Science Bulletin: 自旋输运揭示高阶棱态的拓扑性质

论文

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速递

Topological nature of higher-order hinge states revealed by spin transport

An-Qi Wang, Peng-Zhan Xiang, Tong-Yang Zhao, Zhi-Min Liao

Science Bulletin, 2022, 67(8): 788–793

doi: 10.1016/j.scib.2022.02.003

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简介

根据高阶拓扑相理论, 在三维高阶拓扑材料中, 除了常见的三维体态和二维表面态, 还存在一维无能隙的拓扑棱态. 由于很难通过传统的实验手段(如光谱和量子振荡测量)对一维电子态进行探测, 到目前为止, 人们对于棱态的拓扑性质仍然知之甚少. 本文通过自旋电位测量的手段, 揭示了高阶拓扑半金属Cd₃As₂纳米片中棱态的拓扑特性. 实验发现, 高阶棱态具有和量子自旋霍尔态类似的电子螺旋性特征, 即棱态电子的自旋和动量是相互锁定的. 棱态自旋极化信号能稳定维持到室温条件, 且可以实现长距离的非局域传输, 传输距离超过5 µm.棱态自旋信号的温度鲁棒性和长程非局域传输特性, 表明棱态由于受拓扑保护具备较强的抗环境干扰能力. 该工作不但深化了人们对于高阶拓扑材料输运性质的理解, 而且也为实现低功耗自旋电子学器件提供了重要的材料平台.

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图文速览

Fig. 1 Helical hinge states in the higher-order topological semimetal. (a) Schematic of hinge states of higher-order Dirac semimetal in momentum space. Each hinge mode connects the projection of two bulk Dirac points on the hinge. Red lines denote a single 1D Kramers pair of the gapless states. (b) Hinge states distributed on the top and bottom surface of a Cd₃As₂ film with (112) surface orientation. Cd₃As₂ has two Dirac points along k_z direction, i.e., (001) direction. (c) Current-induced spin polarizations for hinge states. The diagram to the left depicts the population of hinge states, where the blue (red) branch corresponds to spin-down (up) electrons. The current induced spin-polarization directions are opposite for the two neighboring hinges. As changing the polarity of bias current, the spin-polarization directions are reversed accordingly for each hinge.

Fig. 2 Spin transport on the two edges of nanoplate device A. (a) Schematic of the device structure and measurement configuration. Ti/Au and Co electrodes are denoted by yellow and blue, respectively. A 3-nm-thick Al₂O₃ layer is inserted between the Co and Cd₃As₂. The gate voltage V_g is applied onto the Si substrate for tuning the sample Fermi level. (b)–(e) Spin transport measured on the upper edge (b, d) and the lower edge (c, e) with bias current I=±80 µA at 1.4 K. Insets show the corresponding spin-momentum locking. The red and black arrows denote the forward and backward sweeping of magnetic fields, respectively. (f) Schematic of the current-induced opposite spin polarizations for the two edges. The spin S is locked to electron momentum k_e with right-hand and left-hand rules for the upper and lower edges, respectively. The blue balls represent the electrons and the black arrows above denote the spin direction. The purple arrows show the motion of electrons on the edge.

Fig. 3 Influence of electrode configuration, gate voltage and temperature on the edge spin transport. (a) Optical image of the device B. The Co and Ti/Au electrodes are denoted by blue and yellow, respectively. (b)–(c) Spin voltage V_1S and V_2S loop measured on the two sides of device B, respectively at 1.4 K. The applied bias current is I=40 µA. The measurement configuration is shown by the inset of (b). Left-handed spin-momentum locking is detected on the upper edge, while right-handed spin-momentum locking on the lower edge, indicated by the insets. (d) The magnetic hysteresis window height ∆V_2S as a function of bias current I  for the upper and lower edges of device B at 1.4 K. Dashed lines are linear fits to the experimental data. The error bars represent the standard deviation over multiple measurements. (e) Spin voltage V_1-2,S as a function of magnetic fields in device B at 1.4 K. V_1-2 is the voltage drop between the two Hall-bar-like Co electrodes, while the V_1-2,S is obtained after subtracting the background. The applied bias current is I=40 µA and the measurement configuration is illustrated by the inset. (f) Spin voltage V_3S measured as the Co electrode is across the sample in device B at 1.4 K. The applied bias current is I=60 µA. The inset depicts the measurement configuration. (g) The transfer curve of device C, obtained from the standard four-probe measurements at 1.4 K. Device C has nearly the same contact geometry as that of device B. (h) Gate voltage dependence of magnetic hysteresis window height |∆V_1S| and |∆V_2S| for two opposite edges in device C at 1.4 K.The applied current bias I=40 µA. The error bars represent the standard deviation over multiple measurements. (i) Spin transport at 290 K, measured on the upper edge (left panel) and lower edge (right panel) of deviceC.

Fig. 4 Nonlocal spin transport on opposite sides of device A at 1.4 K. (a) Diagram of nonlocal measurement configuration. The nonlocal voltage measured on Co electrode 1–6 is denoted by V₁, V₂, …, V₆, respectively. The bias current locally induces opposite spin polarizations on the upper and lower edges, and the spin diffusion results in the nonlocal signals. (b)–(e) Nonlocal spintransport measured on the upper edge (b, d) and the lower edge (c, e) with bias current I=±2 mA. Insets show the corresponding spin-momentum locking, where the spin direction S is determined according to the measured voltage V_S and the magnetization M of the Co electrode. (f) The |∆V_S| as a function of distance L, where L is the spacing length between the Co electrode and the local source Ti/Au electrode. The Co electrodes 1 (2), 3 (4) and 5 (6) correspond to a distance of 2.75, 4.25 and 5.75 μm, respectively. The error bars represent standard deviation over multiple measurements.

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本文通讯作者

廖志敏 教授 北京大学物理学院. 主要从事低维量子输运实验研究，近年来在外尔费米子手征反常效应、拓扑表面态自旋输运与量子霍尔效应、拓扑超导与马约拉纳零能模等方面取得系列研究进展.

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