  Topological aspects of superconductivity in quantum spin-Hall systems (QSHSs)
such as thin layers of three-dimensional topological insulators (3D Tis) or
two-dimensional Tis are in the focus of current research. We examine hybrid
QSHS/superconductor structures in an external magnetic field and predict a
gapless superconducting state with protected edge modes. It originates entirely
from the orbital magnetic-field effect caused by the locking of the electron
spin to the momentum of the superconducting condensate flow. We show that such
spin-momentum locking can generate a giant orbital g-factor of order of several
hundreds, allowing one to achieve significant spin polarization in the QSHS in
the fields well below the critical field of the superconducting material. We
propose a three-terminal setup in which the spin-polarized edge
superconductivity can be probed by Andreev reflection, leading to unusual
transport characteristics: a non-monotonic excess current and a zero-bias
conductance splitting in the absence of the Zeeman interaction.
