  The Ryu-Takayanagi conjecture provides a holographic description for the
entanglement entropy for the strongly coupled holographic CFTs in the
semi-classical limit. It proposes that the entanglement entropy is given by the
area of the minimal homologous surface in the dual bulk. We show that the
common terms of the entanglement entropy for the free massless fermions or
bosons on a torus in the high-temperature expansion can be described by the sum
of the signed area of extremal surfaces in the BTZ spacetime. The resulting EE
and the corresponding bunch of the exgremal surfaces have preferable properties
rather than those from the Ryu-Takayanagi conjecture.
