Generation and transport of valley-polarized current in transition-metal dichalcogenides

In two-dimensional crystals of transition-metal dichalcogenides (TMDC) having strong spin-orbit interaction such as monolayer ${\mathrm{WSe}}_2$, quantum states can be labeled by a valley index $\tau$ defined in the reciprocal space and the spin index $s$. We developed a first-principles theoretical formalism to both qualitatively and quantitatively predict nonequilibrium quantum transport of valley-polarized currents. We propose a ${\mathrm{WSe}}_2$ TMDC transistor to selectively deliver net valley- and spin-polarized current $I_{\tau ,s}$ to the source or drain by circularly polarized light under external bias. Due to the lack of translational symmetry of the real-space device, we predict a depolarization effect that increases with the decrease of the channel length of the transistor.

Figure 1

Schematic plot of the two-probe monolayer ${\mathrm{WSe}}_2$ transistor having a source, a channel where light impinges, and a drain. The source and drain regions extend to $y=\mp \infty$. The channel can be controlled by a back-gate voltage $V_g$. The light has photon energy $\hslash \omega$.

Figure 2

(a) Top view of monolayer ${\mathrm{WSe}}_2$. Black dash line in left figure indicates a supercell along the armchair direction. The corresponding folded BZ is indicated by the dark dashed line in the right figure. Black curved arrows illustrate folding of the K points. (b) Schematic plot showing the qualitative physics of photocurrent. (c–f) Effective transmission $T_{S/D}(\mathbf{k},E,s)$ at $K$ and $K^{\prime }$ points of the transistor at $V_{\text{ds}}=0.3\text{V}$ and $V_g=0\text{V}$. Dashed and solid lines distinguish the transmission produced by ${\sigma }_{+}$ and ${\sigma }_{-}$ circularly polarized incident light. The reference energy in Figs. 2–2 is the Fermi energy of the system at equilibrium.

Figure 3

(a) Different valley components and total photocurrent in the source and drain of the transistor. (b) The net valley current in the source and drain of the phototransistor. (c) Valley polarization $\eta$ versus bias voltage $V_{\text{ds}}$. (d) Valley polarization $\eta$ versus the channel length of the transistor. ${\sigma }_{-}$ light is shed on the entire central region.

Figure 4

Schematic plot of a two-terminal device consisting of a central scattering region enclosed in the simulation box (between $Z_L$ and $Z_R$), and left and right electrodes extending to electron reservoirs at $Z=\pm \infty$, where bias voltages are applied and electric current is collected. The scattering region includes many layers of the electrode atoms as indicated by the buffer.

Figure 5

Flowchart of the NEGF-DFT self-consistent procedure.

Figure 6

Transmission $T_D(\mathbf{k}=K^{\prime },E)$ for three values of $V_{\text{ds}}$.