  Quantum spin Hall effect is endowed with topologically protected edge modes
with gapless Dirac spectrum. Applying a magnetic field locally along the edge
leads to a gapped edge spectrum with opposite parity for winding of spin
texture for conduction and valence band. Using Pancharatnam's prescription for
geometric phase it is shown that mismatch of this parity across a $p$-$n$
junction, which could be engineered into the edge by electrical gate induced
doping, leads to a phase dependence in the two-terminal conductance which is
purely topological (0 or $\pi$). This fact results in a ${\mathbb{Z}}_2$
classification of such junctions with an associated duality. Current asymmetry
measurements which are shown to be robust against electron-electron
interactions are proposed to infer this topology.
