Dirac Fermion Scattering and Conductance Response in Asymmetric Graphene Wormholes
We calculate massless Dirac scattering and the conductance response to a localized scalar ring gate in a graphene wormhole with two independent curvature scales and no axial magnetic flux. Matching Hankel and Gauss hypergeometric spinors gives the unperturbed scattering states. Interchanging the throat segments preserves the total Landauer conductance, while a gate at a fixed displaced position produces different conductance changes in the two mirror configurations. For $a=5$~nm and $r_L+r_R=13.68$~nm, a $1$~meV gate of width $1$~nm centered at $u_0=7$~nm gives relative conductance changes of $+0.0718\%$ and $-0.0918\%$ at $E=200$~meV for $η=0.5$ and $2$, respectively. Energy--position maps show how asymmetry redistributes the electrical response. Gates centered well inside both curved segments can give different response magnitudes; opposite signs occur near the mouths and farther out. We also find opposite response signs in the fixed-length comparison at the chosen operating point. For equally occupied opposite angular channels, the sublattice imbalances cancel and the conductance responses add. A spatially controlled gate thus probes throat orientation through conductance even when the unperturbed two-terminal measurement cannot distinguish the two configurations.