Absence of localized edge modes in spite of a non-trivial Zak phase in BiCu2PO6

M Malki,G S Uhrig,L Müller

doi:10.1103/physrevresearch.1.033197

Abstract

Topological properties of physical systems are attracting tremendous interest. Recently, magnetic solid state compounds with and without magnetic order have become a focus. We show that ${\text{BiCu}}_{2}{\text{PO}}_{6}$ is the first gapful quantum antiferromagnet with a finite Zak phase, which characterises one-dimensional systems, and only the second with topological non-trivial triplon excitations. Surprisingly, in spite of the bulk-boundary correspondence no localised edge mode occurs. This unexpected behaviour is explained by the distinction between direct and indirect gaps among the triplon bands.

Highlights

The 2016 Nobel Prize awarded to Thouless, Haldane, and Kosterlitz has set an exclamation mark for the significance of topology in condensed matter physics [1]
We studied the localization of all states quantitatively by computing the inverse participation ratio (IPR) [53,54], which is a standard measure for localization
Two key results are presented in this article: One is material specific while the other is general

Summary

INTRODUCTION

The 2016 Nobel Prize awarded to Thouless, Haldane, and Kosterlitz has set an exclamation mark for the significance of topology in condensed matter physics [1]. Since so far fermionic topological insulators have been the focus of research, it is natural to consider a filled valence and an empty conduction band separated by an energy gap with the Fermi level lying within this gap, i.e., a standard band insulator This implies that the direct gap dir with momentum conservation and the indirect gap indir without momentum conservation are both finite. The situation is richer if one considers fermionic bands away from the Fermi energy or bosonic bands These bands, or more precisely the corresponding eigenstates, can display well-defined non-trivial topologies if the bands are energetically separated from each other, i.e., if there are finite direct gaps at each momentum between the bands. A related but different topological invariant is the winding number, which is discussed in Appendix F

MODEL FOR BiCu2PO6

BERRY PHASES IN BOSONIC SYSTEMS

LOCAL DYNAMIC STRUCTURE FACTOR IN BiCu2PO6

CONCLUSIONS