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We study the influence of disorder on the topological transition from atwo-dimensional Dirac semi-metal to an insulating state. This transition isdescribed as a continuous merging of two Dirac points leading to a semi-Diracspectrum at the critical point. The latter is characterized by a dispersionrelation linear in one direction and quadratic in the orthogonal one. Using theself-consistent Born approximation and renormalization group we calculate thedensity of states above, below and in the vicinity of the transition in thepresence of different types of disorder. Beyond the expected disorder smearingof the transition we find an intermediate disordered semi-Dirac phase. On oneside this phase is separated from the insulating state by a continuoustransition while on the other side it evolves through a crossover to thedisordered Dirac phase.

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator