Bismuth antiphase domain wall: A three-dimensional manifestation of the Su-Schrieffer-Heeger model

TL;DR

This paper proposes that bulk bismuth with dimerized layers acts as a three-dimensional analogue of the SSH model, demonstrating topological domain walls with distinct Zak phases and potential experimental realization via laser excitation.

Contribution

It introduces a 3D realization of the SSH model in bulk bismuth, analyzing topological domain walls and their Zak phases, expanding the understanding of topological insulators beyond 1D systems.

Findings

Dimerized Bi structures have different Zak phases of 0 and π.

Existence of topologically non-trivial and trivial domain walls in Bi.

Criteria for domain walls to exhibit π Zak phase based on parity eigenvalues.

Abstract

The Su, Schrieffer and Heeger (SSH) model, describing the soliton excitations in polyacetylene due to the formation of antiphase domain walls (DW) from the alternating bond pattern, has served as a paradigmatic example of one-dimensional (1D) chiral topological insulators. While the SSH model has been realized in photonic and plasmonic systems, there have been limited analogues in three-dimensional (3D) electronic systems, especially regarding the formation of antiphase DWs. Here, we propose that pristine bulk Bi, in which the dimerization of $(111)$ atomic layers renders alternating covalent and van der Waals bonding within and between successive $(111)$ bilayers, respectively, serves as a 3D analogue of the SSH model. First, we confirm that the two dimerized Bi structures belong to different Zak phases of 0 and $\pi$ by considering the parity eigenvalues and Wannier charge centers, while the previously reported bulk topological phases of Bi remain invariant under the dimerization reversal. Next, we demonstrate the existence of topologically non-trivial $(111)$ and trivial $(11\bar{2})$ DWs in which the number of in-gap DW states (ignoring spin) is odd and even respectively, and show how this controls the interlinking of the Zak phases of the two adjacent domains. Finally, we derive general criteria specifying when a DW of arbitrary orientation exhibits a $\pi$ Zak phase based on the flip of parity eigenvalues. An experimental realization of dimerization in Bi and the formation of DWs may be achieved via intense femtosecond laser excitations that can alter the interatomic forces and bond lengths.