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

• URL: http://arxiv.org/abs/2102.08879v1
• Date: Wed, 17 Feb 2021 17:18:18 GMT
• Title: Topological Pauli Phase and Fractional Quantization of Orbital Angular Momentum in the Problems of Classical and Quantum Physics
• Authors: K. S. Krylov, V. M. Kuleshov, Yu. E. Lozovik, V. D. Mur
• Abstract summary: In few-electron circular quantum dots the choice between integer and half-integer quantization of orbital angular momenta is defined by the Pauli principle. In a gapless graphene, as in the case of gapped one, in the presence of overcharged impurity this problem can be solved experimentally.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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