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Large even-odd spacing and $g$-factor anisotropy in PbTe quantum dots

MetadataDetails
Publication Date2022-05-13
JournalarXiv (Cornell University)
AuthorsSofieke C. ten Kate, M. F. Ritter, Sander G. Schellingerhout
AnalysisFull AI Review Included

Technical Analysis and Material Solutions for Anisotropic G-Factors in Quantum Dots

Section titled “Technical Analysis and Material Solutions for Anisotropic G-Factors in Quantum Dots”

This research paper characterizes Lead Telluride (PbTe) nanowire quantum dots (QDs) grown via Selective Area Growth (SAG) on InP substrates, yielding critical data relevant to topological quantum computing platforms. The findings highlight the necessity of highly controlled material properties and precise fabrication techniques, areas where 6CCVD’s specialized MPCVD diamond capabilities provide distinct advantages for extending this research.

  • Quantum Significance: Confirmed high-quality QD behavior at ultra-low temperatures (< 20 mK), demonstrating large even-odd spacing in Coulomb blockade peaks, vital for spin control studies.
  • Material Extremes: The extremely large dielectric constant of PbTe ($\epsilon_{r} \approx 1350$) results in significant screening and small charging energies ($E_{c}$ down to $110 \mu\text{eV}$), a key takeaway for designing high-sensitivity quantum devices.
  • G-Factor Discovery: Extracted an exceptionally anisotropic electron g-factor tensor, ranging dramatically from $g=0.9$ to $g=22.4$, indicating strong Rashba Spin-Orbit Interaction (SOI) and critical directional dependence for magnetic field applications.
  • Methodological Rigor: G-factors were robustly determined using two distinct techniques: Kondo splitting and excited state level splitting, across 360° magnetic field rotations.
  • 6CCVD Relevance: The requirements for high-purity substrates, complex metalization (Ti/Au), and low-decoherence operation align directly with 6CCVD’s core strengths in custom Single Crystal Diamond (SCD) and Boron-Doped Diamond (BDD) material solutions.

The following hard data points were extracted, detailing the physical and electrical parameters achieved in the PbTe QD devices.

ParameterValueUnitContext
Measurement Temperature< 20mKDilution refrigerator base temperature
PbTe Dielectric Constant ($\epsilon_{r}$)~1350-Estimated at low temperatures
Charging Energy ($E_{c}$, Average)110 - 130$\mu\text{eV}$Derived from odd Coulomb diamonds
Single-Particle Excitation ($\Delta$)170 - 500$\mu\text{eV}$Varies by device/confinement strength
Principal G-factor Range ($g_i$)0.9 to 22.4-Highly anisotropic, depending on orientation
Nanowire Width (Device 1)80nm-
Nanowire Width (Device 2)100nm-
Source/Drain Metal Stack5 nm Ti / 50 nm Au-E-beam evaporated
G-Factor Magnetic Field ($B$)100 or 200mTUsed for splitting measurements
AC Bias Voltage ($V_{\text{AC}}$)3$\mu\text{V}$Lock-in measurement stimulus
Estimated QD Length ($L$)160 - 860nmDerived from $\Delta$ and effective mass
Gating Lever Arm ($\alpha_{\text{R}}$)$\approx$ 0.0092-Low value indicates high source/drain coupling

The experiment relied on advanced material growth, nanoscale lithography, and ultra-precise cryogenic electronic measurement techniques.

  1. Material Growth: PbTe nanowires were grown using Selective Area Growth (SAG) via Molecular Beam Epitaxy (MBE) on (111)A InP substrates, defining specific crystal directions (e.g., (110) or (112)).
  2. Device Fabrication (E-Beam Lithography): A double-resist layer (PMMA) was patterned via e-beam lithography to define contact geometry.
  3. Surface Preparation: An Argon (Ar) Reactive Ion Etch (RIE) was performed immediately prior to metal deposition to remove the native oxide layer from the PbTe nanowires.
  4. Metalization: Ti/Au contacts and gates (5 nm Ti adhesion layer, 50 nm Au conductor) were deposited using e-beam evaporation and subsequent lift-off.
  5. Cryogenic Setup: Measurements were performed at ultra-low temperatures (< 20 mK) within a dilution refrigerator equipped with a vector magnet capable of rotating the magnetic field in 15° steps across orthogonal planes ($360^{\circ}$ rotation).
  6. G-Factor Extraction: The electron g-factor was determined by monitoring the Zeeman splitting of:
    • Kondo peaks (extracted from the separation of maxima in $G(V_{\text{SD}})$).
    • Excited state level splittings (preferred method, as Kondo splitting was found to underestimate the g-factor by $\approx 20%$).

The successful execution of this complex quantum physics experiment demands substrates and materials with extreme purity, thermal conductivity, and customizable electronic properties—hallmarks of 6CCVD’s MPCVD diamond offering.

To replicate or extend this research into more robust, low-decoherence platforms, 6CCVD recommends:

  • High Purity Single Crystal Diamond (SCD) Substrates: Essential for acting as a robust, low-noise platform for integrated devices. While PbTe was grown on InP, SCD offers superior thermal management (up to 2000 W/m¡K) and crystalline purity, drastically reducing phonon scattering and thermal fluctuation noise at cryogenic temperatures.
    • 6CCVD Capability Match: Optical Grade SCD Wafers (up to 125mm) providing a near-perfect crystalline structure (Ra < 1 nm polished finish).
  • Thin-Film Single Crystal Diamond (SCD): Required for applications that utilize hybrid material growth (like the SAG PbTe) but demand low optical absorption or specific thermal grounding.
    • 6CCVD Capability Match: SCD Films from $0.1 \mu\text{m}$ up to $500 \mu\text{m}$ thick.
  • Heavy Boron-Doped Diamond (BDD): The paper’s ultimate goal is combining this platform with a superconductor to study topological physics. BDD is a known intrinsic superconductor, making it an ideal candidate to replace or enhance the metallic contacts (Ti/Au) or to function as a superconducting base for proximity effect studies.
    • 6CCVD Capability Match: Superconducting Grade BDD films, offering a robust, chemically inert superconducting component integrated directly into the device architecture.

Customization Potential for Quantum Device Integration

Section titled “Customization Potential for Quantum Device Integration”

The reported fabrication required precise patterning and multi-layer metal contacts, services central to 6CCVD’s engineering capabilities:

Research Requirement6CCVD Custom CapabilityApplication Advantage
Contact Metal Stack (Ti/Au)Custom Metalization Services6CCVD routinely deposits complex metal stacks including Ti/Pt/Au, Ti/W/Cu, and Pd/Cu. We meet the need for low-resistance, cryogenically stable contacts and gates.
Nanoscale Device DimensionsCustom Dicing & Laser CuttingWhile the QDs were nanoscale, the supporting substrate required precise handling. We provide custom plates/wafers up to 125mm and offer advanced laser cutting for complex geometry isolation and device packaging.
Ultra-Smooth Surface FinishPrecision Polishing (Ra < 1 nm)SCD polishing services achieve Ra < 1 nm (SCD) and Ra < 5 nm (inch-size PCD), critical for minimizing interface defects and ensuring reliable E-beam lithography resolution for subsequent layers.

6CCVD’s in-house PhD engineering team understands the challenges of g-factor anisotropy extraction, spin-orbit interaction modeling (Rashba SOI), and material selection for low-temperature quantum applications. We provide specialized consulting to assist researchers and engineers in selecting the optimal SCD or BDD parameters (e.g., nitrogen concentration, boron doping level, surface orientation) for similar topological superconductivity or quantum sensing projects.

We offer global shipping with DDU (Delivery Duty Unpaid) default terms, and DDP (Delivery Duty Paid) options are available for streamlined procurement worldwide.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

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$~\mathrm{ÎźeV}$ 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.