Topological Kondo semimetals emulated in hetero-bilayer transition metal dichalcogenides

The moir\'{e} structure of AB-stacked $\rm{MoTe_2/WSe_2}$ represents a natural platform to realize Kondo lattice models, due to the discrepancy of the bandwidth between the individual layers. Here, we study this system at the commensurate filling of $\nu_{\rm tot}=2$. Our focus is on the $1+1$ filling setting of $\nu_{\rm Mo} =\nu_{\rm W}=1$, which enables a Kondo lattice description. We find a Kondo semimetal due to the sizable intra-orbital hopping among the electrons in the $\rm{MoTe_2}$ layer. The Kondo-driven (emergent) flat band is naturally pinned to the Fermi energy. When combined with the inherent topology of the electronic structure, a topological Kondo semimetal phase ensues. We calculate the valley Hall response and, due to the breaking of inversion symmetry, also identify a spontaneous Hall effect. There is a Berry curvature dodecapole, which leads to a fourth-order spontaneous Hall effect in the perturbative regime of the electric field that is further amplified in the non-perturbative regime. As such, the system provides a tunable setting to simulate topological Kondo semimetals. Finally, we discuss the pathways that connect the physics realized here to the Weyl Kondo semimetals and their proximate phases that have been advanced in recent years in topological Kondo lattice models and materials.