Correlated interaction effects in the three-dimensional semi-Dirac semimetal

Understanding the correlation effects in unconventional topological materials, which fermion excitations take unusual dispersion, is an important topic recent condensed matter physics. We study influence of short-range four-fermion interactions on three-dimensional semi-Dirac semimetal with dispersion that linear along two directions and quadratic third one. Based renormalization group theory, we find all 11 unstable fixed points including five quantum critical points, bicritical one tricritical point. The physical essences are determined by analyzing susceptibility exponents for source terms particle-hole particle-particle channels. also verify phase diagrams system parameter space through numerically studying flows coupling parameters behaviors exponents. These results helpful us to understand properties candidate materials such as ${\mathrm{ZrTe}}_{5}$.