Strong singularities in the electronic density of states amplify correlation
effects and play a key role in determining the ordering instabilities in
various materials. Recently high order van Hove singularities (VHSs) with
diverging power-law scaling have been classified in single-band electron
models. We show that the 110 surface of Bismuth exhibits high order VHS with an
usually high density of states divergence ∼(E)−0.7. Detailed mapping
of the surface band structure using scanning tunneling microscopy and
spectroscopy combined with first-principles calculations show that this
singularity occurs in close proximity to Dirac bands located at the center of
the surface Brillouin zone. The enhanced power-law divergence is shown to
originate from the anisotropic flattening of the Dirac band just above the
Dirac node. Such near-coexistence of massless Dirac electrons and ultra-massive
saddle points enables to study the interplay of high order VHS and Dirac
fermions