  For two- and three-dimensional topological insulators whose unit cells
consist of multiple sublattices, the boundary terminating at which type of
sublattice can affect the time-reversal invariant momentum at which the Dirac
points of helical boundary states are located. Through a general theory and a
representative model, we reveal that this interesting property allows the
realization of Majorana modes at sublattice domain walls forming on the
boundary when the boundary Dirac points of the topological insulator are gapped
by an unconventional superconductor in proximity. Intriguingly, we find that
the sensitive sublattice-dependence of the Majorana modes allows their
positions to be precisely manipulated by locally controlling the terminating
sublattices or boundary potential. Our work reveals that the common sublattice
degrees of freedom in materials open a new route to realize and manipulate
Majorana modes.
