2018/07/31 by Radosław Szmytkowski · 2 citations
Physics and Astronomy · #Atom (system on chip) #Coulomb #Dirac (video compression format) #Dirac equation #Electron #Hamiltonian (control theory) #Magnetic field #Perpendicular #Perturbation theory (quantum mechanics) #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #Topological Materials and Phenomena #Zeeman effect #physics.atom-ph #quant-ph
paper · pdf · doi:10.1016/j.aop.2018.12.007
published in Annals of Physics 401, 174-192 (Elsevier BV) · 24 pages, 4 tables
openalex publication_date 2019/01/02 · openalex created_date 2019/01/11 · arxiv created 2019/01/26 · arxiv updated 2019/01/29 · openalex updated_date 2026/08/05
A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first- and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh-Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are carried out with the use of the Sturmian expansion of the two-dimensional generalized radial Dirac-Coulomb Green function derived in the paper. It is found that, in contrast to the case of the three-dimensional atom [P. Stefańska, Phys. Rev. A 92 (2015) 032504], in two spatial dimensions atomic magnetizabilities (magnetic susceptibilities) are expressible in terms of elementary algebraic functions of a nuclear charge and electron quantum numbers. The problem considered here is related to the Coulomb impurity problem for graphene in a weak magnetic field.