We introduce an effective two-dimer tight-binding model for the family of Shastry-Sutherland models with geometrically tunable triplon excitations. The Rashba pseudospin-orbit coupling induced by the tilted external magnetic field leads to elementary excitations having nontrivial topological properties with $\pi$-Berry flux. The interplay between the in-plane and out-of-plane magnetic field thus allows us to effectively engineer the band structure in this bosonic system. In particular, the in-plane magnetic field gives rise to a Berry curvature hotspot near the bottom of the triplon band and at the same time significantly increases the critical magnetic field for the topological triplon band. We calculate explicitly the experimental signature of the thermal Hall effect (THE) of triplons in ${\mathrm{SrCu}}_2{\left({\mathrm{BO}}_3\right)}_2$ and show pronounced and tunabled transport signals within the accessible parameter range, particularly with a change of sign of the thermal Hall conductance. The tilted magnetic field is also useful in reducing the bandwidth of the lowest triplon band. We show it can thus be a flexible theoretical and experimental platform for the correlated bosonic topological system.

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• Magnetism
• Spin-orbit coupling
• Triplon