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

Jinwoong Kim, Cheng Yi Huang, Hsin Lin, David Vanderbilt, Nicholas Kioussis

Research output: Contribution to journalArticlepeer-review


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 analogs 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 analog of the SSH model. First, we confirm that the two dimerized Bi structures belong to different Zak phases of 0 and π 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 nontrivial (111) and trivial (112¯) 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 π Zak phase based on the flip of parity eigenvalues. An experimental realization of dimerization reversal in Bi and the formation of DWs may be achieved via intense femtosecond laser excitations that can alter the interatomic forces and bond lengths.

Original languageEnglish (US)
Article number045135
JournalPhysical Review B
Issue number4
StatePublished - Jan 15 2023

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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