Orbital microscopic magnetization and persistent currents of a harmonically confined two-dimensional electron gas under strong magnetic field

We provide a comprehensive investigation into a range of key equilibrium properties of a harmonically confined two-dimensional electron gas under a normal magnetic field. Employing single-particle wave functions and the Bloch density matrix approach, we derive exact analytical expressions for local and integral properties, including particle density, current distribution, microscopic magnetization, total magnetic moment and integrated persistent electric current. We demonstrate a direct deduction of the total persistent current from the microscopic magnetization, underscoring their inherent connection. Numerical analysis focuses on strong magnetic fields, unveiling well-defined compressible and incompressible regions within the particle density profile. Specifically, we unravel the underlying structure of the counter-propagating equilibrium currents observed in these high regimes, driven by the oscillatory behavior of the microscopic magnetization, which we derive in exact analytical form in real physical space. Exploring changes in the energy spectrum reveals intricate influences on these properties, resulting in quantum oscillation patterns at high fields.