Transport Theory of Monolayer Transition-Metal Dichalcogenides through Symmetry

We present a theory that elucidates the major momentum and spin relaxation processes for electrons, holes, and hot excitons in monolayer transition-metal dichalcogenides. We expand on spin flips induced by flexural phonons and show that the spin relaxation is ultrafast for electrons in free-standing membranes while being mitigated in supported membranes. This behavior due to interaction with flexural phonons is universal in two-dimensional membranes that respect mirror symmetry, and it leads to a counterintuitive inverse relation between mobility and spin relaxation.

Figure 1

(a) Top and side views of the real space lattice. (b) Typical scheme of primary and satellite valleys in the conduction and valence bands.

Figure 2

Atomic displacements of the $\Gamma$ phonon modes involved in zeroth-order scattering.

Figure 3

Direct and indirect exciton bands. The optical and exciton-phonon scattering processes are sketched under ${\sigma }_{+}$ photon excitation. Real (virtual) scattering is denoted by solid (dashed) lines and phonon IRs are marked. Right blue (left red) paths lead to ${\sigma }_{+}({\sigma }_{-})$ luminescence.

Figure 4

Electron spin lifetimes versus temperature, governed by intravalley scattering with flexural phonon for free-standing [Eq. (4)] and supported SL-TMDs [Eq. (5)].