Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors

Bound states at sharp corners have been widely viewed as the hallmark of two-dimensional second-order topological insulators and superconductors. In this paper, we show that the existence of sublattice degrees of freedom can enrich the tunability of bound states on the boundary and hence lift the constraint on their locations. We take the Kane-Mele model with honeycomb-lattice structure to illustrate the underlying physics. With the introduction of an in-plane exchange field to the model, we find that the boundary Dirac mass induced by the exchange field has a sensitive dependence on the boundary sublattice termination. We find that the sensitive sublattice dependence can lead bound states to emerge at a specific type of boundary defects named as sublattice domain walls if the exchange field is of ferromagnetic nature, even in the absence of any sharp corner on the boundary. Remarkably, this sensitive dependence of the boundary Dirac mass on the boundary sublattice termination allows the positions of bound states to be manipulated to any place on the boundary for an appropriately-designed sample. With a further introduction of conventional s-wave superconductivity to the model, we find that, no matter whether the exchange field is ferromagnetic, antiferromagnetic, or ferrimagnetic, highly controllable Majorana zero modes can be achieved at the sublattice domain walls. Our paper reshapes the understanding of boundary physics in second-order topological phases, and meanwhile opens potential avenues to realize highly controllable bound states for potential applications.