Dependence of Topological Anderson Insulator Phase on the Statistical Distribution of Disorder


We consider the dependence to statistical distribution of disorder for attaining disorder-induced topological Anderson insulator (TAI) phase characterized by quantized conductance plateau established in HgTe quantum well simulations. The renormalization of parameters that explains the transition from metal to TAI phase under the effective medium theory proposed by Groth et al. are proportional to the strength of disorder and not explicitly on its statistics. We then suppose that as long as the strength of disorder can be defined, under the appropriate conditions, the system will exhibit the TAI phase. We compare, for instance, the disorder drawn from Gaussian distribution to the case of disorder drawn from a uniform distribution where TAI phase is initially demonstrated. We found that the first case exhibits TAI phase but is not as robust as the uniform distribution case. Inspection of the Gaussian type of disorder is pursued due to vast observation of such distribution in nature. We consider as well the condition when the uniform distribution is discrete, as opposed to being continuous. Lastly, we discuss a possible generalization under the effective medium theory.