Large even-odd spacing and $g$-factor anisotropy in PbTe quantum dots
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-05-13 |
| Journal | arXiv (Cornell University) |
| Authors | Sofieke C. ten Kate, M. F. Ritter, Sander G. Schellingerhout |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive Summaryâ- Material Suitability for TQC: PbTe nanowire quantum dots (QDs) were characterized, confirming properties advantageous for topological quantum computing (TQC), including strong spin-orbit interaction (SOI) and large LandĂ© g-factors.
- Dielectric Screening Effects: The materialâs extremely large dielectric constant (Δr ~ 1350) results in efficient screening, manifesting as small charging energies (Ec up to 130 ”eV) and a pronounced even-odd spacing in Coulomb blockade peaks.
- G-factor Anisotropy: The effective electron g-factor tensor is highly anisotropic, with principal g-factors ranging widely from 0.9 to 22.4, depending significantly on the magnetic field direction and electronic configuration.
- SOI Confirmation: The observed g-factor anisotropy and its dependence on gate voltage strongly indicate the presence of strong Rashba SOI and asymmetric confinement potentials within the PbTe QDs.
- Excitation Energy Range: Single-particle excitation energies (Î) were measured between 170 ”eV and 500 ”eV, suggesting varying degrees of quantum confinement across different devices/regimes.
- Methodology Comparison: G-factors extracted from Kondo splitting were found to underestimate the true Zeeman splitting by approximately 20% compared to those extracted from excited state level splitting.
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| PbTe Dielectric Constant (Δr) | ~1350 | None | Bulk value at low temperatures |
| Nanowire Growth Method | SAG | None | Selective-Area-Growth |
| Substrate Material | (111)A InP | None | Growth platform |
| Nanowire Width (Device 1) | 80 | nm | Approximate dimension |
| Nanowire Width (Device 2) | 100 | nm | Approximate dimension |
| Lithographic Contact Distance | 720 | nm | Source to Drain |
| Measurement Base Temperature | less than 20 | mK | Dilution refrigerator mixing chamber |
| Average Charging Energy (Ec) | 110 to 130 | ”eV | Extracted from odd Coulomb diamonds |
| Single-Particle Excitation Energy (Î) | 170 to 500 | ”eV | Extracted from even Coulomb diamonds |
| Estimated Quantum Dot Length (L) | 160 to 860 | nm | Derived from Î and effective mass |
| Principal g-factor Range | 0.9 to 22.4 | None | Highly anisotropic tensor components |
| Magnetic Field Magnitude | 100 or 200 | mT | Used for g-factor rotation studies |
| Effective Electron Mass (m*) | 0.024me to 0.24me | None | Estimated range for PbTe |
| AC Voltage Bias (VAC) | 3 | ”V | Applied for differential conductance measurement |
Key Methodologies
Section titled âKey Methodologiesâ- Nanowire Synthesis (SAG): PbTe nanowires were grown on (111)A InP substrates using Molecular Beam Epitaxy (MBE) via the Selective-Area-Growth (SAG) technique.
- Lithography and Patterning: A double resist layer (PMMA AR-P 669.04 and 672.02) was patterned using electron-beam lithography (EBL) to define contacts and gates.
- Surface Preparation: A brief Argon (Ar) reactive ion etch was performed immediately prior to metal deposition to remove the native oxide layer from the PbTe nanowires.
- Contact Metallization: Ti/Au contacts (5 nm Ti / 50 nm Au) were deposited via e-beam evaporation to form source/drain contacts and side gates (VL, VPG, VR).
- Cryogenic Measurement: Devices were characterized in a dilution refrigerator at a base temperature below 20 mK, utilizing a vector magnet for precise magnetic field control.
- Differential Conductance (G) Measurement: G was measured using lock-in amplifiers while applying an anti-symmetrical DC voltage bias (VSD/2) superimposed with a 3 ”V AC bias.
- G-factor Extraction (Dual Method):
- Level Splitting: G-factors were extracted from the Zeeman splitting of the ground and excited states in odd-occupied QDs (preferred method).
- Kondo Splitting: G-factors were extracted from the separation of the two maxima in G(VSD) corresponding to the spin-1/2 Kondo effect.
- Anisotropy Mapping: A fixed magnetic field magnitude (100 mT or 200 mT) was rotated 360° in 15° steps across three orthogonal planes to map the g-factor dependence on direction.
- Tensor Fitting: The measured g-factors were fitted to an effective g-factor tensor model (Equation 2) to determine the principal g-factors (g1, g2, g3) and their spatial orientation (Euler angles).
Commercial Applications
Section titled âCommercial Applicationsâ- Topological Quantum Computing (TQC): PbTe is a leading candidate material for hosting Majorana zero modes due to its strong SOI and large g-factor anisotropy, which are critical for creating robust topological gaps when coupled with a superconductor.
- Spintronic Devices: The ability to tune and control highly anisotropic g-factors via gate voltage and magnetic field direction offers potential for developing novel spin-based memory, logic, and filtering devices.
- High-Mobility Electronics: The exceptionally large dielectric constant of PbTe (Δr ~ 1350) facilitates superior screening of impurities, suggesting potential for high-electron-mobility transistors (HEMTs) or other high-performance semiconductor components.
- Quantum Sensing and Metrology: Materials exhibiting large and tunable g-factors can be utilized in highly sensitive magnetic field sensors or in quantum devices requiring precise manipulation of spin states.
- Nanowire Heterostructures: The successful integration of PbTe nanowires via SAG on InP substrates demonstrates a viable fabrication pathway for complex semiconductor heterostructures necessary for advanced quantum device architectures.
View Original Abstract
PbTe is a semiconductor with promising properties for topological quantum computing applications. Here we characterize quantum dots in PbTe nanowires selectively grown on InP. Charge stability diagrams at zero magnetic field reveal large even-odd spacing between Coulomb blockade peaks, charging energies below 140$~\mathrm{ÎŒeV}$ and Kondo peaks in odd Coulomb diamonds. We attribute the large even-odd spacing to the large dielectric constant and small effective electron mass of PbTe. By studying the Zeeman-induced level and Kondo splitting in finite magnetic fields, we extract the electron $g$-factor as a function of magnetic field direction. We find the $g$-factor tensor to be highly anisotropic, with principal $g$-factors ranging from 0.9 to 22.4, and to depend on the electronic configuration of the devices. These results indicate strong Rashba spin-orbit interaction in our PbTe quantum dots.