Low-dimensional narrow bandgap InSb nanostructures, such as nanowires and quantum wells, have garnered significant interest due to their small electron effective mass, strong spin-orbit interaction (SOI), and large Landé g-factor, making them suitable for applications in high-speed electronics, infrared optoelectronics, spintronics, quantum electronics, and topological quantum computation. Epitaxially grown InSb nanowires have been extensively studied, leading to advancements in field-effect transistors, single and double quantum dots, and semiconductor-superconductor hybrid quantum devices, including topological superconducting quantum devices where zero-energy modes, a signature of Majorana fermions, were detected. However, for convenient manipulation of topological quantum states and the realization of topological quantum computations, a transition from single-nanowire structures to multiple-nanowire and two-dimensional (2D) planar quantum structures is necessary. Recently, high-quality InSb/InAlSb heterostructured quantum wells and free-standing InSb nanosheets have been achieved, offering advantages in direct metal contact, easy transfer to different substrates, and convenient dual-gate structure fabrication. Free-standing InSb nanosheets have enabled the creation of lateral quantum devices, such as planar quantum dots and superconducting Josephson junctions, opening possibilities for constructing topological superconducting structures with Majorana fermions and parafermions for topological quantum computation. A crucial requirement for this is a strong SOI. While SOI studies have been conducted for InSb nanowires and quantum wells, a comprehensive study focusing on SOI and its controllability in free-standing InSb nanosheets was lacking. This article reports on magnetotransport measurements of an epitaxially grown, free-standing InSb nanosheet and the use of dual-gate techniques to achieve tunable SOI, aiming to advance spintronics, spin-orbit qubits, and topological quantum computation technology.

The literature review section extensively cites prior research on InSb nanostructures and their applications in various fields, including high-speed electronics, infrared optoelectronics, spintronics, quantum electronics, and topological quantum computation. The review highlights previous work on InSb nanowires, such as field-effect transistors, quantum dots, and hybrid devices. It emphasizes the significance of moving towards 2D structures for topological quantum computation and cites recent progress in the fabrication of high-quality InSb/InAlSb quantum wells and free-standing InSb nanosheets. The advantages of using free-standing InSb nanosheets for device fabrication are discussed, including the ease of metal contact and dual-gate structure implementation. Finally, the review notes the lack of comprehensive SOI studies specifically for free-standing InSb nanosheets, highlighting the importance of the current research in addressing this gap.

The study employed a dual-gate InSb nanosheet device fabricated using standard nanofabrication techniques starting with molecular beam epitaxy (MBE) grown, free-standing, single-crystalline InSb nanosheets. These nanosheets were transferred onto an n-doped silicon substrate with a SiO2 layer acting as the bottom gate and dielectric. Four Ti/Au contact electrodes were fabricated on the nanosheet, with a HfO2 layer and a Ti/Au top gate completing the dual-gate structure. Low-temperature magnetotransport measurements were performed in a physical property measurement system (PPMS) cryostat using a four-probe configuration with a 17-Hz AC excitation current. The conductance was calculated from the measured voltage drop. Magnetoconductance, ΔG = G(B) – G(B = 0), was measured with a magnetic field perpendicular to the nanosheet plane. Carrier density was estimated from gate transfer characteristics using a capacitance model. Electron mobility and mean free path were also calculated. To determine transport length scales (phase coherence length (Lφ), SOI length (LSO), and mean free path (Le)), low-field magnetoconductance measurements were performed at various bottom-gate voltages (VBG) with the top-gate voltage (VTG) set to 0 V. The data were fitted to the Hikami-Larkin-Nagaoka (HLN) equation, which describes the quantum correction to low-field magnetoconductance in a 2D diffusive system. To isolate the effect of the electric field on SOI, measurements were taken along constant conductance contours, keeping carrier density constant while varying the dual-gate voltage (VD = VTG – VBG). Band diagrams were simulated using COMSOL software to analyze the effect of the dual gate voltage on the band structure and to understand the origin of the intrinsic SOI observed at VD = 0 V. Temperature-dependent magnetotransport measurements were also conducted to study the temperature dependence of the transport length scales. Finally, the fitting of the measured magnetoconductance data to the HLN formula and the band diagram simulation are described in detail.

The study found that the InSb nanosheet exhibits weak antilocalization (WAL) characteristics in its low-field magnetoconductance, indicating the presence of strong spin-orbit interaction (SOI) of the Rashba type. The SOI length (LSO) was extracted from fits to the HLN equation and found to be approximately 130 nm at zero dual-gate voltage, indicating a strong intrinsic SOI. This intrinsic SOI was attributed to the built-in asymmetry in the HfO2-InSb-SiO2 heterostructure, confirmed by band diagram simulations. The SOI strength was found to be tunable by applying a voltage over the dual gate. Measurements along constant conductance contours demonstrated that LSO increases from ~130 nm to ~390 nm as the dual-gate voltage is varied, demonstrating efficient tuning of the SOI strength without changing carrier density. This corresponds to a change in the spin-orbit strength from 0.42 to 0.14 eV Å and a change in the spin-orbit energy from 160 to 18 μeV. The phase coherence length (Lφ) was found to be strongly dependent on both bottom-gate voltage and temperature, while the mean free path (Le) showed weak dependence on both. Temperature-dependent measurements revealed that Lφ follows a power law of Lφ ~ T-0.38, indicating that the dephasing is likely due to electron-electron interactions. The simulations confirmed the presence of band bending in the InSb nanosheet even at zero dual-gate voltage, providing numerical evidence for the tunable structural asymmetry and thus tunable SOI. The extracted Rashba prefactors were 4.26e nm² at n = 7.2 × 10¹¹ cm⁻² and 3.48e nm² at n = 4.3 × 10¹² cm⁻².

The findings demonstrate the existence of a strong and tunable Rashba SOI in a free-standing InSb nanosheet, a crucial parameter for applications in spintronics and topological quantum computing. The ability to efficiently tune the SOI strength via the dual gate is a significant advancement, as it simplifies device design and control. The observed intrinsic SOI at zero dual-gate voltage, originating from the built-in structural asymmetry, is also noteworthy. The results are consistent with theoretical predictions and previous experimental findings in similar systems, further validating the findings. The observation that the SOI strength is comparable to values found in InSb nanowires but significantly larger than those in InAs nanowires and InSb quantum wells highlights the advantages of the InSb nanosheet platform. The temperature dependence of the phase coherence length suggests that electron-electron interactions are the primary dephasing mechanism at low temperatures. The detailed analysis of the transport length scales and their dependence on gate voltage and temperature provides valuable insights into the quantum transport properties of InSb nanosheets and their potential for future applications.

This study successfully demonstrated a strong and tunable Rashba SOI in a single-crystalline InSb nanosheet using a dual-gate device. The tunability of the SOI, along with the presence of a strong intrinsic SOI, opens up exciting possibilities for designing and fabricating advanced spintronic devices and topological quantum computers. Future research could focus on exploring the use of these InSb nanosheets in creating more complex quantum devices, such as topological superconducting structures with braiding of Majorana fermions, and exploring different gate configurations to achieve even finer control over the SOI strength.

The study focused on a single representative device, and further investigations on a larger sample size are needed to confirm the generalizability of the results. The modeling of the device used simplified assumptions, such as a one-dimensional model for the band diagram simulations and certain simplifications in estimating the carrier density. Although the study extensively analyzed the transport lengthscales, other factors potentially influencing the SOI might need further investigation. The temperature range explored was limited to 1.9-20 K; investigating different temperature regimes could offer a more comprehensive understanding of the SOI behavior.