Topological Edge States of a Majorana BBH Model

Abstract

We investigate a Majorana Benalcazar–Bernevig–Hughes (BBH) model showing the emergence of topological corner states. The model, consisting of a two-dimensional Su–Schrieffer–Heeger (SSH) system of Majorana fermions with π flux, exhibits a non-trivial topological phase in the absence of Berry curvature, while the Berry connection leads to a non-trivial topology. Indeed, the system belongs to the class of second-order topological superconductors (HOTSC2), exhibiting corner Majorana states protected by C4 symmetry and reflection symmetries. By calculating the 2D Zak phase, we derive the topological phase diagram of the system and demonstrate the bulk-edge correspondence. Finally, we analyze the finite size scaling behavior of the topological properties. Our results can serve to design new 2D materials with non-zero Zak phase and robust edge states.

Topological Phases of an Interacting Majorana Benalcazar–Bernevig–Hughes Model

“…Following Ref. [13], we consider a system of Majorana fermions with staggered couplings (w, v) confined in a two-dimensional lattice and described by the Hamiltonian:…”

“…The system belongs to the second-order topological superconductors (HOTSC2) class, featuring corner Majorana states [13]. The simultaneous presence of crystalline symmetries and standard symmetries (C, P, T ) is essential to ensure the realization of second-order topological superconductivity.…”

“…In Ref. [13], we introduced a model of second-order topological superconductor (HOTSC 2 ) based on Majorana fermions (Mfs) operators. The model is the equivalent of the Benalcazar-Bernevig-Hughes (BBH) model [?…”

“…In Section 2, we review the main properties of the mean-field MBBH model introduced in Ref. [13]. In Section 3, we study the particular case of an interacting four-chain strip; in Section 3.1, we discuss the analytical operations needed to transform the strip into an effective one-dimensional system and to perform the DMRG simulations with MPSs.…”

Squashed entanglement in one-dimensional quantum matter

“…TSE exhibits the correct scaling at the quantum phase transition, is stable in the presence of interactions and robust against the effects of disorder and local perturbations. In general one can introduce two distinct multipartition-based upper bounds on TSE: the tripartition-based edge-edge QCMI I (3) corresponding to a edge-bulk-edge tripartition, which leads to a TSE equivalent to that of an analogue spin chain obtained via a Jordan-Wigner transformation, and the quadripartition-based edge-edge QCMI I (4) , corresponding to a partially traced out bulk, which discriminates between symmetric topological regimes and ordered phases associated to spontaneously broken symmetries [22][23][24].…”