Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

The low-energy behaviors of gapless double- and triple-Weyl fermions caused by the interplay of long-range Coulomb interaction and quenched disorder are studied by performing a renormalization group analysis. It is found that an arbitrarily weak disorder drives the double-Weyl semimetal to undergo a quantum phase transition into a compressible diffusive metal, independent of the disorder type and the Coulomb interaction strength. In contrast, the nature of the ground state of triple-Weyl fermion system relies sensitively on the specific disorder type in the noninteracting limit: The system is turned into a compressible diffusive metal state by an arbitrarily weak random scalar potential or $z$ component of random vector potential but exhibits stable critical behavior when there is only $x$ or $y$ component of random vector potential. In case the triple-Weyl fermions couple to random scalar potential, the system becomes a diffusive metal in the weak interaction regime but remains a semimetal if Coulomb interaction is sufficiently strong. Interplay of Coulomb interaction and $x$, or $y$, component of random vector potential leads to a stable infrared fixed point that is likely to be characterized by critical behavior. When Coulomb interaction coexists with the $z$ component of random vector potential, the system flows to the interaction-dominated strong coupling regime, which might drive a Mott insulating transition. It is thus clear that double- and triple-Weyl fermions exhibit distinct low-energy behavior in response to interaction and disorder. The physical explanation of such distinction is discussed in detail. The role played by long-range Coulomb impurity in triple-Weyl semimetal is also considered.