  A crucial step in revealing the nature of unconventional superconductivity is
to investigate the symmetry of the superconducting order parameter. Scanning
tunneling spectroscopy has proven a powerful technique to probe this symmetry
by measuring the quasiparticle interference (QPI) which sensitively depends on
the superconducting pairing mechanism. A particularly well suited material to
apply this technique is the stoichiometric superconductor LiFeAs as it features
clean, charge neutral cleaved surfaces without surface states and a relatively
high Tc~18K. Our data reveal that in LiFeAs the quasiparticle scattering is
governed by a van-Hove singularity at the center of the Brillouin zone which is
in stark contrast with other pnictide superconductors where nesting is crucial
for both scattering and s+- superconductivity. Indeed, within a minimal model
and using the most elementary order parameters, calculations of the QPI suggest
a dominating role of the hole-like bands for the quasiparticle scattering. Our
theoretical findings do not support the elementary singlet pairing symmetries
s++, s+-, and d-wave. This brings to mind that the superconducting pairing
mechanism in LiFeAs is based on an unusual pairing symmetry such as an
elementary p-wave (which provides optimal agreement between the experimental
data and QPI simulations) or a more complex order parameter (e.g. s+id-wave
symmetry).
