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We show that a chiral $f+if$-wave superconducting pairing may be induced inthe lowest heavy hole band of a hole-doped semiconductor thin film throughproximity contact with an \textit{s}-wave superconductor. The chirality of thepairing originates from the $3\pi $ Berry phase accumulated for a heavy holemoving along a close path on the Fermi surface. There exist three chiralgapless Majorana edge states, in consistence with the chiral $f+if$% -wavepairing. We show the existence of zero energy Majorana fermions in vortices inthe semiconductor-superconductor heterostructure by solving theBogoliubov-de-Gennes equations numerically as well as analytically in thestrong confinement limit.

Superconducting phase with a chiral $f$-wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor