  We study superconducting quantum interference in a Josephson junction linked
via edge states in two-dimensional (2D) insulators. We consider two scenarios
in which the 2D insulator is either a topological or a trivial insulator
supporting one-dimensional (1D) helical or nonhelical edge states,
respectively. In equilibrium, we find that the qualitative dependence of
critical supercurrent on the flux through the junction is insensitive to the
helical nature of the mediating states and can, therefore, not be used to
verify the topological features of the underlying insulator. However, upon
applying a finite voltage bias smaller than the superconducting gap to a
relatively long junction, the finite-frequency interference pattern in the
non-equilibrium transport current is qualitatively different for helical edge
states as compared to nonhelical ones.
