Interfacial Corner Modes in a Topolectrical Heterojunction

Non-Hermitian topolectrical circuit (TE) networks consisting of capacitors, inductors, and operational amplifiers can be designed to realize higher-order topological states in which all the eigenmodes are exponentially localized at the corners of a square lattice network. Here, we utilize a TE circuit to realize a higher-order non-Hermitian (HONH) heterojunction in which all the eigenstates are localized at the interfacial nodes. The novel localization of these eigenstates, which we dub as the interfacial higher-order non-Hermitian corner modes (INHCM), arises whenever two HONH topological lattices with opposite signs of the non-Hermitian parameter are cascaded together. Furthermore, the INHCMs appear under both open boundary conditions (OBC) and periodic boundary conditions (PBC), in marked contrast to the conventional non-Hermitian skin effect which occurs only under OBC but not under PBC. We analyze the decay lengths of the interfacial corner mode localization and establish its dependence on the asymmetric intra-unit cell couplings in the heterojunction circuit. Our study establishes the conditions for the onset of HONH effects in heterojunction systems and unveils a new type of skin mode localization at the interface.