Inverse Janus design of two-dimensional Rashba semiconductors

The search for optimal Rashba semiconductors with large Rashba constants, strong electric field responses, and potential thermoelectric properties is pivotal for spin field-effect transistors (SFETs) and Rashba thermoelectric devices. Herein, we employ first-principles calculations to explore the intrinsic Rashba spin splitting in a series of two-dimensional (2D) $XY{Z}_2$ (X, $Y=\mathrm{Si}$, Ge, Sn; $X\ne Y$; $Z=\mathrm{P}$, As, Sb, Bi) monolayers via unnatural inverse Janus structural design. Instead of common Janus-type Rashba systems, the $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers within inverse Janus structures are first predicted as ideal Rashba systems with isolated spin-splitting bands near the Fermi level, and the Rashba constants ${\alpha }_{\mathrm{R}}$ are calculated as 0.94 and $1.27\mathrm{eV}\AA$, respectively. More importantly, the Rashba effect in such $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers can be more efficiently modulated by the external electric field compared to the biaxial or uniaxial strain, especially with $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayer exhibiting a strong electric field response rate of $1.34\mathrm{e}{\AA }^2$, leading to a short channel length, $L=64\mathrm{nm}$. Additionally, owing to the inapplicability of work function and potential energy in assessing built-in electric field $\left(E_{in}\right)$ in inverse Janus $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$ structures, we further propose an effective method to characterize $E_{in}$ through a view of fundamental charge transfer to approximately quantize the ${\alpha }_{\mathrm{R}}$ and its variation under an external electric field. Our work not only proposes the $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayer acting as a promising multifunctional material for potential applications in SFETs and Rashba thermoelectric devices but also inspires future research to introduce Rashba spin splitting in 2D materials through inverse Janus design.

Figure 1

(a) Side and top views of honeycomb crystal structure of $XY{Z}_2$ monolayers. Blue, red, and yellow balls denote X, Y, and $Z$ atoms, respectively. (b) First Brillouin zone labeled with high-symmetry points. (c) Phonon spectra and (d) AIMD simulations of total energy fluctuation under 10 ps at 300 K of $\mathrm{SiGe}{\mathrm{Sb}}_2,\mathrm{SiSn}{\mathrm{Sb}}_2$, and $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers.

Figure 2

Band structures of (a) $\mathrm{SiSn}{\mathrm{Sb}}_2$ and (b) $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers. Black and red solid lines indicate methods of PBE and PBE+SOC, respectively. Enlarged view of Rashba spin-splitting bands at CBM near Fermi level is plotted in blue. Right parts represent 2D contour plots of spin textures for $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers at constant energy $E_1\left(E_{\mathrm{f}}+0.07\mathrm{eV}\right),E_2\left(E_{\mathrm{f}}+0.05\mathrm{eV}\right)$ in $k_x-k_y$ plane centered at Г point. Red color represents spin-up states and blue represents spin-down states. Projections of spin components $S_x,S_y$, and $S_z$ are plotted.

Figure 3

Electrostatic potential of (a) SnSb, (b) $\mathrm{SiSn}{\mathrm{Sb}}_2$, and $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers along $z$ direction. (c) Comparative charge-transfer plots of SnSb and $\mathrm{SiSn}{\mathrm{Sb}}_2$, SnSb and $\mathrm{GeSn}{\mathrm{Sb}}_2$, and $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$. (d), (e) Schematic diagram of charge transfer and $E_{in}$ of SnSb, $\mathrm{SiSn}{\mathrm{Sb}}_2$, and $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers. $E_0,E_0^{{}^{\prime }},E_0^{{}^{″}}$ represent localized electric field. $|Q_{d0}|$: $|\left(-e_3^{-}\right)-e_1^{-}|,|Q_{t0}|$: $|e_1^{-}+e_2^{-}+e_3^{-}|$. $e_1^{-},e_2^{-},e_3^{-}$ represent gaining electrons with negative value and $-e_1^{-},-e_2^{-},-e_3^{-}$ represent losing electrons with positive value.

Figure 4

$\left({\text{a}}_1\right)$ Schematic diagrams of electrostatic potential of MXY (taking MoSSe [19] as example), $\mathrm{SiSn}{\mathrm{Sb}}_2$, and $\mathrm{GeSn}{\mathrm{Sb}}_2$. $\left({\text{a}}_2\right)$ Schematic diagrams of structure, charge transfer, $E_0,E_0^{{}^{\prime }},E_0^{{}^{″}},$ and $E_{in}$ of non-Janus SnSb monolayer, common Janus $X{\mathrm{Sn}}_{2}Y$ monolayer [23] $(E_{in}$ as example of $\mathrm{Sb}{\mathrm{Sn}}_2\mathrm{Bi})$, and inverse Janus $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$. $\left({\text{a}}_3\right)$ Schematic diagrams of variation of $|Q_t|,|Q_d|$, and Rashba effect under external electric field $E$. (b) Electric field dependence of charge transfer $|Q_t|,|Q_d|$, and Rashba constant ${\alpha }_{\mathrm{R}}$ for inverse Janus $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$ monolayers. Solid and dashed lines represent slope of fit based on calculated data and Eq. (2). (c) Schematic diagram of SFET based on inverse Janus structures $\mathrm{SiSn}{\mathrm{Sb}}_2$ and $\mathrm{GeSn}{\mathrm{Sb}}_2$ (taking $\mathrm{GeSn}{\mathrm{Sb}}_2$ as example). Spin precession between source and drain can be governed by gate voltage.