Spin-valley caloritronics in silicene near room temperature

Two-dimensional silicene, with an observable intrinsic spin-orbit coupling, has a great potential to perform fascinating physics and new types of applications in spintronics and valleytronics. By introducing an electromotive force from a temperature difference in ferromagnetic silicene, we discover that a longitudinal spin Seebeck effect can be driven even near room temperature, with spin-up and spin-down currents flowing in opposite directions, originating from the asymmetric electron-hole spin band structures. We further propose a silicene field-effect transistor constructed of two ferromagnetic electrodes and a central dual-gated region, and find that a valley Seebeck effect appears, with currents from two different valleys flowing in opposite directions. The forbidden transport channels are determined by either spin-valley dependent band gaps or spin mismatch. By tuning the electric field in the central region, the transport gaps depending on spin and valley vary correspondingly, and a transition from valley Seebeck effect to spin Seebeck effect is observed. These spin-valley caloritronic results near room temperature are robust against many real perturbations, and thus suggest silicene to be an excellent candidate for future energy-saving technologies and bidirectional information processing in solid-state circuits.

Figure 1

Reduced current $I_{\eta }^s/I_0$ vs temperature $T_L$ at $T_{LR}=20\mathrm{K}, M=\lambda$, and $\ell E_z={\varepsilon }_{\mathrm{F}}=0$. The corresponding device is shown by the bottom-left inset and the energy bands of silicene under a ferromagnetic (FM) field are given by the bottom-right inset. $T_{L\left(R\right)}$ indicates the temperature of the left (right) thermoelectrode, and the arrows point to the current directions.

Figure 2

(a) Schematic of silicene-based caloritronic field-effect transistor. A ferromagetic field is applied in the left and right thermoelectrodes, and an interlayer electric field is applied in the central region. A phenomenon of valley Seebeck effect is sketched, corresponding to the energy subbands on the right side, where the shaded areas indicate the transport gaps of spin-up (down) from valley $K\left(K^{\prime }\right)$ due to spin band gaps and spin mismatch. (b) Reduced current $I_{\eta }^s/I_0$ vs temperature $T_L$ at $T_{LR}=20\mathrm{K}, \ell E_z=\lambda$, and ${\varepsilon }_{\mathrm{F}}=0$. (c) Reduced current $I_{\eta }^s/I_0$ vs temperature $T_{LR}$ at $T_L=320\mathrm{K}, \ell E_z=\lambda$. (d) Reduced current $I_{\eta }^s/I_0$ vs electric field $\ell E_z$ at $T_L=300\mathrm{K}, T_{LR}=20\mathrm{K}$. VS and SS represent valley Seebeck effect and spin Seebeck effect, respectively.

Figure 3

Reduced current $I_{\eta }^s/I_0$ vs the Fermi energy ${\varepsilon }_{\mathrm{F}}^{\prime }$ in the central dual-gated region, when the Fermi energy in the two electrodes equals zero. The other parameters are chosen as $M=\ell E_z=\lambda , T_L=300\mathrm{K}$, and $T_{LR}=20\mathrm{K}$. NSP denotes the normal spin-polarized current.