Multi-Dirac and Weyl physics in heavy-fermion systems

We have studied multi-Dirac/Weyl systems with arbitrary topological charge $n$ in the presence of a lattice of local magnetic moments. To do so we propose a multi-Dirac/Weyl Kondo lattice model which is analyzed through a mean-field approach appropriate to the paramagnetic phase. We study both the broken time-reversal and the broken inversion-symmetry Weyl cases. The multi-Dirac and broken time-reversal multi-Weyl cases have similar behavior, which is in contrast to the broken-parity case. For the former, low-energy particle-hole symmetry leads to the emergence of a critical coupling constant below which there is no Kondo quenching, reminiscent of the pseudogap Kondo impurity problem. Away from particle-hole symmetry, there is always Kondo quenching. For the broken inversion symmetry, there is no critical coupling. Depending on the conduction electron filling, Kondo insulator, heavy-fermion metal, or semimetal phases can be realized. In the last two cases, quasiparticle renormalizations can differ widely between opposite chirality sectors, with characteristic dependences on microscopic parameters that could in principle be detected experimentally.