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The hybrid system of low-dimensional electronic and superconducting materials has been an attractive structure for studying mesoscopic transport and low-dimensional superconducting properties. Low-dimensional structures with strong spin-orbit coupling exhibit rich quantum phenomena combined with superconducting macroscopic quantum states, becoming an important platform for exploring novel physical properties and developing new topological quantum devices. The construction of hybrid superconducting devices based on high-quality one-dimensional electronic materials, and the exploration of quantum transport phenomena at the interface emerge as research frontier. It is crucial to understand the characteristic scattering mechanism and quantum transport process in these hybrid systems at the nanoscale. The study of the coupling mechanism between the charge state and the topological localized state, and the experimental probe of the intrinsic transport properties of the topological states are the key issues, which enable the development of the new principles and methods for novel superconducting nanoelectronic devices and topological quantum devices. Due to the competition of multiple energy scales and complicated bound states in these hybrid structures, the device physics and measurement schemes present unprecedented challenges. This paper reviews recent advances in hybrid superconducting devices based on one-dimensional electronic systems, focusing on the material systems based on semiconducting nanowires and carbon nanotubes. Semiconducting nanowires with strong spin-orbit coupling and large Landau $g$-factor are expected to support Majorana bound states and require further improvements in the material quality, interface between superconductors and nanowires, understanding of the transport mechanism, and detection scheme. The construction strategies of extending topological phase space, including broken symmetry, helical modes, semiconducting characteristics, and attenuation of the external magnetic field, are proposed and discussed in hybrid superconducting devices based on carbon nanotubes. We briefly introduce the main phenomena and experimental challenges, ranging from material and device physics. Finally, this paper summarizes and gives an outlook on the development and transport studies of topological quantum devices based on one-dimensional systems.
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Keywords:
- One-dimensional electronics /
- Quantum transport /
- Topological device /
- Hybrid superconducting device
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图 1 半导体纳米线与超导材料复合构筑拓扑量子器件. (a) 具有强自旋轨道耦合的一维体系在磁场下的色散关系. 体系中强自旋轨道耦合效应的存在使能带在k空间发生劈裂, 对应每个动量k都有确定的自旋方向[28]; (b) 复合体系中随化学势和磁场演化的电子相图. 在临界磁场之上, 磁场驱动体系发生拓扑超导相的相变[31]
Figure 1. Topological devices based on the hybrid superconductor-semiconductor nanowire structures. (a) Electronic dispersion of an one-dimensional quantum wire with strong spin-orbit coupling under applied magnetic field[28]. The presence of spin-orbit coupling results in the lifting of spin degeneracy. (b) The phase diagram for a proximitized semiconducting nanowire device as a function of the magnetic field and chemical potential. The interplay of spin–orbit coupling, Zeeman fields can drive a quantum phase transition into a topological superconductivity[31].
图 2 构筑基于纳米线的量子点和超导干涉器件 (a) 基于单根InSb纳米线的器件SEM照片; (b) 纳米线复合器件中的Andreev束缚态能谱. (c)实现了复合器件中不同基态的栅极调控, 观察到0相与π相交替出现的安德烈夫束缚态[11]
Figure 2. The realization of the nanowire quantum dot-superconducting quantum interference device. (a)SEM image of a typical device, showing that individual InSb nanowire is in contact with superconducting electrodes. (b)Differential conductance $dI/dV$ map for the odd charge state as function of voltage bias $V_{sd}$ and backgate voltage $V_{g}$, indicating an Andreev bound state formed. (c)Differential conductance $dI/dV$ plot as a function of $V_{sd}$ and $V_{g}$ at 10 mK and zero magnetic field, demonstrating a realization of continuous gate-tunable Andreev bound states with both 0-type levels and π-type levels[11].
图 3 拓扑态的固态量子器件构筑和探测. (a) 基于强自旋轨道耦合的二维电子气构筑超导界面和量子点接触的复合结构器件, 在磁场驱动下在拓扑相区域, 电导出现半整数的量子化平台[71]; (b) 三端非局域测量方案的器件构型, 用于区分安德烈夫和马约拉纳束缚态[72]; (c) 基于半导体纳米线与超导电极构筑耦合量子点的Kitaev链器件结构[81]. 实验通过栅极实现对交叉安德烈夫反射和弹性共隧穿过程的精确调控[80]
Figure 3. The realization and detection of the one-dimensional topological states in hybrid semiconductor–superconductor structures. (a) The conductance of a quantum point contact placed between superconductor and semiconducting wire with spin–orbit coupling[71]. (b) Three-terminal setup for probing Andreev and Majorana bound states with nonlocal measurement of conductance[72]. (c) Top panel: false color SEM microscopy of a fabricated nanowire device showing the realization of the Kitaev chain with coupled quantum dots through superconductor[81]. Illustration of the realization of the Kitaev chain with coupled quantum dots through superconductor, in which the coupling strength of crossed Andreev reflection and elastic co-tunnelling can be gate-tunable[80].
图 4 单壁碳纳米管的能带结构与可调控性. (a) 碳纳米管卷曲矢量决定的金属型和半导体型碳纳米管能带结构[82]; (b) 基于碳纳米管的分离静电栅构筑的原位可控$PN$结结构; (c) 碳纳米管中随内建电场增加而逐渐降低的磁导拐点, 表明电场和磁场对碳纳米管能带结构的控制; 插图: 非单调磁导的温度依赖特性, 验证了磁导响应的机制[87]
Figure 4. Tunability of electronic band structure in single-wall carbon nanotubes. (a) Band structures of metallic and semiconducting carbon nanotubes determined by the chiral vector[82]. (b) In situ controllable $PN$ junction structure based on split gates of carbon nanotubes. (c) The magnetoconductance peaks move towards lower magnetic fields with increasing built-in electric fields in a carbon nanotube, demonstrating the control of the band structure of carbon nanotubes by electric and magnetic fields; Inset: temperature dependence of nonmonotonic magnetoconductance, suggesting the mechanism of the magnetic response[87].
图 5 半导体型碳纳米管-超导薄膜异质结的拓扑态构建方案. (a) 半导体型碳纳米管-超导体异质结器件示意图, 在面内横向磁场下诱导出马约拉纳束缚态; (b) 马约拉纳束缚态能谱和局域波函数在磁场下的演化, 表明碳纳米管两端处磁场诱导的马约拉纳束缚态[110]
Figure 5. Topological state scheme based on semiconducting carbon nanotubes-superconducting films heterojunction. (a) Schematic diagram of a semiconducting carbon nanotube-superconductor heterojunction device, where Majorana bound states can be induced by in-plane transverse magnetic field. (b) Majorana bound states spectrum and wave function as a function of magnetic field, demonstrating the Majorana bound states in the ends of carbon nanotube induced by magnetic field[110].
图 6 碳纳米管- TMD超导体异质结的拓扑态构建方案. (a) 碳纳米管- TMD超导体异质结器件示意图, 在轴向磁场和横向电场下诱导出马约拉纳束缚态; (b) 自旋轨道耦合、磁通效应、横向电场和伊辛近邻效应导致的半金属态碳纳米管; (c) 磁通和化学势的拓扑相图, –1表示拓扑相; (d) 电子-电子相互作用诱导的无磁场拓扑相图[119]; (e) 碳纳米管-薄层NbSe2近邻下的超导电流和相滑移[105]
Figure 6. Topological state scheme based on semiconducting carbon nanotubes-TMD superconductors heterojunction. (a) Schematic diagram of a carbon nanotube-TMD superconductor heterojunction device, where Majorana bound states can be arised by axial magnetic field and transverse electric field. (b) Semi-metallic carbon nanotubes induced by spin-orbit coupling, magnetic flux effect, transverse electric field and Ising proximity effect. (c) Topological phase diagram of magnetic flux and chemical potential, where –1 denotes topological phase. (d) Topological phase diagram induced by electron-electron interaction without magnetic field[119]. (e) Supercurrent and phase slip in a carbon nanotube with thin NbSe2 proximity[105].
图 7 碳纳米管-超导体异质结的拓扑态电场构建方案. (a) 碳纳米管-超导体异质结器件示意图, 在横向电场下诱导出马约拉纳束缚态; (b) 低电场下, 只有一个能带分支形成p波配对; (c) 高电场下, 两个能带分支都形成p波配对[122]
Figure 7. Topological state scheme based on carbon nanotubes-superconductors heterojunction with electric field. (a) Schematic diagram of a carbon nanotube-superconductor heterojunction device, where Majorana bound states can be induced by strong transverse electric field. (b) One branch is in the p-wave phase at low electric field. (c) Both branches are in the p-wave phase at high electric field[122].
图 8 基于周期性空间分布的化学势和磁场的一维拓扑器件构建方案. (a) 通过静电栅极阵列在一维体系中实现周期性化学势的调控; (b)通过纳米尺度磁体阵列或本征磁畴结构诱导产生周期性磁场[126]
Figure 8. Topological device scheme based on periodically and spatially modulated chemical potential and magnetic fields. (a) Periodically modulated chemical potentials induced by electrostatic gate arrays; (b) Periodically modulated magnetic field induced by nanomagnetic arrays or intrinsic domain structure in magnetic substrates[126].
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