Continued development of high-efficiency multi-junction solar cells requires growth of lattice-mismatched materials. Today, the need for lattice matching both restricts the bandgap combinations available for multi-junctions solar cells and prohibits monolithic integration of high-efficiency III-V materials with low-cost silicon solar cells. The use of III-V nanowires is the only known method for circumventing this lattice-matching constraint, and therefore it is necessary to develop growth of nanowires with bandgaps >1.4 eV. Here we present the first gold-free gallium arsenide phosphide nanowires grown on silicon by means of direct epitaxial growth. We demonstrate that their bandgap can be controlled during growth and fabricate core-shell nanowire solar cells. We further demonstrate that surface passivation is of crucial importance to reach high efficiencies, and present a record efficiency of 10.2% for a core-shell single-nanowire solar cell.