A practical method to detect, analyze, and engineer higher order Van Hove singularities in multi-band Hamiltonians

A practical method is presented to detect, diagnose, and engineer higher order Van Hove singularities in multiband systems, with no restrictions on the number of bands or hopping terms. The method allows us to directly compute the Taylor expansion of the dispersion of any band at arbitrary points in momentum space, using a generalized extension of the Feynman–Hellmann theorem, which is stated and proved. Being fairly, in general scope, it also allows to incorporate and analyze the effect of tuning parameters on the low energy dispersions, which can greatly aid the engineering of higher order Van Hove singularities. A certain class of degenerate bands can be handled within this framework. The use of this method is demonstrated, by applying it to the Haldane model.