  We study a non-relativistic fermionic retarded Green's function by making use
of a fermion on the Lifshitz geometry with critical exponent z = 2. With a
natural boundary condition, respecting the symmetries of the model, the
resultant retarded Green's function exhibits a number of interesting features
including a flat band. We also study the finite temperature and finite chemical
potential cases where the geometry is replaced by Lifshitz black hole
solutions.
