Stability of two-dimensional asymmetric materials with a quadratic band crossing point under four-fermion interaction and impurity scattering
Published 2020-03-15Version 1
We investigate the impacts of combination of fermion-fermion interactions and impurity scatterings on the low-energy stabilities of two-dimensional asymmetric materials with a quadratic band crossing point by virtue of the renormalization group that allows to treat distinct sorts of physical ingredients on the same footing. The coupled flow evolutions of all interaction parameters which carry the central physical information are derived by taking into account one-loop corrections. Several intriguing results are manifestly extracted from these entangled evolutions. At first, we realize that the quadratic band touching structure is particularly robust once the fermionic couplings flow towards the Gaussian fixed point. Otherwise, it can either be stable or broken down against the impurity scattering in the vicinity of nontrivial fixed points. In addition, we figure out two parameters $\eta$ and $\lambda$ that measure rotational and particle-hole asymmetries are closely energy-dependent and exhibit considerably abundant behaviors depending upon the fates of fermion-fermion couplings and different types of impurities. Moreover, as both $\eta$ and $\lambda$ can be remarkably increased or heavily reduced in the low-energy regime, asymmetric system exhibits a sensational phenomenon that transition either from rotational or particle-hole asymmetry to symmetric situation would be activated under certain restricted condition.