From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model

Abstract

We consider one-dimensional topological insulators hosting fractionally charged midgap states in the presence and absence of induced superconductivity pairing. Under the protection of a discrete symmetry, relating positive and negative energy states, the solitonic midgap states remain pinned at zero energy when superconducting correlations are induced by proximity effect. When the superconducting pairing dominates the initial insulating gap, Majorana fermion phases develop for a class of insulators. As a concrete example, we study the Creutz model with induced $s$-wave superconductivity and repulsive Hubbard-type interactions. For a finite wire, without interactions, the solitonic modes originating from the nonsuperconducting model survive at zero energy, revealing a fourfold-degenerate ground state. However, interactions break the aforementioned discrete symmetry and completely remove this degeneracy, thereby producing a unique ground state which is characterized by a topological bulk invariant with respect to the product of fermion parity and bond inversion. In contrast, the Majorana edge modes are globally robust to interactions. Moreover, the parameter range for which a topological Majorana phase is stabilized expands when increasing the repulsive Hubbard interaction. The topological phase diagram of the interacting model is obtained using a combination of mean-field theory and density matrix renormalization group techniques.