Angular–momentum–resolved Aharonov–Bohm coupling energy

Abstract We derive an angular–momentum–resolved interaction energy for the Aharonov–Bohm (AB) response of a confined Dirac electron using two gauge–invariant interaction functionals: a magnetization–field functional and a current–potential functional. Using exact Dirac eigenmodes in a cylindrical cavity threaded by a solenoidal flux, we show that the magnetization–field functional yields a core–localized interaction energy restricted to the l = 0 channel, with all higher angular–momentum contributions suppressed and vanishing entirely in the limit a → 0. The current–potential functional, by contrast, produces a finite, mode–dependent energy shift for l ⩾ 1 in the same limit, arising from a local coupling between the solenoidal vector potential and the spatially distributed Dirac current, thereby encoding the geometric and topological structure of the interaction.