Abstract This work reports the theoretical investigation into the mechanism underpinning the anomalous
Josephson effect within ballistic systems; currently, there is no agreed upon microscopic mechanism
behind the origin of this effect. The prototypical system we study is a ballistic two-dimensional
junction containing a two-dimensional Rashba spin-orbit interaction. In this paper we demonstrate
how this two-dimensional Rashba interaction mixes the spins of adjacent transverse subbands which
leads to significant spin-asymmetry within the junction. Under an external magnetic field, applied
perpendicular to both the axis of transport and the normal vector of the junction, the sinusoidal
Josephson current can then experience an anomalous phase shift. The role of this spin mixing in the
limit of a single sub-band is initially explored by deriving an analytical expression for the resulting
anomalous phase shift. The analysis is then extended to systems with multiple occupied sub-bands;
in this later section, starting from a microscopic model, we derive an analytic formula for the
resulting anomalous phase shift indicating it is linear in both magnetic field and spin-orbit strength.
We then verify and validate all findings by comparing them with numerical results evaluated by a
tight-binding model.