  The Berry phase on the Fermi surface and its influence on the conserved spin
current in a two-dimensional system with generic $k$-linear spin-orbit
interaction are investigated. We calculate the response of the effective
conserved spin current to the applied electric field, which is composed of
conventional and spin torque currents, by using the Kubo formula. We find that
the conventional spin current is not determined by the Berry phase effect.
Remarkably, the spin torque Hall current is found to be proportional to the
Berry phase, and the longitudinal spin torque current vanishes because of the
Berry phase effect. When the $k$-linear spin-orbit interaction dominates the
system, the Berry phase on the Fermi surface maintains two invariant
properties. One is that the magnitude of the spin torque current protected by
the Berry phase is unchanged by a small fluctuation of energy dispersion. The
other one is that the change in the direction of the applied electric field
does not change the magnitude of the spin torque current even if the energy
dispersion is not spherically symmetric; i.e., the Berry phase effect has no
dependence on the two-dimensional material orientation. The spin torque current
is a universal value for all $k$-linear systems, such as Rashba, Dresselhaus,
and Rashba-Dresselhaus systems. The topological number attributed to the Berry
phase on the Fermi surface represents the phase of the orbital chirality of
spin in the $k$-linear system. The change in the topological number results in
a phase transition in which the orbital chirality of spin $s_z$ and $-s_z$ is
exchanged. We found that the spin torque current can be experimentally
measured.
