  The entanglement entropy of free fermions with a Fermi surface is known to
obey a logarithmic scaling and violate the area law in all dimensions. Here, we
would like to see how temperature affects the logarithmic scaling behavior. To
this end, we compute the entanglement negativity of free fermions using the
fermionic partial transpose developed in our earlier paper [Phys. Rev. B 95,
165101 (2017)]. In one dimension, we analytically derive the leading order term
in the finite-temperature entanglement negativity and show how the entanglement
negativity indicates a crossover from a quantum entangled state to a classical
thermal state, where the entanglement is completely lost. We explain how the
one-dimensional result can be generalized to codimension-one Fermi surface of
arbitrary shape in higher dimensions. In both one and two dimensions, we check
that our analytical results agree with the numerical simulation of free
fermions on a lattice.
