In the first part of my talk, I will talk about transport scaling theories in disordered Weyl semimetal [1,2]. In electronic band structure of solid state material, two band touching points with linear dispersion (called as `Weyl node') appear in pair in the momentum space. When they annihilate with each other, the system undergoes a quantum phase transition from Weyl semimetal (WSM) phase to a band insulator (BI) phase. The phase transition is described by a critical theory with a `magnetic dipole' like object in the momentum space. The critical theory hosts a disorder-driven quantum multicritical point, which is encompassed by three quantum phases, WSM phase, BI phase, and diffusive metal (DM) phase. Based on the renormalization group argument, we clarify novel transport scaling properties around the Weyl node at the quantum multicritical point as well as all phase boundaries among these three phases
In the second part of my talk, I will argue that three-dimensional topological excitonic insulator is realized in graphite under high magnetic field [3,4]. Graphite under high magnetic field exhibits consecutive metal-insulator (MI) transitions as well as re-entrant insulator-metal (IM) transition at low temperature. We explain these enigmatic insulator phases as manifestation of excitonic insulator phases with spin nematic orderings. Especially, we explain unusual field-dependences of in-plane resistivity in the graphite experiment by surface transports via 2+1 massless surface Dirac fermion in one of the SNEI phases [3,4].
 https://arxiv.org/abs/1803.09051, under review
 https://arxiv.org/abs/1710.00572, selected as PRB editors’ suggestion  https://arxiv.org/abs/1802.10253, under review
 in preparation