Interplay of Coulomb interaction and disorder in a two-dimensional semi-Dirac fermion system

It was recently found that Coulomb interaction can induce a series of nontrivial spectral and transport properties in a two-dimensional semi-Dirac fermion system. Different from graphene that is basically an ordinary Fermi liquid, the Coulomb interaction in this system invalidates the Fermi liquid description over a wide range of energy scales. We present a systematic renormalization group analysis of the interplay of Coulomb interaction and quenched disorder, and show that they have substantial mutual effects on each other, which leads to a variety of quantum phase transitions and non-Fermi liquid behaviors. The low-energy behaviors of the system depend sensitively on the effective strength of Coulomb interaction and disorder.