Hall effect of triplons in a dimerized quantum magnet

TL;DR

This paper demonstrates that SrCu$_2$(BO$_3$)$_2$, modeled by the Shastry Sutherland model with Dzyaloshinskii-Moriya interactions, hosts topologically nontrivial triplon bands with protected edge modes, akin to a quantum Hall effect for magnetic excitations.

Contribution

It reveals the topological nature of triplon bands in a dimerized quantum magnet and predicts observable thermal Hall effects.

Findings

Triplon bands exhibit nonzero Chern numbers of ±2.

Magnetic field induces band splitting and topological edge modes.

A critical magnetic field causes band touching and loss of topology.

Abstract

The celebrated Shastry Sutherland model has a gapped dimer singlet ground state. The material SrCu$_2$(BO$_3$)$_2$ serves as a good realization of this model, upto small anisotropies arising from Dzyaloshinskii-Moriya (DM) interactions. The DM interactions admix a triplet component into the singlet ground state and give rise to weakly dispersing triplon bands. We show that an applied magnetic field splits the triplon modes and opens band gaps. Surprisingly, we are left with topological bands with Chern numbers $\pm 2$. SrCu$_2$(BO$_3$)$_2$ thus supports topologically protected triplonic edge modes and is a magnetic analogue of the integer quantum Hall effect. At a critical value of the magnetic field set by the strength of DM interactions, the three triplon bands touch once again in a spin-1 generalization of a Dirac cone, and lose their topological character. We predict a strong thermal Hall signature in the topological regime.