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The Mott transition in honeycomb compounds with significant spin-orbitcoupling is explored. At finite temperatures we identify a novel semimetallicphase located between a topological insulator and a topological Mott insulator.This semimetal is characterized by having no charge gap, no quasiparticles andgapped spin excitations with non-trivial topological properties. While chargeconduction is incoherent involving mean-free paths violating theMott-Ioffe-Regel limit, spin excitations can be transported ballistically alongthe edges giving rise to a quantized spin conductance. Such bad topologicalsemimetal could be searched for close to the Mott transition in certain twistedbilayers of transition metal dicalchogenides.

Bad topological semimetals in layered honeycomb compounds