  In a first-order topological phase with sublattice degrees of freedom, a
change in the boundary sublattice termination has no effect on the existence of
gapless boundary states in dimensions higher than one. However, such a change
may strongly affect the physical properties of those boundary states. Motivated
by this observation, we perform a systematic study of the impact of sublattice
terminations on the boundary physics on the two-dimensional kagome lattice. We
find that the energies of the Dirac points of helical edge states in
two-dimensional first-order topological kagome insulators sensitively depend on
the terminating sublattices at the edge. Remarkably, this property admits the
realization of a time-reversal invariant second-order topological
superconducting phase with highly controllable Majorana Kramers pairs at the
corners and sublattice domain walls by putting the topological kagome insulator
in proximity to a $d$-wave superconductor. Moreover, substituting the $d$-wave
superconductor with a conventional $s$-wave superconductor, we find that highly
controllable Majorana zero modes can also be realized at the corners and
sublattice domain walls if an in-plane Zeeman field is additionally applied.
Our study reveals promising platforms to implement highly controllable Majorana
zero modes.
