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Compact localized boundary states in a quasi-1D electronic diamond-necklace chain

MetadataDetails
Publication Date2023-02-28
JournalQuantum Frontiers
AuthorsS. N. Kempkes, Pierre Capiod, S. Ismaili, J. Mulkens, L. Eek
InstitutionsUtrecht University
Citations12
AnalysisFull AI Review Included

Technical Documentation & Analysis: Compact Localized Boundary States in Diamond-Necklace Chains

Section titled “Technical Documentation & Analysis: Compact Localized Boundary States in Diamond-Necklace Chains”

This research demonstrates a critical advancement in solid-state quantum computing by identifying a highly robust boundary state suitable for fault-tolerant qubits. 6CCVD provides the high-purity MPCVD diamond materials necessary to transition this theoretical and simulated lattice structure into a scalable, functional quantum device.

  • Breakthrough: Experimental realization of Compact Localized Zero-Energy Modes (CLZEMs) in a quasi-1D diamond-necklace chain structure.
  • Quantum Advantage: CLZEMs exhibit strictly zero-energy localization at the boundaries with no exponential decay into the bulk, overcoming the primary hybridization and decoherence challenges faced by traditional Majorana bound states (e.g., in Kitaev chains).
  • Robustness: The states are protected by a latent symmetry, ensuring robustness against bulk disorder and a wide range of boundary perturbations.
  • Tunability: The amplitude of the localized wave function is precisely controllable by tuning the boundary hopping parameter ($t_3$).
  • Methodology: The lattice structure was simulated using CO molecules patterned on a Cu(111) surface, measured via STM/STS at 4 K.
  • 6CCVD Value Proposition: SCD (Single Crystal Diamond) provides the ideal wide-bandgap, high-coherence platform required for the solid-state realization and integration of these CLZEM structures for next-generation quantum networks.

The following hard data points were extracted from the experimental and simulation parameters used to verify the existence of the CLZEMs.

ParameterValueUnitContext
Experimental Temperature4KScanning Tunneling Microscopy (STM) operation.
Onsite Energy (es)-0.1eVTight-binding calculation parameter.
Strong Hopping (t1)0.095eVStrong hopping within the diamond unit cell.
Weak Hopping (t2)0.1t1eVWeak hopping within the diamond unit cell (t2 = 0.0095 eV).
Connecting Hopping (t4)0.4t1eVHopping connecting adjacent diamond units.
Boundary Hopping (t3) Range0.3t1 to 0.8t1eVParameter tuned experimentally to control wave function amplitude.
Muffin-Tin Potential Barrier Height (V)0.9eVUsed to simulate CO molecules on Cu(111).
Muffin-Tin Broadening (FWHM)0.08eVApplied to energy levels to account for surface-bulk coupling.
Tight-Binding Broadening (Γ)80meVApplied to spectra to simulate scattering with bulk states.
STM Modulation Voltage (rms)10mVUsed for differential conductance (dI/dV) measurements.

The experimental verification relied on creating an artificial quantum lattice using atomic manipulation techniques on a metallic surface, followed by detailed spectroscopic analysis.

  1. Substrate and Environment: A Cu(111) surface was used as the 2D electron gas source, with experiments conducted in an ultra-high vacuum (UHV) STM system at 4 K.
  2. Lattice Fabrication: CO molecules were individually positioned using the STM tip to act as repulsive scatterers, confining the surface electrons and defining the sites of the quasi-1D diamond-necklace chain.
  3. Boundary Tuning: The boundary hopping parameter ($t_3$) was controlled by precisely adjusting the distance of specific CO molecules at the chain ends (ranging from 1.024 nm to 1.28 nm).
  4. Spectroscopic Measurement: Local Density of States (LDOS) maps and tunneling spectra (dI/dV) were acquired at constant height using a lock-in amplifier (10 mV rms modulation at 769 Hz) to identify the zero-energy modes.
  5. Theoretical Modeling: Results were verified using two complementary simulation techniques:
    • Muffin-tin simulations: Solving the Schrödinger equation for the 2D electron gas system.
    • Tight-binding calculations: Solving a finite-size Hamiltonian (N=82 sites) incorporating four hopping parameters ($t_1$ to $t_4$) and orbital overlaps ($s_1$ to $s_4$).

The successful simulation of the diamond-necklace chain structure provides a clear roadmap for realizing robust quantum states in a solid-state platform. 6CCVD specializes in providing the high-quality MPCVD diamond required to transition this research from a metallic simulator to a scalable quantum device.

To replicate or extend this research into a functional quantum device (e.g., integrating quantum defects or utilizing diamond’s intrinsic properties), Single Crystal Diamond (SCD) is the required material.

6CCVD MaterialGrade RecommendationRationale for CLZEM Implementation
Single Crystal Diamond (SCD)Electronic or Optical GradeEssential for high-coherence quantum applications. The wide bandgap (5.5 eV) and high Debye temperature ensure superior stability and minimal decoherence compared to metallic substrates (Cu(111)).
Boron-Doped Diamond (BDD)Lightly Doped (p-type)Potential use as a conductive layer or gate electrode for electrostatic control of the hopping parameters ($t_i$) in a solid-state device architecture.

The realization of a quasi-1D lattice structure in diamond requires precise material engineering and fabrication capabilities, all available in-house at 6CCVD.

  • Custom Dimensions: 6CCVD supplies SCD plates and wafers up to 125mm (PCD) or custom-sized SCD pieces, allowing researchers to design large-scale quantum networks based on the diamond-necklace geometry.
  • Precision Thickness Control: We offer SCD layers from 0.1 ”m up to 500 ”m. Ultra-thin layers are ideal for surface-sensitive quantum experiments, while thicker substrates (up to 10mm) provide robust mechanical support.
  • Surface Engineering (Lattice Fabrication): While the paper used CO/STM, a scalable diamond device requires lithographic patterning and etching. 6CCVD provides ultra-smooth polishing (Ra < 1 nm for SCD) essential for high-resolution lithography needed to define the nanoscale lattice sites.
  • Custom Metalization: The experimental setup relies on precise control of coupling/hopping ($t_3$). In a solid-state device, this control is often achieved via gate electrodes. 6CCVD offers custom metalization stacks (Au, Pt, Pd, Ti, W, Cu) for creating integrated electrical contacts and gates directly onto the diamond surface, enabling dynamic tuning of the CLZEM wave function amplitude.

The theoretical foundation of this work—involving latent symmetry, tight-binding models, and destructive interference—is highly complex. 6CCVD’s in-house PhD team specializes in the material science and quantum physics of diamond systems. We can assist researchers with:

  • Material Selection: Optimizing SCD purity and doping levels for integrating CLZEMs with established quantum defects (e.g., NV or SiV centers) to create functional qubits.
  • Fabrication Recipe Development: Consulting on the optimal etching and metalization processes to accurately translate the simulated quasi-1D diamond-necklace geometry onto a robust SCD substrate.

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