  Fermi condensation is usually a phenomena of strongly correlated system. In
this letter, we point out a novel mechanism for condensation of Dirac fermions
due to Weyl anomaly. The condensation has its physical origin in the nontrivial
response of the fermion vacuum to changes in the background spacetime (either
boundary location or the background metric), and can be felt when a background
scalar field is turned on. The scalar field can be, for example, the Higgs
field in a fundamental theory or the phonon in condensed matter system. For a
spacetime with boundaries, the induced Fermi condensate is inversely
proportional to the proper distance from the boundary. For a conformally flat
spacetime without boundaries, Fermi condensation depends on the conformal
factor and its derivatives. We also generalize the Banks-Casher relation which
relates the Fermi condensate to the zero mode density of the Dirac operator to
a local form. Due to its universal nature, this anomaly induced Fermi
condensate can be expected to have a wide range of applications in physics.

High Energy Physics - Theory;General Relativity and Quantum Cosmology