Field-Free Transverse Aharonov--Bohm Phase Gate for an Orbital l-Qubit

Free-space Aharonov--Bohm (AB) Bessel modes are known to carry a flux-dependent azimuthal Schr"odinger probability current and kinetic orbital angular momentum. We extend this response to the spin-resolved conserved Dirac current of a core-excluded finite-wall annular guide and show that confinement converts its surviving orbital component into a transverse Aharonov--Bohm (TAB) propagation phase for a straight traveling mode whose centroid path has zero projection onto mathbf A. The radial-gradient current reverses under spin reversal; retaining the complete evanescent tail closes it as a boundary contribution, leaving a spin-independent orbital phase Δφ_lnpropto lPhi L_{rm int}langleρ^-2rangle_ln/v_z. Opposite-winding modes |pm lrangle form a same-path qubit implementing R_z\(2delta_l\) with differential readout and common-mode phase rejection, while direct first-order crosstalk requires the angular harmonic m=pm2l. For a 100 mum section with a=20 nm, R=30 nm, E_z=10 meV, and |l|=10, the sensitivity is 0.1885 mrad/mG and R_z\(pi\) occurs at 16.67 G. Finite-wall confinement thus turns intrinsic azimuthal Dirac current into a guided field-free phase operation.