Zero and Nonzero Energy Majorana Modes in an Extended Kitaev Chain

Abstract

This paper studies an extended Kitaev chain with three sublattices per unit cell. This extended version is obtained by hybridizing a modified Su-Schrieffer-Heeger model featuring trimerized unit cells with the standard Kitaev chain, resulting in a hexamer structure on the Majorana basis. Due to the interplay between the sublattice configuration and the $p$-wave superconducting pairing, a rich structure of edge modes beyond the expected Majorana zero modes is obtained. The various Majorana edge modes are further found to demonstrate considerable robustness against some generic perturbations and disorder. The presence of the non-zero Majorana edge modes in our system has the potential advantage that they could, in principle, be more unambiguously detected as compared to their zero energy counterparts, the detection of which remains an open problem. Therefore, while our system does not directly solve this open problem, it potentially offers a route to an intermediate solution that involves unambiguously detecting non-zero energy Majorana edge modes instead.