly altered by the nanostructure symmetry and its interplay with wave function parity.