Perfectly localized Majorana corner modes in fermionic lattices

Focusing on examples of Majorana zero modes on the corners of a two-dimensional lattice, we introduce a method to find parameter regions where the Majorana modes are perfectly localized on a single site. Such a limit allows us to study the dimerization structure of the sparse bulk Hamiltonian that results in the higher-order topology of the system. Furthermore, such limits typically provide an analytical understanding of the system energy scales. Based on the dimerization structure we extract from the two-dimensional model, we identify a more general stacking procedure to construct Majorana zero modes in arbitrary corners of a $d$-dimensional hypercube, which we demonstrate explicitly in $d\le 3$.