Exotic quantum criticality in pyrochlore iridates

Luttinger semimetals are three-dimensional strongly-spin-orbit-coupled systems, in which valence and conduction bands touch quadratically at the Fermi level. They provide a rich playground for highly unconventional physics and serve as a parent state to a number of exotic states of matter, such as Weyl semimetals, topological insulators, or spin ice. Here, we discuss various quantum critical phenomena beyond standard quantum criticality, including quasiuniversality and fixed point annihilation scenarios. Our results are relevant for the low-temperature behavior of rare-earth pyrochlore iridates, such as Pr₂Ir₂O₇ or Nd₂Ir₂O₇.