Wigner Transport in Linear Magnetic Fields: The Quantum Magnetic Term Effect

Modeling the single electron dynamics under the influence of an electromagnetic field is important for next-generation electronic solid-state quantum systems for electron quantum optics and nanoelectronics. To that end, we focus on the gauge-invariant Wigner equation, which explicitly depends on the kinetic momentum of the electron. However, the obtained equation is complex and multidimensional, which poses signif-icant numerical challenges. Therefore, simplifying assumptions are needed to gain first experiences with this new theoretical description. Recent advancements allow for the setting of an elec-tron in a linear magnetic field. The high-order mixed derivative term, caused by the linearity of the field, leads to quantum effects of the electron evolution. Here, we study this so-called quantum magnetic term effect by analyzing its interplay with the single-electron dynamics of a snake state type of evolution. We observe a redistribution of the density while the main path of the electron is preserved, which is supported by the Ehrenfest theorem.