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

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