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The major challenge of spintronics lies in how to generate, manipulate, and detect spin current. Multiple methods, such as using magnetic materials, magnetic field, and polarized light field to manipulate the spin of electrons, have been proposed. Owing to the possible applications in spintronic devices, there is currently great interest in the field of spin caloritronics, which focuses on the interplay of spin and heat currents. Stanene is a type of two-dimensional topological insulator consisting of a single layer of Sn atoms arranged in a hexagonal lattice. In this paper, the effects of light and electric fields on the spin-dependent thermoelectric effect of the stanene nanoribbon are studied theoretically based on the non-equilibrium Green’s function method. The results show that the properties and intensity of the thermoelectric current can be effectively controlled by the intensity and the polarization direction of the circularly polarized light field. Under the joint action of a strong circularly-polarized light field and an electric field, the stanene can transform from a quantum spin-Hall insulator into a spin-polarized quantum Hall insulator. When the left-circularly-polarized light field is applied, the spin-down edge states of stanene undergo a phase transition to form a bandgap, and a 100% spin-polarized spin-down current driven by temperature gradient can be obtained. When the right-circularly-polarized light is applied, the edge states of spin-up electrons are destroyed, and a completely polarized spin-up thermal current can be generated. In the weak external field, the properties of the edge state do not change, and the system does not output a thermoelectric current. In addition, the study shows that the intensity of the thermal spin current is related to the width of the bandgap, and a moderate increase in temperature can significantly increase the peak value of the current, but the higher equilibrium temperature and temperature gradient will restrain the spin thermoelectric effect.
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图 1 (a) 施加温度差的锡烯纳米带俯视图. 红色和蓝色区域表示高温和低温热极, 热极的温度分别为
$T_{\rm L} = T+ $ $ \Delta T/2$ 和$ T_{\rm R} = T-\Delta T/2 $ , 灰色区域表示圆偏振光场辐照的区域. (b) 施加圆偏振光场和电场的锡烯纳米带俯视图, 中间灰色区域的背电极为锡烯提供Z轴方向的电场Figure 1. (a) Top view of a stanene nanoribbon with temperature difference. The red and blue regions represent the high-temperature and low-temperature leads. The temperatures of the thermal leads are
$ T_{\rm L} = T+\Delta T/2 $ and$ T_{\rm R} = T-\Delta T/2 $ , respectively. The gray central region represents the area irradiated by the circularly polarized light field. (b) Top view of the stanene nanoribbon with circularly polarized light and electric fields, the back gate in the gray area provides the electric field in the Z-axis direction.
图 2 (a) 电场交错势能
$ \lambda_E $ 和偏振光场强度参数$ \lambda_\varOmega $ 分别取$ \lambda_E = \lambda_\varOmega = 0 $ , 0.02, 0.04, 0.06, 0.08, 0.10 eV时, 自旋相关的电流$ I_\sigma $ 随左(右)热极费米能级$ E_{\rm F} $ 的变化; (b)$ \lambda_E = \lambda_\varOmega = 0.04 $ eV和(c)$ \lambda_E = \lambda_\varOmega = 0.08 $ eV时的电子能带结构, 其中红色虚线代表自旋向上电子形成的能带, 蓝色实线对应自旋向下的能带Figure 2. (a) Spin dependent current
$ I_\sigma $ as a function of the Fermi energy$ E_{\rm F} $ with different values of electric-field-induced staggered potential and light parameter$ \lambda_E = \lambda_\varOmega = 0 $ , 0.02, 0.04, 0.06, 0.08, and 0.10 eV. Energy-band diagrams of stanene with different values of$ \lambda_E $ and$ \lambda_\varOmega $ : (b)$ \lambda_E = \lambda_\varOmega = 0.04 $ eV; (c)$ \lambda_E = \lambda_\varOmega = 0.08 $ eV. The red dash and blue solid lines represent spin-up and spin-down energy states, respectively.
图 3 (a) 电场交错势能
$ \lambda_E = 0.1 $ eV, 圆偏振光场参数分别取$ \lambda_\varOmega = -0.025 $ , –0.050, –0.075, –0.100 eV时自旋相关电流$ I_\sigma $ 随电极费米能级$ E_{\rm F} $ 的变化关系; (b)$ \lambda_E = 0.1 $ eV且$\lambda_\varOmega = -0.050$ eV时锡烯的电子能带结构, 其中红色虚线代表自旋向上电子形成的能带, 蓝色实线对应自旋向下的能带Figure 3. (a) Spin dependent current
$ I_\sigma $ as a function of the Fermi energy$ E_{\rm F} $ with$ \lambda_E = 0.1 $ eV and$ \lambda_\varOmega = -0.025 $ , –0.050, –0.075, –0.100 eV; (b) energy-band diagram of stanene with$ \lambda_E = 0.1 $ eV and$\lambda_\varOmega = -0.050$ eV. The red dash and blue solid lines represent spin-up and spin-down energy states, respectively.
图 4 (a) 热极费米能级
$ E_{\rm F} = 0.05 $ eV时, 总的热电电流$ I_{\rm e} $ 随着圆偏振光场参数$ \lambda_\varOmega $ 和电场交错势能$ \lambda_E $ 的变化; (b) 系统温度$ T = 100 $ K、温度梯度$ \Delta T $ 取不同值时热自旋相关电流$ I_\sigma $ 随着热极费米能级$ E_{\rm F} $ 的变化; (c) 温度梯度$ \Delta T = 50 $ K、系统温度$ T = 200 $ , 300, 400 K时总的热电电流$ I_{\rm e} $ 随着热极费米能级的变化. 图(b)和图(c)中光场强度参数和电场交错势能分别为$ \lambda_\varOmega = -0.05 $ eV和$ \lambda_E = 0.1 $ eVFigure 4. (a) Total thermoelectric current
$ I_{\rm e} $ as a function of electric-field-induced staggered potential$ \lambda_E $ and light parameter$ \lambda_\varOmega $ with the Fermi energy of thermal electrode$ E_{\rm F} = 0.05 $ eV; (b) spin dependent current$ I_\sigma $ versus Fermi energy$ E_{\rm F} $ with system equilibrium temperature$ T = 100 $ K and various temperature gradient$ \Delta T $ ; (c) total thermoelectric current$ I_{\rm e} $ as a function of Fermi energy$ E_{\rm F} $ with system equilibrium temperature$T = 200$ , 300, and 400 K and$ \Delta T = 50 $ K. The electric-field-induced staggered potential and light parameter in panel (b) and panel (c) are$ \lambda_\varOmega = -0.05 $ eV and$ \lambda_E = 0.1 $ eV, respectively. -
[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] Sahin H, Cahangirov S, Topsakal M, Bekaroglu E, Ciraci S 2009 Phys. Rev. B 80 155453
Google Scholar
[4] Xu Y, Yan B, Zhang H J, Wang J, Xu G, Tang P, Duan W H, Zhang S C 2013 Phys. Rev. Lett. 111 136804
Google Scholar
[5] Xu Y, Gan Z X, Zhang S C 2014 Phys. Rev. Lett. 112 226801
Google Scholar
[6] Zhu F F, Chen W J, Xu Y, Gao C L, Guan D D, Liu C H, Qian D, Zhang S C, Jia J F 2015 Nat. Mater. 14 1020
Google Scholar
[7] Gou J, Kong L J, Li H, Zhong Q, Li W B, Cheng P, Chen L, Wu K H 2017 Phys. Rev. Mater. 1 054004
Google Scholar
[8] Zang Y Y, Jiang T, Gong Y, Guan Z Y, Liu C, Liao M H, Zhu K J, Li Z, Wang L L, Li W, Song C L, Zhang D, Xu Y, He K, Ma X X, Zhang S C, Xue Q K 2018 Adv. Funct. Mater. 28 1802723
Google Scholar
[9] Xu C Z, Chan Y H, Chen P, Wang X X, Flototto D, Hlevyack J A, Bian G, Mo S K, Chou M Y, Chiang T C 2018 Phys. Rev. B 97 035122
Google Scholar
[10] Yuhara J, Fujii Y, Nishino K, Isobe N, Nakatake M, Xian L, Rubio A 2018 2D Mater. 5 025002
[11] Deng J L, Xia B Y, Ma X C, Chen H Q, Shan H, Zhai X F, Li B, Zhao A D, Xu Y, Duan W H, Zhang S C, Wang B, Hou J G 2018 Nat. Mater. 17 1081
Google Scholar
[12] Slachter A, Bakker F L, Adam J P, Van Wees B J 2010 Nat. Phys. 6 879
Google Scholar
[13] 陈晓彬, 段文晖 2015 64 186302
Google Scholar
Chen X B, Duan W H 2015 Acta Phys. Sin. 64 186302
Google Scholar
[14] 郑军, 李春雷, 杨曦, 郭永 2017 66 097302
Google Scholar
Zheng J, Li C L, Yang X, Guo Y 2017 Acta Phys. Sin. 66 097302
Google Scholar
[15] Hicks L D, Dresselhaus M S 1993 Phys. Rev. B 47 12727
Google Scholar
[16] Venkatasubramanian R, Siivola E, Colpitts T, O’Quinn B 2001 Nature 413 597
Google Scholar
[17] Harman T, Taylor P, Walsh M, LaForge B 2002 Science 297 2229
Google Scholar
[18] Zheng J, Chi F, Guo Y 2012 J. Phys. Condens. Matter 24 265301
Google Scholar
[19] Shi L B, Yang M, Cao S, You Q, Zhang Y J, Qi M, Zhang K C, Qian P 2020 J. Mater. Chem. C 8 5882
[20] Cao S, Chen H B, Su Ye, Shi L B, Qian P 2021 Appl. Surf. Sci. 546 149075
Google Scholar
[21] Zberecki K, Wierzbicki M, Barnas J, Swirkowicz R 2013 Phys. Rev. B 88 115404
Google Scholar
[22] Niu Z P, Dong S H 2014 Appl. Phys. Lett. 104 202401
Google Scholar
[23] Zberecki K, Wierzbicki M, Barnas J 2014 Phys. Rev. B 89 165419
Google Scholar
[24] Zheng J, Chi F, Guo Y 2014 J. Phys. Condens. Matter 27 295302
[25] Zheng J, Chi F, Guo Y 2015 J. Appl. Phys. 118 195101
Google Scholar
[26] Wierzbicki M, Barnas J, Swirkowicz R 2015 Phys. Rev. B 91 165417
Google Scholar
[27] Fu H H, Wu D D, Wu M H, Wu R Q 2015 Phys. Rev. B 92 045418
Google Scholar
[28] Fu H H, Wu D D, Zhang Z Q, Gu L 2015 Sci. Rep. 5 10547
Google Scholar
[29] Krompiewski S, Cuniberti G 2017 Phys. Rev. B 96 155447
Google Scholar
[30] Zheng J, Chi F, Guo Y 2018 Phys. Rev. Appl. 9 024012
Google Scholar
[31] Zhai X C, Wang Y T, Wen R, Wang S X, Tian Y, Zhou X F, Chen W, Yang Z H 2018 Phys. Rev. B 97 085410
Google Scholar
[32] Zhai X C, Gu J W, Wen R, Liu R W, Zhu M, Zhou X F, Gong L Y, Li X A 2019 Phys. Rev. B 99 085421
Google Scholar
[33] Sengupta P, Rakheja S 2020 Physica E 118 113862
Google Scholar
[34] Kane C L, Mele E J 2015 Phys. Rev. Lett. 95 146802
[35] Liu C C, Jiang H, Yao Y 2011 Phys. Rev. B 84 195430
Google Scholar
[36] Ezawa M 2012 Phys. Rev. Lett. 109 055502
Google Scholar
[37] Zheng J, Chi F, Guo Y 2018 Appl. Phys. Lett. 113 112404
Google Scholar
[38] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
Google Scholar
[39] Kane C L, Mele E J 2005 Phys. Rev. Lett. 95 226801
Google Scholar
[40] Ezawa M 2013 Phys. Rev. Lett. 110 026603
Google Scholar
[41] Zheng J, Xiang Y, Li C L, Yuan R Y, Chi F, Guo Y 2020 Phys. Rev. Appl. 14 034027
Google Scholar
[42] Meir Y, Wingreen N S 1992 Phys. Rev. Lett. 68 2512
Google Scholar
[43] Lee D H, Joannopoulos J D 1981 Phys. Rev. B 23 4988
Google Scholar
[44] Lee D H, Joannopoulos J D 1981 Phys. Rev. B 23 4997
Google Scholar
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