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, 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.

19 pages

References in corpus (6)

• Isospin magnetism and spin-triplet superconductivity in Bernal bilayer graphene
• Competing orders at higher-order Van Hove points
• Van Hove tuning of AV3Sb5 kagome metals under pressure and strain
• Effect of disorder on density of states and conductivity in higher order van Hove singularities in two dimensional bands
• Magnetic fluctuations and specific heat in NaxCoO2 near a Lifshitz topological transition
• Semiclassical transport with Berry curvature: Chambers formula and applications to systems with Fermi surface topological transitions

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• Kondo effect in twisted bilayer graphene
• Fate of density waves in the presence of a higher order van Hove singularity
• Single monkey-saddle singularity of a Fermi surface and its instabilities
• Strain-dependent one-dimensional confinement channels in twisted bilayer 1T${}^{\prime }$-WTe${}_2$
• Inversion and Tunability of Van Hove Singularities in $A$V${}_3$Sb${}_5$ ($A$ = K, Rb, and Cs) kagome metals
• Designing Topological High-Order Van Hove Singularities: Twisted Bilayer Kagomé
• Brightening dark excitons and trions in systems with a Mexican-hat energy dispersion: example of InSe
• Kekulé order from diffuse nesting near higher-order Van Hove points
• Triplet superconductivity supported by an X${}_9$ high-order Van Hove singularity