  When non-magnetic impurity immerses in Fermi sea, a regular modulation of
charge density around impurity will appear and such phenomena is called Friedel
oscillation (FO). Although both Luttinger liquid and Landau Fermi liquid show
such characteristic oscillation, FO in generic non-Fermi liquid (NFL) phase is
still largely unknown. Here, we show that FO indeed exists in NFL state of an
exactly solvable model, i.e. the Hatsugai-Kohmoto model which has been
intensively explored in recent years. Combining T-matrix approximation and
linear-response-theory, an interesting picture emerges, if two
interaction-induced quasi-particles bands in NFL are partially occupied, FO in
this situation is determined by a novel structure in momentum space, i.e. the
'average Fermi surface' (average over two quasi-particle Fermi surface), which
highlights the inter-band particle-hole excitation. We hope our study here
provides a counterintuitive example in which FO with Fermi surface coexists
with NFL quasi-particle, and it may be useful to detect hidden 'average Fermi
surface' structure in other correlated electron systems.
