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We study systems with energy bands in two dimensions, hosting higher orderVan Hove singularities (HOVHS) in the presence of disorder, using standarddiagrammatic techniques for impurity averaging. In the clean limit, suchsingularities cause power-law divergence in the density of states (DOS), andthis is expected to strongly affect electronic correlation. In order to analysethe signatures of these singularities in disordered systems, we employ variousBorn approximations, culminating in the self-consistent (non) Bornapproximation. Although the divergence of the DOS is smeared, we find that theshape of the DOS, as characterized by the power law tail and the universalratio of prefactors, is retained slightly away from the singularity. This couldhelp us to understand current and future experiments on materials that can betuned to host HOVHS. The impurity induced smearing is calculated and analysedfor several test cases of singularities. We also study the effects ofimpurities on electrical conductivity and determine the regimes where thequantitative features of the power law DOS manifest in the conductivity.

Effect of disorder on density of states and conductivity in higher order van Hove singularities in two dimensional bands