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

We present a practical method to detect, diagnose and engineer higher order Van Hove singularities in multiband systems, with no restrictions on the number of bands and 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 generalised extension of the Feynman Hellmann theorem, which we state and prove. Being fairly general in scope, it also allows us to incorporate and analyse 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. We demonstrate the use of the method, by applying it to the Haldane model.