Yang–Mills field strength and classical trajectories of electrons in Rashba spin–orbit-coupled systems

It is a long standing issue how non-Abelian entities take shape in macroscopic real space and are measured technically. Based on the gauge theory cast on recent spintronic researches, we obtained the expectation values of the Yang–Mills field strength in Rashba systems interfaced with a hard wall. This non-Abelian quantity is proportional to the spin density near the walls, when an external electric field is applied. The Yang–Mills field strength exerts a force on electrons, analogous to the influence of a magnetic field, and this effect is further clarified through the introduction of an effective scalar potential derived from a Landau-like gauge transformation and the analysis of electron’s classical trajectories. Our work demonstrates the feasibility of measuring the Yang–Mills field strength employing the magneto-optical Kerr effect, and provides calculated projections of the expected outcomes. Notably, these results, using gauge transformations, can be applied to other systems, including the Dresselhaus system.