Transport Signatures of Quasiparticle Poisoning in a Majorana Island
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2017-03-27 |
| Journal | Physical Review Letters |
| Authors | S. M. Albrecht, Esben Bork Hansen, Andrew Higginbotham, Ferdinand Kuemmeth, Thomas Sand Jespersen |
| Institutions | Norwegian University of Science and Technology, University of Copenhagen |
| Citations | 106 |
| Analysis | Full AI Review Included |
Technical Documentation and Analysis: Quasiparticle Poisoning in Majorana Islands
Section titled âTechnical Documentation and Analysis: Quasiparticle Poisoning in Majorana IslandsâExecutive Summary
Section titled âExecutive SummaryâThis documentation analyzes the research into quasiparticle (QP) poisoning in InAs/Al hybrid Majorana islands using Coulomb Blockade (CB) spectroscopy. The findings directly inform the material requirements for stable topological quantum computing platforms.
- Core Achievement: Quantified the quasiparticle poisoning time ($T_{p}$) in a strongly coupled Majorana island regime.
- Key Findings: $T_{p}$ was determined to be $\mathbf{\sim 1.2 \text{ ”s}}$ for strongly coupled devices, setting a constraint on parity lifetime. A conservative bound of $\mathbf{T_{p} > 10 \text{ ”s}}$ was established for weakly coupled devices.
- Methodology: Observed and modeled secondary, weaker âshadowâ Coulomb diamonds shifted by $1e$ in gate voltage, which are attributed to transport occurring via an excited (poisoned) state.
- Quantum Significance: High magnetic field data confirmed the transition to the topological phase, exhibiting characteristic peak spacing oscillations consistent with Majorana mode hybridization.
- 6CCVD Relevance: This research emphasizes the critical need for ultra-stable, high-purity material platforms (like MPCVD Diamond) to minimize environmental noise, manage thermal loads at mK temperatures, and achieve the required extended coherence times for scalable Majorana qubits.
- Direct Material Solution: 6CCVD offers high-purity SCD substrates and custom, patterned BDD elements capable of delivering the thermal and electrical performance necessary for extending $T_{p}$ and optimizing complex quantum device integration.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the paper, focusing on the measured physical parameters and derived results:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Base Temperature | $\sim 50$ | mK | Dilution refrigerator operation. |
| Charging Energy ($E_{c}$) | $210$ | ”eV | Extracted from main CB diamonds (Zero field). |
| Subgap State Energy ($E_{0}$) | $75$ | ”eV | Zero field measurement. |
| Induced Superconducting Gap ($\Delta$) | $140$ | ”eV | Chosen to match onset of NDC. |
| Poisoning Time ($T_{p}$) (Strong Coupling) | $1.2 \pm 0.1$ | ”s | Inferred from $g_{m}/g_{s}$ ratio of main/shadow peaks. |
| Poisoning Time Bound (Weak Coupling) | $> 10$ | ”s | Conservative bound on parity lifetime. |
| Gate Lever Arm ($\eta$) | $6.2$ | meV/V | Extracted from $E_{c}$ and peak spacings. |
| Source Tunnel Coupling ($\Gamma_{S}$) | $\sim 1$ | GHz | Fitted asymmetric coupling to leads. |
| Drain Tunnel Coupling ($\Gamma_{D}$) | $\sim 6$ | GHz | Significantly stronger than previous reports. |
| Perpendicular Critical Field ($B_{c,\perp}$) | $\sim 0.7$ | T | Required to suppress superconductivity in $10 \text{ nm}$ Al shell. |
| Majorana Hybridization Amplitude ($A$) | $59$ | ”eV | Extracted from peak spacing oscillations at high $B$. |
Key Methodologies
Section titled âKey MethodologiesâThe experiment utilized advanced low-temperature quantum transport methods combined with theoretical modeling to isolate and quantify quasiparticle effects.
-
Device Fabrication:
- MBE-grown [0001] wurtzite InAs nanowires with a thin ($\sim 10 \text{ nm}$) epitaxial Al shell on two facets were used to create a hybrid superconducting segment (the Majorana island, length $L \sim 400 \text{ nm}$).
- Normal-metal (Ti/Au) ohmic contacts were established at the ends of chemically etched, exposed InAs segments.
- Electrostatic gates were patterned lithographically near the exposed segments to control carrier depletion and island chemical potential ($V_{G}$).
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Cryogenic Transport Measurement:
- Measurements were conducted in a dilution refrigerator at a base temperature of $\sim 50 \text{ mK}$ to ensure operation deep within the Coulomb blockade regime.
- Differential conductance ($g = dI/dV_{SD}$) was measured using standard lock-in methods with a small AC bias ($5 \text{ ”V}$ at $314 \text{ Hz}$).
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Spectroscopy and Field Application:
- Coulomb Blockade Spectroscopy: Used to map charge-state energies and identify degeneracies (conductance peaks). Observation of âshadowâ diamonds was critical for identifying poisoned states.
- Magnetic Field Application: Fields were applied perpendicular ($B_{\perp}$) and in-plane ($B_{tr}$) relative to the nanowire axis to induce Zeeman splitting and transition the island towards the topological (Majorana) phase.
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Modeling and Analysis:
- A simple model of a hybrid Coulomb island was developed, incorporating a BCS continuum, a subgap state, and charging energy ($E_{c}$).
- Transport dynamics were simulated using a steady-state Pauli master equation, including rates for sequential tunneling, internal relaxation ($\Gamma_{relax} = 10 \text{ MHz}$), and phenomenological quasiparticle poisoning ($\Gamma_{qp}$).
- The poisoning time $T_{p}$ was determined by fitting the ratio of the main peak conductance ($g_{m}$) to the shadow peak conductance ($g_{s}$) using the derived relationship $T_{p} = a(g_{m}/g_{s}) + b$.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the significant engineering challenges associated with maintaining quantum coherence, particularly the management of quasiparticle poisoning, which directly limits the parity lifetime of Majorana devices. 6CCVD provides critical material solutions to stabilize and advance these complex quantum systems.
Applicable Materials for Coherence Enhancement
Section titled âApplicable Materials for Coherence EnhancementâTo extend the quasiparticle poisoning time ($T_{p}$) and maximize the coherence of low-temperature quantum circuits, researchers require substrates offering extreme thermal stability and superior surface purity.
| 6CCVD Material | Recommended Grade | Application Benefit | Customization Potential |
|---|---|---|---|
| Single Crystal Diamond (SCD) | Optical/Electronic Grade | Thermal Management: Highest known thermal conductivity, essential for rapidly sinking heat and maintaining $50 \text{ mK}$ base temperature stability across the chip area, minimizing temperature fluctuations which generate QPs. | Custom SCD wafers up to $5 \text{ mm}$ substrates and $500 \text{ ”m}$ thick. |
| Polycrystalline Diamond (PCD) | Electronic/High Purity | Platform Integration: Offers large-area, high-stability platform (up to $125 \text{ mm}$ wafers) for heterogeneous integration of III-V nanowire structures (InAs/Al) or other quantum materials. | Wafers up to $125 \text{ mm}$. Polishing available down to $\mathbf{Ra < 5 \text{ nm}}$ for inch-size PCD. |
| Boron-Doped Diamond (BDD) | Heavy Doped (Conductive) | Integrated Gating/Superconductivity: Can be used as a robust, conductive backgate, or potentially as an active superconducting element in high-field environments, leveraging diamondâs intrinsic stability. | Custom doping levels and thickness (SCD or PCD). |
Customization Potential for Quantum Devices
Section titled âCustomization Potential for Quantum DevicesâThe InAs/Al device required precise normal-metal leads (Ti/Au) and specific geometries. 6CCVD specializes in matching these precise fabrication needs to accelerate quantum research.
- Custom Metalization Stacks: 6CCVD offers in-house capability for depositing custom metal films directly onto diamond substrates, including the materials used in this study (Au, Ti) as well as Pt, Pd, W, and Cu, ensuring robust ohmic contacts and low-noise interfaces critical for mK experiments.
- Precision Dimensional Control: We provide SCD and PCD plates with custom dimensions and specific thicknesses (from $0.1 \text{ ”m}$ films up to $10 \text{ mm}$ substrates) suitable for integration into specialized cryogenic holders and flip-chip assemblies.
- Ultra-Low Surface Roughness: Achieving high-fidelity epitaxial growth or stable interfaces for hybrid quantum devices requires atomically smooth surfaces. 6CCVD guarantees surface roughness of $\mathbf{Ra < 1 \text{ nm}}$ for SCD and $\mathbf{Ra < 5 \text{ nm}}$ for inch-size PCD, significantly improving device yield and performance.
Engineering Support & Global Logistics
Section titled âEngineering Support & Global Logisticsâ6CCVDâs in-house PhD team can assist researchers with material selection and optimization protocols for similar Topological Quantum Computing and Majorana Qubit projects, ensuring that the diamond platform minimizes extraneous noise sources contributing to quasiparticle poisoning.
We provide global shipping services (DDU default, DDP available), guaranteeing that high-purity, custom diamond materials reach your laboratory efficiently and reliably.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, âshadowâ diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (âŒ1 ÎŒs) and sets a bound for a weakly coupled island (>10 ÎŒs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.