Topological Pauli Phase and Fractional Quantization of Orbital Angular Momentum in the Problems of Classical and Quantum Physics

TL;DR

This paper explores the role of topological Pauli phases in fractional angular momentum quantization across classical and quantum physics, with applications to quantum dots, graphene, and classical diffraction phenomena.

Contribution

It introduces the concept of topological Pauli phases in 2D systems and demonstrates their impact on angular momentum quantization in various physical contexts.

Findings

Fractional quantization of angular momentum occurs in 2D systems.

Experimental data supports the theoretical predictions for quantum dots.

Topological phases influence classical diffraction and electrostatic problems.

Abstract

Physical problems for which the existence of non-trivial topological Pauli phase (i.e. fractional quantization of angular orbital angular momenta that is possible in 2D case) is essential are discussed within the framework of two-dimensional Helmholtz, Schroedinger and Dirac equations. As examples in classical field theory we consider a "wedge problem" -- a description of a field generated by a point charge between two conducting half-planes -- and a Fresnel diffraction from knife-edge. In few-electron circular quantum dots the choice between integer and half-integer quantization of orbital angular momenta is defined by the Pauli principle. This is in line with precise experimental data for the ground state energy of such quantum dots in a perpendicular magnetic field. In a gapless graphene, as in the case of gapped one, in the presence of overcharged impurity this problem can be solved experimentally, e.g., using the method of scanning tunnel spectroscopy.