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  New Class of Landau Levels and Hall Phases in a 2D Electron Gas Subject to an Inhomogeneous Magnetic Field: An Analytic Solution

Sidler, D., Rokaj, V., Ruggenthaler, M., & Rubio, A. (2022). New Class of Landau Levels and Hall Phases in a 2D Electron Gas Subject to an Inhomogeneous Magnetic Field: An Analytic Solution.

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2201.05069.pdf (Preprint), 4MB
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https://arxiv.org/abs/2201.05069 (Preprint)
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 Creators:
Sidler, D.1, 2, 3, Author              
Rokaj, V.1, 2, 4, Author              
Ruggenthaler, M.1, 2, 3, Author              
Rubio, A.1, 2, 3, 5, 6, Author              
Affiliations:
1Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
2Center for Free-Electron Laser Science, ou_persistent22              
3The Hamburg Center for Ultrafast Imaging, ou_persistent22              
4ITAMP, Harvard-Smithsonian Center for Astrophysics, ou_persistent22              
5Center for Computational Quantum Physics, Flatiron Institute, ou_persistent22              
6Nano-Bio Spectroscopy Group, University of the Basque Country (UPV/EHU), ou_persistent22              

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Free keywords: Condensed Matter, Mesoscale and Nanoscale Physics, cond-mat.mes-hall,Quantum Physics, quant-ph
 Abstract: An analytic closed form solution is derived for the bound states of electrons subject to a static, inhomogeneous (1/r-decaying) magnetic field, including the Zeeman interaction. The solution provides access to many-body properties of a two-dimensional, non-interacting, electron gas in the thermodynamic limit. Radially distorted Landau levels can be identified as well as magnetic field induced density and current oscillations close to the magnetic impurity. These radially localised oscillations depend strongly on the coupling of the spin to the magnetic field, which give rise to non-trivial spin currents. Moreover, the Zeeman interaction introduces a lowest flat band for EF=0+ assuming a spin gs-factor of two. Surprisingly, in this case the charge and current densities can be computed analytically in the thermodynamic limit. Numerical calculations show that the total magnetic response of the electron gas remains diamagnetic (similar to Landau levels) independent of the Fermi energy. However, the contribution of certain, infinitely degenerate energy levels may become paramagnetic. Furthermore, numerical computations of the Hall conductivity reveal asymptotic properties of the electron gas, which are driven by the anisotropy of the vector potential instead of the magnetic field, i.e. become independent of spin. Eventually, the distorted Landau levels give rise to different Hall conductivity phases, which are characterized by sharp sign flips at specific Fermi energies. Overall, our work merges "impurity" with Landau-level physics, which provides novel physical insights, not only locally, but also in the asymptotic limit. This paves the way for a large number of future theoretical as well as experimental investigations.

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 Dates: 2022-03-25
 Publication Status: Published online
 Pages: 17
 Publishing info: -
 Table of Contents: -
 Rev. Type: No review
 Identifiers: arXiv: 2201.05069
 Degree: -

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