Disorder driven multifractality transition in Weyl nodal loops*

The effect of short-range disorder in a three dimensional nodal line
semimetal is studied numerically. A diffusive semimetal phase already
exists for small disorder, as the latter mixes all the degenerate nodal states
and prevents a ballistic regime. The zero energy wavefunction exhibits
multifractality in momentum space, with a quasi one dimensional probability
density following the co-dimension 2 of the Fermi surface. At a critical
disorder strength, a semimetal to compressible metal transition occurs,
coinciding with a multi- to single-fractality transition in momentum
space. The correlation length and dynamical critical exponents are
obtained through a scaling analysis of the data. At considerably higher
disorder, an Anderson metal-insulator transition takes place.