We study the effect of a magnetic field on the current-phase relation of a
topological Josephson junction formed by connecting two superconductors through
the helical edge states of a quantum spin-Hall insulator. We predict that the
Zeeman effect along the spin quantization axis of the helical edges results in
an anomalous Josephson relation that allows for a supercurrent to flow in the
absence of superconducting phase bias. We relate the associated field-tunable
phase shift ϕ0 in the Josephson relation of such a ϕ0-junction to
the existence of a so-called helical superconductivity, which may result from
the interplay of the Zeeman effect and spin-orbit coupling. We analyze the
dependence of the magneto-supercurrent on the junction length and discuss its
observability in suitably designed hybrid structures subject to an in-plane
magnetic field.Comment: 7 pages, 3 figures, Appendix and references adde