Dephasing effect of quantum spin topological states in HgTe/CdTe quantum well

Yan Jie; Wei Miao-Miao; Xing Yan-Xia

doi:10.7498/aps.68.20191072

Abstract

HgTe/CdTe quantum well is a typical two dimensional topological material which supports the helical edge states and quantum spin Hall effect that is imposing in applying of spin electronic devices. The special plateau valued with $0.25\;h/e^{2}$ of nonlocal resistance in H-shaped four terminal devices can be used as the fingerprint of quantum spin Hall effect. Based on the HgTe/CdTe quantum well, with the aid of nonequilibrium Green's function theory and multi-terminal Landauer-Büttiker formula, we calculate the nonlocal resistance and study the dephasing effect of spin topological states in the presence of exchange field and external magnetic field. It is found the dephasing processes play a role completely different from exchange field and external magnetic field. The latter destroy time reversal symmetry and change the width and relative position of topological gap, but do not influent the topological stability of helical edge states. In the contrary, dephasing processes don't change the width and relative position, however, they broke the topological stability. We consider two kinds of dephasing: normal dephasing and spin dephasing. In the first kind, the carriers lose only the phase memory while maintaining the spin memory. In the second kind, the carriers lose both phase and spin memories. Because of the spin locking properties, normal dephasing almost have no influence on the helical edge states. While the spin dephasing will induce spin flip backscattering and finally destroy helical edge states seriously.

Keywords:

Authors and contacts

Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement, Micronano Centre, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems, School of Physics, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Xing Yan-Xia, xingyanxia@bit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11674024)

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References

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Cited By

图 1 (a) 四端口HgTe/CdTe量子阱模型, 其中1、4端口为电流输入端口, 2、3端口为电压测量端口. 图中蓝色和绿色区域分别由两个独立的门电压控制, 通过调节门电压, 两个区域可分别独立地在图(b)中所示的三个区间自由切换； (b) HgTe/CdTe量子阱二维系统的能带结构, 包含简并的螺旋边缘态和明显不对称的价带和导带. 体带隙分割出三个区域: 量子自旋霍尔区(QSH), n型自旋霍尔区(n-SH)和p型自旋霍尔区(n-SH)

Figure 1. (a) Four-terminal device based on HgTe/CdTe quantum well with two current terminals 1, 4 and two voltage terminals 2, 3; the blue region and green region can be independently tuned into the three region shown in panel (b); (b) band structure of 2 D HgTe/CdTe quantum well. Bulk energy gap divides three region: QSH region, n-SH region and p-SH region.

DownLoad: Full-Size Img PowerPoint

图 2 手性边缘态和螺旋边缘态在多端口体系中的电压降示意图

Figure 2. Sketch map of voltage drop induced by chiral edge states and helical edge states in multi-terminal system.

DownLoad: Full-Size Img PowerPoint

图 3 纵向非局域电阻$R_{23, 14}$和部分透射系数$T_{14}$和$T_{41}$随电流输入区(图1绿色区)在位能$E_1$的变化. 左右两栏分别对应铁磁交换场$M=0$和$M=5\;{\rm{meV}}$的情况, 探测区(图1蓝色区)在位能$E_2=0$. 为便于比较, 顶栏给出了相应能量区间的能带图. 能带图中, 蓝色和红色分别表示自旋上和自旋下的能带

Figure 3. Nonlocal resistors $R_{23, 14}$ and transmission coefficient $T_{14}$ and $T_{41}$ vs energy $ E_1 $ with energy of detector region $E_2=0$. left and right panels are for $ M= 0$ and $ M=5 \;{\rm{meV}} $, respectively. Top panels are band structure of infinite ribbon, the blue lines and red lines correspond to spin up and spin down, respectively.

DownLoad: Full-Size Img PowerPoint

图 4 (a)不同退相干条件下$\varGamma_{\rm {dc}}$随费米能的变化; (b)和(c): 在普通退相干(图(b))和自旋退相干(图(c))作用下, 纵向非局域电阻$R_{23, 14}$随入射端能量$E_1$的变化, 不同曲线对应不同的退相干强度. 图(b)和图(c)共享图例

Figure 4. Panel (a) $\varGamma_{\rm {dc}}$ vs energy $E_1$. Panel (b) and (c): longitudinal non-local resistance $R_{23, 14}$ vs energy $E_1$ with different $\varGamma_d$ for normal dephasing [panel (b)] and spin dephasing [panel (c)].

DownLoad: Full-Size Img PowerPoint

图 5 磁场从弱到强作用下无穷长条带在零磁交换场(上栏)和非零磁交换场(下栏)条件下的能带演化

Figure 5. Band structures of infinite ribbon with various magnetic field B for exchange field $M=0$(top panels) and $5\rm {\;meV}$(bottom panels). Red lines denotes the chiral edge states. The red lines and blue lines are correspond to the states of spin up and spin down.

DownLoad: Full-Size Img PowerPoint

图 6 零磁交换场和非零磁交换场能带随外磁场的演化趋势示意图

Figure 6. Schematic diagram of the developing tendency of band structure in the presence of magnetic field for the zero exchange field (top panels) and nonzero exchange field (bottom panels).

DownLoad: Full-Size Img PowerPoint

图 7 普通退相干和磁场作用下, 纵向非局域电阻$R_{23, 14}$随入射端能量$E_1$的变化. 左栏: 零磁交换场; 右栏: 非零磁交换场. 上下两栏共享图例

Figure 7. $R_{23, 14}$ vs energy $E_1$ for different normal dephasing strength $\varGamma_{\rm d}$ with (right panels) or without (left panels) exchange field. The gray region signs the energy gap in zero magnetic field.

DownLoad: Full-Size Img PowerPoint

图 8 自旋退相干作用下的纵向非局域电阻, 其余参数设置同图7

Figure 8. $R_{23, 14}$ vs energy $E_1$, the dephasing precesses are spin non-conserved. The other parameters are the same as Fig. 7

DownLoad: Full-Size Img PowerPoint

map

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[2]	Zhang F, Zhou J, Xiao D, Yao Y 2017 Phys. Rev. Lett. 119 266804 Google Scholar
[3]	Schindler F, Cook A M, Vergniory M G, Wang Z, Parkin S S, Bernevig B A, Neupert T 2018 Sci. Adv. 4 eaat0346 Google Scholar
[4]	Hasan M Z, Kane C L 2010 Rev. Mod. Phys. 82 3045 Google Scholar
[5]	Alexandradinata A, Wang Z, Bernevig B A 2016 Phys. Rev. X 6 021008
[6]	König M, Wiedmann S, Brüne C, Roth A, Buhmann H, Molenkamp L W, Qi X L, Zhang S C 2007 Science 318 766 Google Scholar
[7]	Bernevig B A, Hughes T L, Zhang S C 2006 Science 314 1757 Google Scholar
[8]	Yang W, Chang K, Zhang S C 2008 Phys. Rev. Lett. 100 056602 Google Scholar
[9]	Liu C C, Feng W, Yao Y 2011 Phys. Rev. Lett. 107 076802 Google Scholar
[10]	Xu Y, Yan B, Zhang H J, Wang J, Xu G, Tang P, Duan W, Zhang S C 2013 Phys. Rev. Lett. 111 136804 Google Scholar
[11]	Hsieh D, Qian D, Wray L, Xia Y, Hor Y S, Cava R J, Hasan M Z 2008 Nature 452 970 Google Scholar
[12]	Chen Y L, Analytis J G, Chu J H, Liu Z K, Mo S K, Qi X L, Zhang H J, Lu D H, Dai X, Fang Z, Zhang S C, Fisher I R, Hussain Z, Shen Z X 2009 Science 325 178 Google Scholar
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[22]	Xue F, MacDonald A H 2018 Phys. Rev. Lett. 120 186802 Google Scholar
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[24]	Sticlet D, Cayssol J 2014 Phys. Rev. B 90 201303 Google Scholar
[25]	Väyrynen J I, Pikulin D I, Alicea J 2018 Phys. Rev. Lett. 121 106601 Google Scholar
[26]	Zhou B, Lu H Z, Chu R L, Shen S Q, Niu Q 2008 Phys. Rev. Lett. 101 246807 Google Scholar
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[37]	Shimazaki Y, Yamamoto M, Borzenets I V, Watanabe K, Taniguchi T, Tarucha S 2015 Nat. Phys. 11 1032 Google Scholar
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[47]	Qi J, Liu H, Jiang H, Xie X C 2019 Front. Phys. 14 43403 Google Scholar
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[49]	Zhang L, Yu Z, Xu F, Wang J 2018 Carbon 126 183 Google Scholar
[50]	Datta S 1995 Electronic Transport in Mesoscopic Systems (1st ed.) (New York: Cambridge university press) pp79–93
[51]	Jiang H, Wang L, Sun Q F, Xie X C 2009 Phys. Rev. B 80 165316 Google Scholar
[52]	Sun Q F, Li Y X, Long W, Wang J 2011 Phys. Rev. B 83 115315 Google Scholar

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