  As platforms of Majorana modes, topological insulator (quantum anomalous Hall
insulator)/superconductor (SC) heterostructures have attracted tremendous
attention over the past decade. Here we substitute the topological insulator by
its higher-order counterparts. Concretely, we consider second-order topological
insulators (SOTIs) without time-reversal symmetry and investigate SOTI/SC
heterostructures in both two and three dimensions. Remarkably, we find that
such novel heterostructures provide natural realizations of second-order
topological superconductors (SOTSCs) which host Majorana corner modes in two
dimensions and chiral Majorana hinge modes in three dimensions. As here the
realization of SOTSCs requires neither special pairings nor magnetic fields,
such SOTI/SC heterostructures are outstanding platforms of Majorana modes and
may have wide applications in future.
