Fluctuation spectroscopy in granular superconductors with application to boron-doped nanocrystalline diamond
At a Glance
Section titled “At a Glance”| Metadata | Details |
|---|---|
| Publication Date | 2021-09-13 |
| Journal | Physical review. B./Physical review. B |
| Authors | David T. S. Perkins, Georgina M. Klemencic, J. M. Fellows, Robert A. Smith |
| Institutions | University of Bristol, University of Birmingham |
| Citations | 1 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled “Executive Summary”This research presents a comprehensive theoretical model for fluctuation conductivity (σfl) in metallic granular superconductors, integrating both intragrain and intergrain degrees of freedom (DOFs).
- Complete Fluctuation Theory: The study combines existing granular diagrammatic formalisms (intergrain DOFs) with intragrain DOF analysis to provide a complete theory of Aslamazov-Larkin (AL), Maki-Thompson (MT), and Density of States (DOS) contributions.
- Three Distinct Regions: The model predicts three distinct power-law regimes in the reduced temperature (η = (T - Tc)/Tc), defined by crossovers at the dimensionless tunneling rate (Γ/Tc) and the Thouless energy (ETh/Tc).
- BNCD Application: The theory is numerically compared against experimental data from Boron-doped Nanocrystalline Diamond (BNCD) films, a known granular superconductor.
- Intermediate Region Discrepancy: The experimental observation of an η-3 power law in the intermediate region (attributed to the AL term) contradicts the theoretical prediction that the anomalous MT term (η-1) should dominate in the absence of phase breaking.
- Phase Breaking Requirement: Semi-quantitative agreement with the experimental η-3 behavior requires the inclusion of a significant phase breaking rate (τφ-1), which suppresses the anomalous MT contribution, allowing the AL term to dominate.
- Novel Mechanism Proposed: The findings suggest the existence of a novel phase breaking mechanism in granular metals, potentially temperature-dependent, that warrants further investigation.
Technical Specifications
Section titled “Technical Specifications”The following parameters were used for numerical comparison, derived from experimental characterization of the BNCD films (329 nm thick) by Klemencic et al. [13, 14].
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Critical Temperature (Tc) | 3.8 | K | Observed superconducting transition temperature. |
| Thouless Energy (ETh) | 1 | K | Intragrain energy scale (D0/a2). |
| Tunneling Rate (Γ) | 2.62 x 10-2 | K | Intergrain electron tunneling rate. |
| Intragrain Diffusion (D0) | 13.1 | cm2s-1 | Electron diffusion coefficient within a single grain. |
| Typical Grain Size (a) | 10-7 | m | Assumed cubic lattice side length. |
| Mean Level Spacing (δ) | 5.6 x 10-3 | K | Energy level spacing within a grain. |
| Carrier Concentration (n) | 1027 | m-3 | High concentration typical of metallic BNCD. |
| Granular Diffusivity (DT) | Γa2 | m2s-1 | Effective diffusion coefficient for the granular system. |
Fluctuation Conductivity Power Laws (σfl ~ ηα)
Section titled “Fluctuation Conductivity Power Laws (σfl ~ ηα)”The theoretical model predicts distinct power-law exponents (α) for the total fluctuation conductivity (σfl) based on the reduced temperature (η), assuming zero phase breaking (τφ-1 = 0).
| Region | Condition | Dominant Term(s) | Predicted Exponent (α) |
|---|---|---|---|
| Close-to-Tc | η < Γ/Tc | AL, Anomalous MT | -1/2 |
| Intermediate | Γ/Tc < η < ETh/Tc | Anomalous MT, DOS | -1 |
| Far-from-Tc | ETh/Tc < η < 1 | Anomalous MT, DOS | -1/2 |
Note: The experimentally observed intermediate region exponent is α = -3, which is only achieved theoretically when a large phase breaking rate suppresses the anomalous MT term.
Key Methodologies
Section titled “Key Methodologies”The study is primarily theoretical, extending the granular diagrammatic formalism to fully describe superconducting fluctuations in the metallic regime (δ < Γ < ETh < Tc).
- Hamiltonian Formulation: A general Hamiltonian was established for the granular system, including terms for free electrons, impurity scattering, intergrain tunneling, Coulomb repulsion, and the s-wave BCS interaction.
- Granular Diagrammatics: The standard rules of diagrammatics were adapted to granular systems, incorporating grain indices and Gaussian-distributed tunneling matrix elements for nearest-neighbor hopping.
- Pair Propagator Derivation: The granular cooperon (Γpp) was derived, leading to the granular pair propagator L(Q, q, iω), which simultaneously includes external momentum (Q, intergrain) and internal momentum (q, intragrain) DOFs.
- Dimensional Crossover Definition: The three temperature regions (Close-to-Tc, Intermediate, Far-from-Tc) were defined based on the relative singularity of the internal (D0q2) and external (ΓλQ) energy scales in the pair propagator compared to the reduced temperature (η).
- Close-to-Tc: External DOFs relevant (d-dimensional).
- Intermediate: Neither DOF relevant (quasi-zero dimensional).
- Far-from-Tc: Internal DOFs relevant (d-dimensional).
- Fluctuation Correction Calculation: Explicit calculations were performed for the leading-order fluctuation corrections to conductivity:
- Aslamazov-Larkin (AL)
- Maki-Thompson (MT, including regular and anomalous parts)
- Density of States (DOS)
- Numerical Comparison: Analytical power laws and numerical evaluations (using BNCD material parameters) were performed to compare the total theoretical σfl against experimental data, highlighting the necessity of including a non-zero phase breaking rate (τφ-1) to match the observed η-3 intermediate behavior.
Commercial Applications
Section titled “Commercial Applications”The research focuses on the fundamental transport properties of Boron-doped Nanocrystalline Diamond (BNCD), a material known for its robust superconductivity and extreme physical properties.
- Quantum Computing and Devices: BNCD is a promising material for superconducting quantum circuits due to its high Tc (relative to other diamond materials) and compatibility with microfabrication techniques. Understanding fluctuation effects is crucial for device stability near Tc.
- High-Frequency Electronics: Superconducting granular films can be used in high-frequency filters, resonators, and detectors, where minimizing noise and understanding transport mechanisms near the transition temperature is essential.
- Extreme Environment Sensors: Diamond-based materials offer superior thermal and chemical stability. Superconducting diamond films could be used in sensors operating in harsh or high-radiation environments.
- Josephson Junction Arrays: The granular structure of BNCD naturally forms a Josephson junction array, which is fundamental to voltage standards and superconducting quantum interference devices (SQUIDs).
- Novel Phase Breaking Mechanisms: The theoretical need for a large phase breaking rate to explain experimental results suggests new physics relevant to coherence and dissipation in highly disordered metallic systems.
View Original Abstract
We perform a detailed calculation of the various contributions to the fluctuation conductivity of a granular metal close to its superconducting transition. We find three distinct regions of power law behavior in reduced temperature, η = ( T − T c ) / T c , with crossovers at Γ / T c and E Th / T c , where Γ is the electron tunneling rate, and E Th is the Thouless energy of a grain. The calculation includes both intergrain and intragrain degrees of freedom. This complete theory of the fluctuation region in granular superconductors is then compared to experimental results from boron-doped nanocrystalline diamond, using the assumption of a constant phase breaking rate τ − 1 ϕ . We find a semiquantitative agreement between the theoretical and experimental results only in the case of large phase breaking. We argue that there may be a phase breaking mechanism in granular metals worthy of further experimental and theoretical investigation.
Tech Support
Section titled “Tech Support”Original Source
Section titled “Original Source”References
Section titled “References”- 1995 - Metal-Insulator Transitions Revisited