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

Abstract

We present a practical method to detect and diagnose higher order Van Hove singularities in multiband systems, with no restrictions on number of bands and hopping terms. The method allows us to directly compute the Taylor expansion of the dispersion of any band at arbitrary k points, using an extension of the Feynman Hellmann theorem. 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 search for higher order Van Hove singularities. A restricted class of degenerate bands can be handled within this framework, which can be readily computationally implemented. Subsequently, we demonstrate the use of the method, taking the Haldane model as an example. Contents

Kondo effect in twisted bilayer graphene

“…where ψ k is the wavefunction of the lowest positive energy band at momentum k. A more extended analysis of this method has been introduced recently in [85].…”