Quantum dot version of topological phase: half-integer orbital angular momenta

We show that there exists a topological phase equal to $\pi$ for circular quantum dots with an odd number of electrons. The non-zero value of the topological phase is explained by axial symmetry and two-dimensionality of the system. Its particular value ($\pi$) is fixed by the Pauli exclusion principle and leads to half-integer values for the eigenvalues of the orbital angular momentum. Our conclusions agree with the experimental results of T. Schmidt et al., Phys. Rev. B 51, 5570 (1995), which can be considered as the first experimental evidence for the existence of the new topological phase and half-integer quantization of the orbital angular momentum in a system of an odd number of electrons in circular quantum dots.