Hall effect of triplons in a dimerized quantum magnet

SrCu$_2$(BO$_3$)$_2$ is the archetypal quantum magnet with a gapped dimer-singlet ground state and triplon excitations. It serves as a realization of the Shastry Sutherland model, up to small anisotropies arising from Dzyaloshinskii-Moriya (DM) interactions. We demonstrate that the DM couplings give rise to topological character in the triplon band structure. The triplons form a new kind of a Dirac cone with three bands touching at a single point, a spin-1 generalization of graphene. An applied magnetic field opens band gaps and as a result topological bands with Chern numbers $\pm 2$ develop. Thus SrCu$_2$(BO$_3$)$_2$ is a magnetic analogue of the integer quantum Hall effect and supports topologically protected edge modes. At a critical value of the magnetic field set by the strength of DM interactions, the three triplon bands touch again in a spin-1 Dirac cone, and lose their topological character. We predict thermal Hall signature in the topological regime.