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Strong singularities in the electronic density of states amplify correlationeffects and play a key role in determining the ordering instabilities invarious materials. Recently high order van Hove singularities (VHSs) withdiverging power-law scaling have been classified in single-band electronmodels. We show that the 110 surface of Bismuth exhibits high order VHS with anusually high density of states divergence $\sim (E)^{-0.7}$. Detailed mappingof the surface band structure using scanning tunneling microscopy andspectroscopy combined with first-principles calculations show that thissingularity occurs in close proximity to Dirac bands located at the center ofthe surface Brillouin zone. The enhanced power-law divergence is shown tooriginate from the anisotropic flattening of the Dirac band just above theDirac node. Such near-coexistence of massless Dirac electrons and ultra-massivesaddle points enables to study the interplay of high order VHS and Diracfermions.

Visualizing near-coexistence of massless Dirac electrons and ultra-massive saddle point electrons