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Topological phase transitions in condensed matters accompany emergingsingularities of the electronic wave function, often manifested by gap-closingpoints in the momentum space. In conventional topological insulators in threedimensions (3D), the low energy theory near the gap-closing point can bedescribed by relativistic Dirac fermions coupled to the long range Coulombinteraction, hence the quantum critical point of topological phase transitionsprovides a promising platform to test the novel predictions of quantumelectrodynamics. Here we show that a new class of quantum critical phenomenaemanates in topological materials breaking either the inversion symmetry or thetime-reversal symmetry. At the quantum critical point, the theory is describedby the emerging low energy fermions, dubbed the anisotropic Weyl fermions,which show both the relativistic and Newtonian dynamics simultaneously. Theinterplay between the anisotropic dispersion and the Coulomb interaction bringsabout a new screening phenomena distinct from the conventional Thomas-Fermiscreening in metals and logarithmic screening in Dirac fermions.

Quantum Criticality of Topological Phase Transitions in 3D Interacting Electronic Systems