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An analytic closed form solution is derived for the bound states of electronssubject to a static, inhomogeneous ($1/r$-decaying) magnetic field, includingthe Zeeman interaction. The solution provides access to many-body properties ofa two-dimensional, non-interacting, electron gas in the thermodynamic limit.Radially distorted Landau levels can be identified as well as magnetic fieldinduced density and current oscillations close to the magnetic impurity. Theseradially localised oscillations depend strongly on the coupling of the spin tothe magnetic field, which give rise to non-trivial spin currents. Moreover, theZeeman interaction introduces a lowest flat band for $E_F=0^+$ assuming a spin$g_s$-factor of two. Surprisingly, in this case the charge and currentdensities can be computed analytically in the thermodynamic limit. Numericalcalculations show that the total magnetic response of the electron gas remainsdiamagnetic (similar to Landau levels) independent of the Fermi energy.However, the contribution of certain, infinitely degenerate energy levels maybecome paramagnetic. Furthermore, numerical computations of the Hallconductivity reveal asymptotic properties of the electron gas, which are drivenby the anisotropy of the vector potential instead of the magnetic field, i.e.become independent of spin. Eventually, the distorted Landau levels give riseto different Hall conductivity phases, which are characterized by sharp signflips at specific Fermi energies. Overall, our work merges "impurity" withLandau-level physics, which provides novel physical insights, not only locally,but also in the asymptotic limit. This paves the way for a large number offuture theoretical as well as experimental investigations.

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