  We study topological phase transitions and topological quantum field effect
transistor in monolayer Molybdenum Disulfide (MoS2) using a two-band
Hamiltonian model. Without considering the quadratic (q^2) diagonal term in the
Hamiltonian, we show that the phase diagram includes quantum anomalous Hall
(QAH), quantum spin Hall (QSH), and spin quantum anomalous Hall effect (SQAH)
regions such that the topological Kirchhoff law is satisfied in the plane. By
considering the q^2 diagonal term and including one valley, it is shown that
MoS2 has a non-trivial topology, and the valley Chern number is non-zero for
each spin. We show that the wave function is (is not) localized at the edges
when the q^2 diagonal term is added (deleted) to (from) the spin-valley Dirac
mass equation. We calculate the quantum conductance of zigzag MoS2 nanoribbons
by using the nonequilibrium Green function method and show how this device
works as a field effect topological quantum transistor.
