Linear temperature behavior of the resistivity in the new high-Tcsuperconductors

We propose that the linear temperature behavior of the resistivity observed in the new high-$T_c$ materials might be linked to their two-dimensional character for electron transport. For three-dimensional electron transport a linear temperature law for the resistivity is obtained for temperatures above the Debye temperature ${\Theta }_D$. For two-dimensional transport, however, such a linear law holds above a characteristic temperature $T^{*}=2\mathrm{}\hslash s{p}_F$ which can be well below ${\Theta }_D$ ($s$ denoting the sound velocity and $p_F$ the Fermi momentum) provided that $p_F\ll \frac{\pi }{a}$, which is the case for these high-$T_c$ materials.