  We consider a new model system supporting Majorana zero modes based on
semiconductor nanowires with a full superconducting shell. We demonstrate that,
in the presence of spin-orbit coupling in the semiconductor induced by a radial
electric field, the winding of the superconducting order parameter leads to a
topological phase supporting Majorana zero modes. The topological phase
persists over a large range of chemical potentials and can be induced by a
predictable and weak magnetic field piercing the cylinder. The system can be
readily realized in semiconductor nanowires covered by a full superconducting
shell, opening a pathway for realizing topological quantum computing proposals.
