We derive the two-dimensional counter-differential rotation equilibria of two-component plasmas, composed of both ion and electron (
$e^-$
) clouds with finite temperatures, for the first time. In the equilibrium found in this study, as the density of the
$e^{-}$
cloud is always larger than that of the ion cloud, the entire system is a type of non-neutral plasma. Consequently, a bell-shaped negative potential well is formed in the two-component plasma. The self-electric field is also non-uniform along the
$r$
-axis. Moreover, the radii of the ion and
$e^{-}$
plasmas are different. Nonetheless, the pure ion as well as
$e^{-}$
plasmas exhibit corresponding rigid rotations around the plasma axis with different fluid velocities, as in a two-fluid plasma. Furthermore, the
$e^{-}$
plasma rotates in the same direction as that of
$\boldsymbol {E \times B}$
, whereas the ion plasma counter-rotates overall. This counter-rotation is attributed to the contribution of the diamagnetic drift of the ion plasma because of its finite pressure.
Effective potential and pressure of two-component plasma at high temperature
