Topological Phase and Half-Integer Orbital Angular Momenta in Circular Quantum Dots

Abstract

We show that there exists a non-trivial topological phase in circular two-dimensional quantum dots with an odd number of electrons. The possible non-zero value of this phase is explained by axial symmetry of two-dimensional quantum systems. The particular value of this phase ( $$\pi $$ ) is fixed by T-invariance and the Pauli exclusion principle and leads to half-integer values of the angular orbital momentum for ground states of such systems. This conclusion agrees with the experimental data for ground-state energies of few-electron circular quantum dots in perpendicular magnetic field (Schmidt et al. in Phys Rev B 51:5570, 1995). Hence, these data may be considered as the first experimental evidence for the existence of topological phase leading to half-integer quantization of the orbital angular momentum in circular quantum dots with an odd number of electrons.