Strong and tunable spin-orbit interaction in a single crystalline InSb nanosheet

The study addresses how strong spin-orbit interaction (SOI) in free-standing, single-crystalline InSb nanosheets can be quantified and electrically tuned, and what physical mechanisms underlie intrinsic SOI in such structures. Narrow-gap InSb nanostructures offer low effective mass, strong SOI, and large g-factors, promising for high-speed electronics, spintronics, quantum devices, and topological quantum computation. While InSb nanowires and quantum wells have been widely studied, transitioning to planar 2D platforms is desirable for scalable networks and braiding operations. Free-standing InSb nanosheets enable facile metal/superconductor contact and dual-gate architectures, but the controllability of SOI in these nanosheets had not been demonstrated. This work uses a dual-gate device to extract quantum transport length scales and to isolate/tune Rashba SOI via a vertical electric field at fixed carrier density, and to reveal the intrinsic SOI origin from built-in structural asymmetry.

Prior efforts established InSb nanowire devices (field-effect transistors, quantum dots, and superconductor hybrids) and reported Majorana signatures in nanowires. 2D platforms and networks are pursued for braiding and scalable topological operations. High-quality InSb/InAlSb quantum wells and free-standing InSb nanosheets have been realized; nanosheets facilitate direct metal contact, substrate transfer, and dual-gate fabrication, enabling planar quantum dots and Josephson junctions. Strong SOI (short spin-orbit length and sizable spin-orbit energy) is a key ingredient for topological states. SOI has been characterized in InSb nanowires and quantum wells, but a detailed and controllable SOI study in free-standing InSb nanosheets was missing. Theoretical frameworks include weak (anti)localization described by HLN theory for 2D diffusive transport, and spin-relaxation mechanisms: Elliott–Yafet (momentum-scattering-induced), D’yakonov–Perel’ (precession between scattering events), with Dresselhaus contributions expected negligible or absent for current flow along <111>/<110> in zincblende nanosheets, implying Rashba SOI dominates in structurally asymmetric environments.

Materials: Free-standing, single-crystalline zincblende InSb nanosheets were grown by MBE on Si(111) via Ag-seeded InAs nanowires followed by switching to Sb. Nanosheets (thickness ~10–30 nm; micrometer lateral size) were transferred to n-doped Si substrates with 300 nm SiO2 (global bottom gate and dielectric). Device fabrication: Ti/Au (5/90 nm) contacts defined by EBL/EBE; prior to metallization, nanosheets were treated with diluted (NH4)2S to remove oxides and passivate surfaces. A 20 nm HfO2 top dielectric was deposited by ALD, followed by Ti/Au top gate. The measured device used four contacts with 1.1 µm inner spacing and ~550 nm channel width; thickness ~30 nm. Measurements: Low-temperature (1.9–20 K) four-probe conductance G=I/V in a PPMS with perpendicular magnetic field; AC excitation 100 nA at 17 Hz. Magnetoconductance ΔG=G(B)−G(0) was measured at low fields (|B|≤20 mT). Gate control: Bottom gate (Si/SiO2) and top gate (Ti/Au over HfO2). Carrier density estimates used transfer characteristics and capacitor models; mobility μ from σ/(ne). Dual-gate strategy: To vary vertical electric field at fixed density, measurements were taken along constant-conductance contour lines in the (VTG,VBG) plane while sweeping dual-gate voltage VD=VTG−VBG. Data analysis: Low-field ΔG traces were fitted to the 2D Hikami–Larkin–Nagaoka equation with characteristic fields βφ, βSO, βe (related to Lφ, LSO, Le via β=ħ/(4eL2)). Fits used least-squares (SciPy curve_fit and Origin) with bounds (e.g., Le≤200 nm). Spin-orbit parameters were converted to Rashba coefficient αR via LSO≈ħ2/(m*αR) and spin-orbit energy ESO. Simulations: One-dimensional Poisson solutions (COMSOL) for the HfO2–InSb–SiO2 stack using material bandgaps, dielectric constants, effective masses, and electron affinities. Simulated band diagrams and effective vertical electric fields inside the InSb layer at various VD corroborated structural asymmetry and its tunability.

- Device characteristics: Top gate strongly coupled; bottom gate weakly coupled. At VTG=0 V, estimates yield carrier densities n≈7.2×10^11 cm^-2 at G≈9 e^2/h and n≈4.3×10^11 cm^-2 at G≈5 e^2/h. Mobility μ≈6000 cm^2 V^-1 s^-1 at both operating points. Mean free path from transport parameters: Le≈84 nm (n=7.2×10^11 cm^-2) and ≈65 nm (n=4.3×10^11 cm^-2). Fermi wavelength λF≈30 nm (comparable to nanosheet thickness), indicating few-subband, dominantly 2D transport. - Weak antilocalization (WAL): Low-field ΔG shows WAL peaks consistent with strong SOI. HLN fits across VBG (VTG=0 V) give: LSO≈130 nm (weak VBG dependence), Le≈80 nm (weak VBG dependence), and Lφ up to ≈530 nm at VBG=0 V, decreasing with reduced carrier density due to Nyquist dephasing. - Dual-gate tuning at fixed density: Along constant-conductance contours: • At G≈9 e^2/h: Lφ≈460 nm (independent of VD), Le≈85 nm (independent), while LSO increases from ~130 to ~390 nm as VD sweeps from −2 to 11 V, evidencing weakening SOI with more positive VD. • At G≈5 e^2/h: Lφ≈340 nm and Le≈78 nm constant; LSO increases from ~130 to ~270 nm as VD sweeps from −4.4 to 10.7 V. These changes correspond to αR tuning from ~0.42 to ~0.14 eV·Å and ESO from ~160 to ~18 µeV. - Spin-relaxation mechanism: Elliott–Yafet estimates yield LSO,EY>500 nm (using EG≈0.23 eV, EF≈50 meV, ΔSO≈0.8 eV, Le≈80 nm), much longer than measured LSO≈130 nm; Dresselhaus expected negligible for crystal orientation; thus Rashba (D’yakonov–Perel’) dominates. - Intrinsic SOI at VD=0: Despite zero dual-gate bias, strong SOI persists (LSO small), traced to built-in structural asymmetry from band offsets. COMSOL band diagrams show conduction/valence band bending at VD=0 and stronger bending for negative VD, reduced towards flat band for positive VD, matching experimental SOI trends. Extracted Rashba prefactors FR≈4.26 e·nm^2 at n≈7.2×10^11 cm^-2 (and ≈3.48 e·nm^2 at higher density condition). - Temperature dependence (VD≈2 V, G≈9 e^2/h): LSO and Le weakly dependent on T (1.9–20 K); Lφ decreases from ~470 to ~210 nm following Lφ∝T^-0.38, indicative of Nyquist dephasing in a dimensionality between 1D and 2D due to comparable Lφ and channel width (~550 nm).

The study directly addresses the origin and controllability of SOI in free-standing InSb nanosheets. WAL-based HLN analysis reveals strong Rashba SOI at low temperatures. By using a dual-gate scheme to vary the vertical electric field while keeping the carrier density approximately constant (along equal-conductance contours), the Rashba SOI is tuned over a factor of ~3 in LSO (and corresponding αR, ESO). The persistence of strong SOI at zero dual-gate voltage is explained by built-in structural asymmetry arising from band offsets across the HfO2–InSb–SiO2 stack, as confirmed by Poisson simulations showing intrinsic band bending and its modulation with VD. The dephasing behavior (Lφ vs carrier density and temperature) is consistent with Nyquist electron–electron interactions and supports the diffusive regime with effectively 2D transport characteristics. These findings validate a practical route to engineer and electrically control SOI in planar InSb platforms, which is crucial for spintronic devices, spin–orbit qubits, and realizing/topologically manipulating superconducting states.

A dual-gate planar device based on a single-crystalline InSb nanosheet exhibits strong Rashba-type SOI that can be efficiently tuned by a vertical electric field at fixed carrier density. Quantum transport analysis using HLN fits yields key length scales (Le ~80 nm, LSO ~130–390 nm, Lφ up to ~530 nm), and demonstrates electrical control of αR (~0.42→0.14 eV·Å) and ESO (~160→18 µeV). Simulations identify intrinsic band bending in the HfO2–InSb–SiO2 stack as the origin of strong SOI even at zero dual-gate bias. The results provide a robust foundation for designing planar spintronic components, spin–orbit qubits, and topological superconducting devices based on InSb nanosheets. Potential future directions include integrating superconducting contacts to exploit tunable SOI for gate-defined topological junctions and exploring multi-gate geometries and material stacks to further optimize SOI strength and uniformity.

- The HLN analysis assumes 2D diffusive transport at low magnetic fields; however, the phase coherence length is comparable to the channel width, placing the device in an intermediate 1D–2D regime, which may introduce model approximations. - Measurements are limited to low magnetic fields (|B|≤20 mT) and temperatures 1.9–20 K; behavior outside these ranges is not addressed. - Results are presented from a representative device; device-to-device variability is not systematically explored. - The band diagram simulation uses an effective 1D Poisson model and material parameters; while indicative of structural asymmetry, it does not capture full 3D device complexities. - Separation of Rashba and possible residual Dresselhaus contributions relies on symmetry arguments for current direction in zincblende crystals rather than a direct experimental decomposition.