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The transistor is the core unit of digital integrated circuits, and its performance and integration are the main determinants of chip performance. With the continuous progress of nano-manufacturing technology and process, high power and heat consumption have become a major problem restricting the development of integrated circuits. Using topological insulators instead of traditional semiconductors, and the spin and valley degrees of freedom instead of charge as information carriers, to design and fabricate transistors, and the use of optical interconnections to replace metal interconnections between functional units, are effective solutions of the thermal power consumption problem of nano-integrated circuits. Based on the two-dimensional topological insulators-silicene and germanene, we theoretically propose a kind of optically controlled transistor suitable for spin bias. The effects of off-resonant circularly polarized light on the output currents of silicene and germanene transistors are calculated by using the non-equilibrium Green's function method. It is shown that the topological properties of silicene (germanene) and the output characteristics of drain current are controlled by the chirality and intensity of incident light. Under the coaction of weak left circularly polarized light and spin bias, the silicene transistors output pure spin current and fully polarized spin-up current. Under the action of strong field, the phase transition of the edge state of the silicene forms a band gap, the transistor is cut off, and the output current is almost zero. Different from the silicene transistor, the germanene transistor can obtain stable pure spin current under a weak light field, and output 100% polarized spin-down current under a strong field. By simultaneously applying off-resonant circularly polarized light of different chirality to the central device region, the germanene transistor can be turned off effectively by using the edge state phase transition induced by the polarized light field and the energy band mismatch caused by the local light field. The output poles of spin-dependent currents are almost equal for silicene and germanene transistors in the ON state, however, the breakdown voltage of the germanene transistor is significantly higher than that of the silicene transistor, and optically controlled germanene transistor can maintain effective operation at higher temperatures.
1. 引 言
新材料的提出和制备、材料新物性的发现和调控是器件发展的主要驱动力. 1994年, Takeda和Shiraishi[1]基于密度泛函理论研究指出硅和锗可以形成单原子层结构, 并给出了相应的能带结构. 2004年, Novoselov等[2]利用机械剥离方法成功制备出一种真正意义上的二维材料——石墨烯, 长程有序的二维纳米结构逐渐受到科研人员的关注. 2007年, 基于紧束缚理论, Guzman-Verri和Lew-Yan-Voon[3]的研究表明硅原子形成的蜂窝状结构同样具有狄拉克-费米子特征并将单层硅原子材料命名为硅烯. 2009年, Cahangirov等[4]利用第一性原理计算, 明确了原子之间较大的成键间距会削弱π电子交叠, 具有
D3d 点群对称性的硅烯和锗烯在能量上最稳定. 2011年, Liu等[5]的计算结果表明sp2 和sp3 杂化轨道混合构成的低翘曲结构可以增强自旋-轨道耦合, 锗烯具有比硅烯更大的体能隙. 此后的一系列研究工作从理论上证实了带隙之间受时间反演对称性保护的边缘态的存在, 自由状态的硅烯和锗烯都能表现出非平庸的拓扑特性[6,7].目前科研人员利用分子束外延生长已经在不同的金属和半导体表面实现了硅烯和锗烯的生长制备. 2012年, Chen等[8]、Vogt等[9]、Fleurence等[10]分别在Ag(111), ZrB2(0001)衬底上成功制备了硅烯. 2013年, Meng等[11]基于Ir(111)衬底实现了硅烯的制备. 2014年, Li等[12]在Pt(111)衬底上首次制备出了锗烯. 随后研究人员采用同样的方法相继在Au(111), Al(111)和Ge(110)衬底上实现了锗烯的制备[13-15].
晶体管是数字集成电路的核心单元, 其性能和集成度是决定芯片性能强弱的关键指标. 随着纳米制造技术和工艺的不断进步, 单位面积晶体管的数量不断增加、特征尺寸不断缩小. 非弹性散射所引起的热耗散以及量子隧穿效应所引起的关态漏电, 导致集成电路动态和静态能耗成倍增加[16]. 拓扑绝缘体的边缘(表面)态是由体能带的拓扑性质决定的, 能够完全抑制背散射和免疫缺陷、杂质(磁性杂质和短程有序的非磁性杂质除外)的输运性质[17,18], 为设计和实现突破传统技术极限的低功耗电子器件提供了理想平台. 近些年, 一些理论和实验研究工作对适用于普通偏压的硅(锗)烯晶体管开展了研究[19-33]. 本文从理论上提出一种受自旋偏压驱动的硅烯和锗烯光控晶体管. 如图1所示, 中心器件区域分成了两个受光区域, 可以分别(同时)施加非共振左旋或右旋圆偏振光场, 并对左右电极施加自旋偏压. 本文将重点讨论在自旋偏压驱动下, 通过调整非共振圆偏振光场参数将光信号转换为不同性质和强度的电流信号.
图 1 (a)自旋偏压驱动的硅(锗)烯光控晶体管结构示意图. 图中左旋圆偏振光和右旋圆偏振光同时照射器件中心区域, 硅(锗)烯层的下方是栅极电介质层和背栅极. 左右电极区域红色和蓝色长方体是自旋偏压产生的化学势示意图. (b)左旋圆偏振光场和电场共同作用时, 自旋向下边缘态相变后的锗烯能带图. (c) 右旋圆偏振光场作用下, 自旋向上边缘态相变后的锗烯能带图. 图(b)和图(c)的外场参数与图2(j)和图4(f)一致Fig. 1. (a) Schematic of a spin bias driven optically controlled silicene (germanene) transistor. In this figure, the left- and right-circularly polarized light illuminates simultaneously in the center of the device, and the gate dielectric layer and the back gate are below the silicene (germanene) sheet. The red and blue cuboids in the left and right electrode regions show the chemical potentials generated by the spin bias. (b) Energy band of germanene after the phase transition of the spin-down edge states under the joint action of the left-circularly polarized optical field and electric field. (c) Energy band diagram of germanene after the phase transition of the spin-up edge states under the effect of right-circularly polarized light. The field parameters of panels (b) and (c) are consistent with Fig. 2(j) and Fig. 4(f)2. 研究方法
在紧束缚近似下, 受圆偏振光场辐照时六角晶格系统的含时哈密顿量可以表示为[34]
H_{{\rm{dr}}}(\tau) = - \sum\limits_{\langle ij \rangle,\sigma}t_x {\boldsymbol{c}}_{i\sigma}^{\dagger}{\boldsymbol{c}}_{j\sigma}+\sum\limits_{i,\sigma} V_i(\tau) {\boldsymbol{c}}_{i\sigma}^{\dagger}{\boldsymbol{c}}_{i\sigma}, (1) 式中右侧第一项描述的是隧穿动力学过程, 下标
\langle ij \rangle 表示求和遍布所有最近邻格点. 隧穿参数t_x 为最近邻原子之间的电子跃迁能.{\boldsymbol{c}}_{i\sigma}^\dagger ({\boldsymbol{c}}_{i\sigma} )表示位置矢量为{{\boldsymbol{r}}}_i 的第i个晶格格点产生(湮灭)一个自旋为σ的电子. 自旋指标\sigma = +1 (\sigma = -1 )代表自旋向上(向下)的电子. (1)式右侧第二项中时间相关的在位势能V_i(\tau) = -{{\boldsymbol{r}}}_i\cdot {{\boldsymbol{A}}}(\tau) , 对于圆偏振光磁矢势{{\boldsymbol{A}}}(\tau) = A[\sin(\varOmega \tau) {{\boldsymbol{e}}}_x, \cos(\varOmega \tau) {{\boldsymbol{e}}}_y] , 其中τ是时间变量, Ω是光场频率.利用幺正算符
{\boldsymbol{U}}(\tau) = \exp \left\{ {\rm{i}} \displaystyle\sum\nolimits_i \dfrac{A {{\rm{r}}}_i}{\hbar \varOmega}\cdot [-\sin(\varOmega \tau) {{\boldsymbol{e}}}_x,\cos(\varOmega \tau) {{\boldsymbol{e}}}_y] n_{i\sigma} \right\} \begin{split} H(\tau) =\;& {\boldsymbol{U}}^{\dagger}(\tau) H_{{\rm{dr}}}(\tau) {\boldsymbol{U}}(\tau) -{\rm{i}}\hbar {\boldsymbol{U}}^{\dagger}(\tau) {\boldsymbol{U}}(\tau)\\ =\;& -t_x \sum\limits_{ \langle ij \rangle,\sigma} {\rm{e}}^{{\rm{i}} A_{ij}(\tau)} {\boldsymbol{c}}_{i\sigma}^{\dagger}{\boldsymbol{c}}_{j\sigma}, \end{split} (2) 式中时间周期的Peierls项
A_{ij}(\tau) = \dfrac{e}{\hbar}({{\boldsymbol{r}}}_j-{{\boldsymbol{r}}}_i)\cdot {{\boldsymbol{A}}} (\tau) = \dfrac{e}{h}aA\sin(\varOmega \tau +\varphi_{ij}) = \varLambda \sin(\varOmega \tau +\varphi_{ij}) , 其中a为晶格常数,\varphi_{ij} 对应的是从格点i指向格点j的矢量方向. 当\hbar \varOmega \gg t_x 且\varLambda^2 \ll 1 时, 哈密顿量可以表示成近邻相互作用项和次近邻相互作用项- \sum\nolimits_{ \langle ij \rangle }t_x {\boldsymbol{c}}_{i\sigma}^{\dagger}{\boldsymbol{c}}_{j\sigma}+{\rm{i}}\dfrac{\lambda_{\varOmega}}{3\sqrt{3}} \sum\nolimits_{ \langle\langle ij \rangle\rangle }v_{ij}{\boldsymbol{c}}_{i\sigma}^\dagger {\boldsymbol{c}}_{j \sigma}, 其中
\lambda_{\varOmega} 是光场参数,\lambda_{\varOmega} < 0 和\lambda_{\varOmega} > 0 分别对应左旋和右旋圆偏振光, 当次近邻相互作用沿顺时针(逆时针)方向时符号函数\upsilon_{ij} = +1 (\upsilon_{ij} = -1 ). 考虑到自旋轨道耦合和垂直方向电场引起的交错势, 受光场和电场作用的中心器件区域哈密顿量[7,32,36,37]:\begin{split} H =\;& -t_x \sum\limits_{\langle ij \rangle,\sigma}{\boldsymbol{c}}_{i\sigma}^{\dagger}{\boldsymbol{c}}_{j\sigma}+{\rm{i}}\dfrac{\lambda_{{\rm{so}}}}{3\sqrt{3}} \sum\limits_{\langle\langle ij \rangle\rangle \sigma\bar{\sigma}}v_{ij}{\boldsymbol{c}}_{i\sigma}^\dagger\sigma_{\sigma\bar{\sigma}}^z{\boldsymbol{c}}_{j\bar{\sigma}}\\ &+\lambda_E \sum\limits_{\langle i \rangle,\sigma}\mu_i {\boldsymbol{c}}_{i\sigma}^{\dagger}{\boldsymbol{c}}_{i\sigma}+{\rm{i}}\dfrac{\lambda_{\varOmega}}{3\sqrt{3}} \sum\limits_{ \langle\langle ij \rangle\rangle \sigma\bar{\sigma}}v_{ij}{\boldsymbol{c}}_{i\sigma}^\dagger {\boldsymbol{c}}_{j\bar{\sigma}},\end{split} (3) 硅烯(锗烯)的最近邻原子之间的电子跃迁能
t_x 和有效自旋轨道耦合强度\lambda_{{\rm{so}}} 分别为t_{{\rm{Si}}} = 1.6 eV (t_{{\rm{Ge}}} = 1.3 eV)和\lambda_{{\rm{so}}}^{{\rm{Si}}} = 3.9 meV(\lambda_{{\rm{so}}}^{{\rm{Ge}}} = 43\;{\rm{meV}} ) .\lambda_{E}=\ell E_z 为z轴方向电场引起的交错势能,E_z 为电场强度, 硅烯和锗烯翘曲结构顶部和底部原子之间的距离\ell_{{\rm{Si}}} = 0.23 Å和\ell_{{\rm{Ge}}} = 0.33 Å[6]. 计算中位于翘曲结构顶部的原子\mu_i = +1 , 翘曲结构底部的原子\mu_i = -1 .在自旋偏压驱动下, 漏电极中自旋相关的电流可以表示成Landauer-Büttiker公式的形式[38,39]:
\begin{split} J_{\sigma} =\;& \dfrac{e}{h}\int{T_{{\rm{LR}}\sigma} \,[f_{{\rm{L}}\sigma}(E)-f_{{\rm{R}}\sigma}(E)]} {\rm{d}}E,\; (\mu_{{\rm{L}}\sigma} > \mu_{{\rm{R}}\sigma}) \\ =\;& \dfrac{e}{h}\int{T_{{\rm{RL}}\sigma}[f_{L\sigma}(E)-f_{{\rm{R}}\sigma}(E)]} {\rm{d}}E,\; (\mu_{{\rm{L}}\sigma} < \mu_{{\rm{R}}\sigma}),\end{split} (4) 利用格林函数方法得到电极与器件接触区域的表面格林函数[40], 器件中心区域的推迟格林函数
{{G}}^{\rm{r}}_{\sigma} 和线宽函数{\varGamma}_{\sigma} , 可求出电子从L(R)电极到R(L) 电极的透射系数T_{{\rm{LR}}\sigma} = {\rm{Tr}}[{\varGamma}_{{\rm{L}}\sigma} {{G}}^{\rm{r}}_{\sigma} {\varGamma}_{{\rm{R}}\sigma} {{G}}^{\rm{a}}_{\sigma} ] (T_{{\rm{RL}}\sigma} = {\rm{Tr}} [{\varGamma}_{{\rm{R}}\sigma} {{G}}^{\rm{r}}_{\sigma} {\varGamma}_{{\rm{L}}\sigma} {{G}}^{\rm{a}}_{\sigma} ] ). (4)式中f_{\alpha \sigma}(E) = 1/{\Big[{{\rm{e}}^{\tfrac{(E-\mu_{\alpha \sigma})}{k_{\rm{B}} T_\alpha}} + 1}\Big]} 是自旋相关的费米分布函数, 当考虑自旋偏压的作用时, 左右电极的自旋相关的化学势固定选取为\mu_{{\rm{L}} \uparrow} = -\mu_{{\rm{L}} \downarrow} = e V_S 和\mu_{{\rm{R}} \uparrow} = -\mu_{{\rm{R}} \downarrow} = 0 [41,42].3. 结果与讨论
在数值计算中器件中心区域横向和纵向的原子数固定为
N_x = N_y = 40 (图1中所示x轴方向分成13个单元N_x = 13 ,每个单元沿y轴方向的原子数为N_y = 16 ). 硅烯和锗烯最近邻原子之间的电子跃迁能分别为t_{{\rm{Si}}} = 1.6 eV和t_{{\rm{Ge}}} = 1.3 eV. 有效自旋轨道耦合强度分别选取为\lambda_{{\rm{so}}}^{{\rm{Si}}} =3.9 meV和\lambda_{{\rm{so}}}^{{\rm{Ge}}} = 43 meV. 在漏极电流的计算中系统平衡温度固定为T = 4.2 K.首先讨论沿z轴方向对硅烯中心器件区域施加不同强度的左旋圆偏振光场和电场对自旋相关电流的影响. 图2(a)—(e)和图2(f)—(j)分别给出了弱场 (
-\lambda_{\varOmega} = \lambda_{E}\in [0.002, 0.01] )和强场(-\lambda_{\varOmega} = \lambda_{E}\in [0.02, 0.1] )条件下自旋相关电流I_\sigma 随自旋偏压V_{\rm{S}} 的变化. 从图中可以看出, 外场强度改变并不影响自旋电流的属性. 当自旋偏压窗口小于体带隙且V_{\rm{S}} > 0 时, 在自旋偏压的驱动下I_\uparrow > 0 (如图2中红色实线所示), 自旋向上的电子都将通过上边缘态从左电极流入右电极. 由于自旋正偏压时右电极自旋向下的化学势大于左电极, 自旋向下的电子可以通过上边缘态从右电极流入左电极,I_\downarrow < 0 (如图中蓝色实线所示). 当自旋偏压V_{\rm{S}} < 0 时, 左电极自旋向下化学势大于自旋向上化学势, 自旋向下(上)电子可以通过下边缘态从左(右)电极输运到右(左)电极I_\downarrow > 0 (I_\uparrow < 0 ).
图 2 左旋圆偏振光场参数\lambda_{\varOmega} \lambda_{E} I_\sigma V_{\rm{S}} Fig. 2. Spin dependent currentI_\sigma V_{\rm{S}} \lambda_{\varOmega} \lambda_{E} 对器件中心区域施加强度较弱的左旋圆偏振光(
\lambda_\varOmega < 0 )时, 由于硅烯对圆偏振光的二色性选择吸收, 自旋向上的电流几乎不发生变化, 但是自旋向下的电子能带结构变化显著(如图3(a)所示), 器件与电极区域自旋向下的电子能带不匹配, 自旋向下的电流小于自旋向上的电流. 值得注意的是在|\lambda_{\varOmega}|+|\lambda_{E}| > \lambda_{{\rm{so}}}^{{\rm{Si}}} 条件下, 自旋向下的边缘态发生相变并出现带隙, 但是自旋向上的能带性质并不发生改变, 此时在低偏压区域自旋向下的电流值为0, 自旋向上电流与偏压呈线性关系, 漏极电流的极化率P = (I_\uparrow-I_\downarrow)/(I_\uparrow+I_\downarrow) = 100\% . 在强场条件下, 不同自旋取向的边缘态都将发生相变(如图3(b)所示), 边缘态带隙的宽度与外场强度成正比, 在低偏压窗口电流值I_\sigma = 0 , 此时晶体管处于关断状态.
图 3 (a) 左旋圆偏振光场参数\lambda_{\varOmega} \lambda_{E} \lambda_{\varOmega}=\lambda_{E}=-0.002 \lambda_{\varOmega}=\lambda_{E}=-0.02 Fig. 3. (a) Edge-states band structure of silicene when the left-circularly-polarized light parameter\lambda_{\varOmega} \lambda_{E} \lambda_{\varOmega}=\lambda_{E}=-0.002 \lambda_{\varOmega}=\lambda_{E}=-0.02 在引入光场的Haldane相互作用项中, 电磁势项的正负与非共振光场的偏振方向有关, 因此硅烯和锗烯的边缘态和能谷性质与光场的偏振状态有关. 接下来讨论与图2中相同强度的右旋圆偏振光对锗烯晶体管输出电流的调控. 图4(a)对应的是无外场(
\lambda_{\varOmega} = \lambda_{E} = 0 )和\lambda_{\varOmega} = \lambda_{E} < 0.01 的弱场条件下的自旋相关电流. 从图中容易看出, 弱光场和电场的共同作用并不能使锗烯晶体管输出100%自旋极化的电流, 原因在于锗烯的有效自旋轨道耦合强度相比于硅烯增大近10倍, 尽管弱圆偏振光场可以解除相同边缘不同自旋取向的边缘态简并, 但Kramers简并依然保持. 弱光场对锗烯能带结构性质的影响有限, 锗烯晶体管的输出电流强度近似相等. 此外, 漏极电流与无外场时的电流性质相同, 在正(负)自旋偏压的驱动下, 锗烯晶体管通过上(下)边缘态传输纯自旋流.
图 4 对锗烯晶体管施加与图2相同强度的右旋圆偏振光场和电场时, 自旋相关电流I_\sigma V_{\rm{S}} \lambda_{\varOmega}=\lambda_{E} < 0.01 \lambda_{\varOmega}=\lambda_{E}=0.02 \lambda_{\varOmega}=\lambda_{E}=0.04 \lambda_{\varOmega}=\lambda_{E}=0.06 \lambda_{\varOmega}=\lambda_{E}=0.08 \lambda_{\varOmega}=\lambda_{E}=0.1 Fig. 4. Variation of spin-dependent currentI_\sigma V_{\rm{S}} \lambda_{\varOmega}=\lambda_{E}<0.01 \lambda_{\varOmega}=\lambda_{E}=0.02 \lambda_{\varOmega}= \lambda_{E}=0.04 \lambda_{\varOmega}=\lambda_{E}=0.06 \lambda_{\varOmega}=\lambda_{E}=0.08 \lambda_{\varOmega}=\lambda_{E}=0.1 增大右旋圆偏振光场和电场的强度, 锗烯自旋向上电子的体带隙将逐渐减小, 当
|\lambda_{\varOmega}|+|\lambda_{E}| = \lambda_{{\rm{so}}}^{{\rm{Ge}}} 时带隙完全闭合, 此后继续增大外场强度, 自旋向上边缘态的能隙将逐渐被打开, 费米面附近能量范围仅有自旋向下的边缘态. 从图4(b)—(f)可以看出, 锗烯晶体管在强外场和正(负)自旋偏压条件下, 可以通过自旋向下电子形成的上(下)边缘态持续对外线性输出P = -100\% 的自旋极化电流. 并且随着外场增强, 完全极化电流对应的电压窗口明显增大. 与图2(a)—(e)中讨论的硅烯晶体管相比, 锗烯晶体管输出完全极化自旋流的偏压范围可以增大一个数量级. 但是在与图2完全相同的强场(\lambda_{\varOmega} = \lambda_{E}\in [0.02, 0.1] )条件下, 锗烯晶体管无法实现关断状态. 需要指出的是, 从器件应用角度出发, 我们并未考虑更大光场的情况.最后讨论一种在图2和图4讨论的外场强度范围有效关断锗烯晶体管. 将锗烯中心器件分成左右两个区域, 分别施加与图2(g)—(j)(
\lambda_{\varOmega} < 0 )和图4(c)—(f)(\lambda_{\varOmega} > 0 )相同的圆偏振光场, 由于电场的方向对相变没有影响, 因此考虑在中心器件区域施加+z 或-z 方向的电场. 从图5可以看出, 通过对器件同时施加不同极化方向的偏振光场, 可以使得锗烯光控自旋偏压晶体管对外输出的电流为零, 并且电流截止的击穿电压随着外场的增强而增大. 锗烯晶体管关态的工作原理是通过光场将量子自旋霍尔绝缘体转变为光场诱导的自旋极化拓扑绝缘体, 使得螺旋边缘态相变为具有相反传播方向的手性边缘态. 施加负自旋偏压时, 自旋向下的电子无法从左电极入射到器件左侧区域, 同时自旋向上的电子也被禁止从右电极进入器件右侧区域. 正自旋偏压时, 尽管左右电极中的电子可以进入近邻的器件区域, 但是由于器件左右区域能带不匹配, 流经器件的电流为零. 需要指出的是, 在弱场条件下硅烯晶体管按照上述原理同样可以使晶体管从开态转换到关态, 但是图5中讨论的利用边缘态不匹配实现开关功能与图2中强场产生带隙实现关态的方式在原理上有本质上的区别. 另外, 与硅烯晶体管相比, 锗烯晶体管的击穿电压从0.01 V量级(图2(j))增大到了0.1 V量级(图5(e)). 锗烯晶体管可以更好地抵御热涨落的影响, 可以在更高的温度保持有效的关闭状态.
图 5 对锗烯晶体管同时施加不同光参数的左旋和右旋圆偏振光时, 晶体管关态漏极电流I_\sigma V_s |\lambda_\varOmega|= 0.02 |\lambda_\varOmega|=0.04 |\lambda_\varOmega|=0.06 |\lambda_\varOmega|=0.08 |\lambda_\varOmega|= 0.1 \lambda_{E}=|\lambda_{\varOmega}| Fig. 5. Drain current of germanene transistor in the OFF stateI_\sigma V_{\rm{S}} |\lambda_\varOmega|=0.02 |\lambda_\varOmega|=0.04 |\lambda_\varOmega|=0.06 |\lambda_\varOmega|=0.08 |\lambda_\varOmega|=0.1 4. 结 论
本文理论研究了不同强度的圆偏振光场和电场对硅烯和锗烯晶体管自旋相关输出电流性质和强度的影响.研究表明光控晶体管的导通和截止状态可以通过光场的手征性和强度进行调节. 对硅烯施加强度较弱的左旋圆偏振光场时, 通过施加正或负自旋偏压可以分别通过上或下边缘态输出极化率
P = 100\% 的电流. 在强场条件下边缘态发生相变产生带隙, 在低偏压窗口自旋相关电流为零. 对锗烯晶体管施加右旋圆偏振光, 在弱外场和自旋偏压作用下可以对外线性输出纯自旋流, 在与硅烯晶体管相同强场条件下只有极化率P = -100\% 的电流输出. 当对锗烯晶体管同时施加左旋和右旋圆偏振光且外场满足|\lambda_{\varOmega}|+|\lambda_{E}| > \lambda_{{\rm{so}}}^{{\rm{Ge}}} 时, 可以使晶体管从开态转换到关态. 利用边缘态不匹配实现开关功能的锗烯晶体管的击穿电压比硅烯晶体管高出一个数量级, 可以更好地抑制热涨落的影响.[1] Takeda K, Shiraishi K 1994 Phys. Rev. B 50 1491
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Google Scholar
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Google Scholar
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[13] Davila M E, Xian L, Cahangirov S, Rubio A, Le-Lay G 2014 New J. Phys. 16 095002
Google Scholar
[14] Derivaz M, Dentel D, Stephan R, Hanf M C, Mehdaoui A, Sonnet P, Pirri C 2015 Nano Lett. 15 2510
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[15] Zhang L, Bampoulis P, van Houselt A, Zandvliet H J W 2015 Appl. Phys. Lett. 107 111605
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Li M, Huang R 2018 Sci. Sin. Inform. 48 963
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Google Scholar
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Google Scholar
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Google Scholar
[20] Ezawa M 2013 Appl. Phys. Lett. 102 172103
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-
图 1 (a)自旋偏压驱动的硅(锗)烯光控晶体管结构示意图. 图中左旋圆偏振光和右旋圆偏振光同时照射器件中心区域, 硅(锗)烯层的下方是栅极电介质层和背栅极. 左右电极区域红色和蓝色长方体是自旋偏压产生的化学势示意图. (b)左旋圆偏振光场和电场共同作用时, 自旋向下边缘态相变后的锗烯能带图. (c) 右旋圆偏振光场作用下, 自旋向上边缘态相变后的锗烯能带图. 图(b)和图(c)的外场参数与图2(j)和图4(f)一致
Figure 1. (a) Schematic of a spin bias driven optically controlled silicene (germanene) transistor. In this figure, the left- and right-circularly polarized light illuminates simultaneously in the center of the device, and the gate dielectric layer and the back gate are below the silicene (germanene) sheet. The red and blue cuboids in the left and right electrode regions show the chemical potentials generated by the spin bias. (b) Energy band of germanene after the phase transition of the spin-down edge states under the joint action of the left-circularly polarized optical field and electric field. (c) Energy band diagram of germanene after the phase transition of the spin-up edge states under the effect of right-circularly polarized light. The field parameters of panels (b) and (c) are consistent with Fig. 2(j) and Fig. 4(f)
图 2 左旋圆偏振光场参数
\lambda_{\varOmega} 和电场引起的交错势能\lambda_{E} 取不同值时, 硅烯晶体管对外输出的自旋相关电流I_\sigma 随自旋偏压V_{\rm{S}} 的变化 (a) –0.002; (b) –0.004; (c) –0.006; (d) –0.008; (e) –0.01; (f) –0.02; (g) –0.04; (h) –0.06; (i) –0.08; (j) –0.1 eV. 图中红色和蓝色实线代表通过上边缘态输运的自旋向上和向下的电流, 虚线表示利用下边缘态输运的自旋相关的电流Figure 2. Spin dependent current
I_\sigma as a function of the spin biasV_{\rm{S}} when the left-circularly-polarized light parameter\lambda_{\varOmega} and the electric field induced staggered potential\lambda_{E} are chosen as: (a) –0.002; (b) –0.004; (c) –0.006; (d) –0.008; (e) –0.01; (f) –0.02; (g) –0.04; (h) –0.06; (i) –0.08; (j) –0.1 eV. The solid red and blue lines in the figures represent the spin-up and spin-down currents transported through the upper edge states, the dashed lines indicate the spin dependent currents using the lower edge states transport
图 3 (a) 左旋圆偏振光场参数
\lambda_{\varOmega} 和电场引起的交错势能\lambda_{E} 为\lambda_{\varOmega}=\lambda_{E}=-0.002 eV时, 硅烯的边缘态能带结构; (b)\lambda_{\varOmega}=\lambda_{E}=-0.02 eV时, 硅烯的边缘态能带结构. 图中实线和虚线分别对应上边缘态和下边缘态, 红色和蓝色分别表示自旋向下和自旋向上电子形成的能带Figure 3. (a) Edge-states band structure of silicene when the left-circularly-polarized light parameter
\lambda_{\varOmega} and the electric field induced staggered potential\lambda_{E} are chosen as\lambda_{\varOmega}=\lambda_{E}=-0.002 eV; (b) Edge-states band structure of silicene when\lambda_{\varOmega}=\lambda_{E}=-0.02 eV. The solid and dashed lines correspond to the upper and lower edge states, and the red and blue lines indicate the energy bands formed by spin-down and spin-up electrons, respectively
图 4 对锗烯晶体管施加与图2相同强度的右旋圆偏振光场和电场时, 自旋相关电流
I_\sigma 随自旋偏压V_{\rm{S}} 的变化 (a)\lambda_{\varOmega}=\lambda_{E} < 0.01 ; (b)\lambda_{\varOmega}=\lambda_{E}=0.02 ; (c)\lambda_{\varOmega}=\lambda_{E}=0.04 ; (d)\lambda_{\varOmega}=\lambda_{E}=0.06 ; (e)\lambda_{\varOmega}=\lambda_{E}=0.08 ; (f)\lambda_{\varOmega}=\lambda_{E}=0.1 eV. 图中红色和蓝色实线代表通过上边缘态输运的自旋向上和向下的电流. 红色和蓝色虚线表示利用下边缘态输运的自旋向上和自旋向下的电流Figure 4. Variation of spin-dependent current
I_\sigma with spin biasV_{\rm{S}} when applying the same intensity of right-hand circularly polarized optical and electric fields to the germanene transistor as in Fig. 2: (a)\lambda_{\varOmega}=\lambda_{E}<0.01 ; (b)\lambda_{\varOmega}=\lambda_{E}=0.02 ; (c)\lambda_{\varOmega}= \lambda_{E}=0.04 ; (d)\lambda_{\varOmega}=\lambda_{E}=0.06 ; (e)\lambda_{\varOmega}=\lambda_{E}=0.08 ; (f)\lambda_{\varOmega}=\lambda_{E}=0.1 eV. The solid red and blue lines in the figures represent the spin-up and spin-down currents transported through the upper edge states. The red and blue dashed lines indicate the spin-up and spin-down currents using the lower edge states transport
图 5 对锗烯晶体管同时施加不同光参数的左旋和右旋圆偏振光时, 晶体管关态漏极电流
I_\sigma 随自旋偏压V_s 的变化 (a)|\lambda_\varOmega|= 0.02 ; (b)|\lambda_\varOmega|=0.04 ; (c)|\lambda_\varOmega|=0.06 ; (d)|\lambda_\varOmega|=0.08 ; (e)|\lambda_\varOmega|= 0.1 . 图中电场交错势能\lambda_{E}=|\lambda_{\varOmega}| . 图中红色和蓝色实线代表通过上边缘态输运的自旋向上和向下的电流, 虚线表示利用下边缘态输运的自旋相关的电流Figure 5. Drain current of germanene transistor in the OFF state
I_\sigma versus the spin biasV_{\rm{S}} when the left and right circularly polarized light fields of (a)|\lambda_\varOmega|=0.02 、(b)|\lambda_\varOmega|=0.04 、(c)|\lambda_\varOmega|=0.06 、(d)|\lambda_\varOmega|=0.08 、(e)|\lambda_\varOmega|=0.1 are applied simultaneously to the germanene transistor. The solid (dash) red and blue lines in the figures represent the spin-up and spin-down currents transported through the upper (lower) edge states. -
[1] Takeda K, Shiraishi K 1994 Phys. Rev. B 50 1491
Google Scholar
[2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
Google Scholar
[3] Guzman-Verri G G, Lew-Yan-Voon L C 2007 Phys. Rev. B 76 075131
Google Scholar
[4] Cahangirov S, Topsakal M, Akturk E, Sahin H, Ciraci S 2009 Phys. Rev. Lett. 102 236804
Google Scholar
[5] Liu C C, Feng W X, Yao Y G 2011 Phys. Rev. Lett. 107 076802
Google Scholar
[6] Liu C C, Jiang H, Yao Y G 2011 Phys. Rev. B 84 195430
Google Scholar
[7] Ezawa M 2012 Phys. Rev. Lett. 109 055502
Google Scholar
[8] Chen L, Liu C C, Feng B J, He X Y, Cheng P, Ding Z J, Meng S, Yao Y G, Wu K H 2012 Phys. Rev. Lett. 109 056804
Google Scholar
[9] Vogt P, Padova P D, Quaresima C, Avila J, Frantzeskakis E, Asensio M C, Resta A, Ealet B, Le-Lay G 2012 Phys. Rev. Lett. 108 155501
Google Scholar
[10] Fleurence A, Friedlein R, Ozaki T, Kawai H, Wang Y, Yamada-Takamura Y 2012 Phys. Rev. Lett. 108 245501
Google Scholar
[11] Meng L, Wang Y L, Zhang L Z, Du S X, Wu R T, Li L F, Zhang Y, Li G, Zhou H T, Hofer W A, Gao H J 2013 Nano Lett. 13 685
Google Scholar
[12] Li L F, Lu S Z, Pan J B, Qin Z H, Wang Y Q, Wang Y L, Cao G Y, Du S X, Gao H J 2014 Adv. Mater. 26 4820
Google Scholar
[13] Davila M E, Xian L, Cahangirov S, Rubio A, Le-Lay G 2014 New J. Phys. 16 095002
Google Scholar
[14] Derivaz M, Dentel D, Stephan R, Hanf M C, Mehdaoui A, Sonnet P, Pirri C 2015 Nano Lett. 15 2510
Google Scholar
[15] Zhang L, Bampoulis P, van Houselt A, Zandvliet H J W 2015 Appl. Phys. Lett. 107 111605
Google Scholar
[16] 黎明, 黄如 2018 中国科学: 信息科学 48 963
Google Scholar
Li M, Huang R 2018 Sci. Sin. Inform. 48 963
Google Scholar
[17] Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045
Google Scholar
[18] Qi X L, Zhang S C 2011 Rev. Mod. Phys. 83 1057
Google Scholar
[19] Ni Z Y, Liu Q H, Tang K C, Zheng J X, Zhou J, Qin R, Gao Z X, Yu D P, Lu J 2012 Nano Lett. 12 113
Google Scholar
[20] Ezawa M 2013 Appl. Phys. Lett. 102 172103
Google Scholar
[21] Kaneko S, Tsuchiya H, Kamakura Y, Mori N, Ogawa M 2014 Appl. Phys. Express 7 035102
Google Scholar
[22] Ni Z Y, Zhong H X, Jiang X H, Quhe R G, Luo G F, Wang Y Y, Ye M, Yang J B, Shi J J, Lu J 2014 Nanoscale 6 7609
Google Scholar
[23] Tao L, Cinquanta E, Chiappe D, Grazianetti C, Fanciulli M, Dubey M, Molle A, Akinwande D 2015 Nat. Nanotechnol. 10 227
Google Scholar
[24] Pan F, Wang Y, Jiang K, Ni Z, Ma J, Zheng J, Quhe R G, Shi J, Yang J, Chen C and Lu J 2015 Sci. Rep. 5 9075
Google Scholar
[25] Wang Y Y, Ni Z Y, Liu Q H, Quhe R G, Zheng J X, Ye M, Yu D P, Shi J J, Yang J B, Li J, Lu J 2015 Adv. Funct. Mater. 25 68
Google Scholar
[26] Mahmoudi M, Ahangari Z, Fathipour M 2016 Chin. Phys. B 25 018501
Google Scholar
[27] Zhao Y, AlMutairi A, Yoon Y 2017 IEEE Electron Device Lett. 38 1743
Google Scholar
[28] Lima M P, Fazzio A, da Silva A J R 2018 IEEE Electron Device Lett. 39 1258
Google Scholar
[29] Zheng J, Chi F, Guo Y 2018 Appl. Phys. Lett. 113 112404
Google Scholar
[30] Kharadi M A, Malik G F A, Shah K A, Khanday F A 2019 IEEE Trans. Electron Devices 66 4976
Google Scholar
[31] Poljak M 2020 IEEE Trans. Electron Devices 67 354
Google Scholar
[32] Zheng J, Xiang Y, Li C L, Yuan R Y, Chi F, Guo Y 2020 Phys. Rev. Appl. 14 034027
Google Scholar
[33] Zheng J, Xiang Y, Li C L, Yuan R Y, Chi F, Guo Y 2021 Phys. Rev. Appl. 16 024046
Google Scholar
[34] Eckardt A, Anisimovas E 2015 New J. Phys. 17 093039
Google Scholar
[35] Eckardt A, Hauke P, Soltan-Panahi P, Becker C, Sengstock K, Lewenstein M 2010 Europhys. Lett. 89 10010
Google Scholar
[36] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 146802
Google Scholar
[37] Ezawa M 2013 Phys. Rev. Lett. 110 026603
Google Scholar
[38] Meir Y, Wingreen N S 1992 Phys. Rev. Lett. 68 2512
Google Scholar
[39] Datta S 1995 Electronic Transport in Mesoscopic Systems (New York: Cambridge University Press) p103
[40] Lee D H, Joannopoulos J D 1981 Phys. Rev. B 23 4997
Google Scholar
[41] Sun Q F, Guo H, Wang J 2003 Phys. Rev. Lett. 90 258301
Google Scholar
[42] Wang D K, Sun Q F, Guo H 2004 Phys. Rev. B 69 205312
Google Scholar
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