Fingerprints of quantum criticality in locally resolved transport
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2022-07-21 |
| Journal | SciPost Physics |
| Authors | Xiaoyang Huang, Andrew Lucas |
| Institutions | University of Colorado Boulder |
| Citations | 8 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis technical analysis focuses on the theoretical prediction of âquantum criticalâ transport signatures in strange metals, utilizing holographic models and proposing validation via high-resolution local imaging techniques. 6CCVD provides the enabling materials required for these advanced quantum sensing experiments.
- Core Research Goal: Identify the unique âfingerprintâ of quantum critical dynamics in electrical current flow, distinguishing it from Ohmic, Ballistic, or Viscous regimes.
- Key Signature: Quantum critical transport is predicted to exhibit an approximately sinusoidal current profile (peaked at the center of a constriction), contrasting sharply with Ohmic flow (peaked at the edges).
- Enabling Technology: Validation requires high-resolution local imaging, specifically Nitrogen Vacancy Center Magnetometry (NVCM) or Scanning Single-Electron Transistors (SET).
- Critical Length Scales: The quantum critical regime is observed when the constriction width ($W_x$) approaches or falls below the Planckian length scale ($l_{pl} \sim \hbar c / k_B T$), potentially requiring device features down to 10 nm.
- 6CCVD Value Proposition: High-purity Single Crystal Diamond (SCD) is the essential host material for NV centers, making 6CCVD the foundational supplier for the state-of-the-art magnetometers required to perform these spatially resolved transport measurements.
- Target Materials: The framework is applied to charge-neutral graphene (Dirac fluid) and is proposed for use in high-Tc superconductors and magic-angle twisted bilayer graphene (MATBG).
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| Constriction Width ($W_x$) | 3 | ”m | Simulated geometry for current flow analysis. |
| Constriction Height ($W_y$) | 0.04 | ”m | Simulated geometry (slit). |
| Planckian Length Scale ($l_{qc}$) | $\sim 300$ | nm | Estimated for charge neutral graphene at experimental T. |
| Critical Feature Size | $\sim 10$ | nm | Required resolution for imaging quantum critical flows at low T. |
| Experimental Temperature (High) | 297 | K | Graphene experiment data fit (Ohmic regime). |
| Experimental Temperature (Low) | 128 | K | Graphene experiment data fit (Ohmic regime). |
| Effective Speed of Light ($c$) | $\sim 10^{6}$ | m/s | Chosen to correspond to Fermi velocity ($v_F$) in the holographic model. |
| Dimensionless Constant ($C$) | $\approx 0.18$ | - | Extracted from fitting holographic model to graphene data. |
| Quantum Critical Conductance ($G$) | $\sim \exp(-\tilde{\alpha}/W_x)$ | - | Exponential suppression with constriction width. |
Key Methodologies
Section titled âKey MethodologiesâThe research employs a combination of theoretical modeling and computational simulation to predict observable phenomena in engineered device geometries.
- Holographic Modeling: Utilizes the Einstein-Maxwell theory in 4 bulk spacetime dimensions (AdS4-RN geometry) to model the strange metal (2+1 dimensional Conformal Field Theory, CFT) at finite temperature ($T$) and density ($\mu$).
- Locally Resolved Transport Framework: A method is established to calculate the local current density $J_i(x)$ in response to an applied electric field $E_i(x)$ in non-trivial geometries (constrictions).
- Conductivity Calculation: The Fourier transform of the conductivity $\sigma(k)$ is calculated via the holographic correspondence using the retarded Greenâs function $G^R_{J_y J_y}(\omega, k)$.
- Constriction Geometry Simulation: Current flow patterns are simulated through a narrow slit ($W_x \gg W_y$) to observe the crossover between Ohmic/Viscous regimes (long length scales, high T) and the Quantum Critical regime (short length scales, low T).
- Experimental Comparison: Theoretical predictions are quantitatively compared to existing experimental data on current flow in monolayer graphene constrictions at charge neutrality (297 K and 128 K).
- Vorticity Analysis: Current flow is also analyzed in a strip geometry to predict the development of multi-vortex structures, serving as an additional signature to distinguish quantum critical flow from ballistic or viscous flow.
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThe validation of this critical theoretical work hinges on the ability to perform high-resolution, spatially resolved transport measurements, primarily using NV Center Magnetometry (NVCM). 6CCVD is uniquely positioned to supply the foundational materials and engineering services necessary for the next generation of quantum transport experiments.
Applicable Materials
Section titled âApplicable MaterialsâThe primary material required to enable the NVCM technique is high-purity Single Crystal Diamond (SCD).
| Application Requirement | 6CCVD Material Recommendation | Key Capability Match |
|---|---|---|
| NV Center Host | Optical Grade SCD | Ultra-low nitrogen concentration (for high NV yield/coherence) and superior surface quality (Ra < 1 nm). |
| Advanced Transport Substrates | High-Purity SCD | Excellent thermal conductivity for precise temperature control (T $\sim$ 100 K regime) and robust mechanical stability for nanodevice fabrication. |
| Electrochemical/Doping Studies | Heavy Boron Doped PCD (BDD) | While not the focus of this paper, BDD offers a stable, conductive platform for future strange metal studies requiring high carrier density or electrochemical gating. |
Customization Potential
Section titled âCustomization PotentialâThe research emphasizes the need for engineered device geometries (constrictions down to 10 nm) and the integration of local probes. 6CCVDâs in-house capabilities directly support these requirements:
- Custom Dimensions: 6CCVD provides SCD plates and PCD wafers up to 125mm, allowing researchers to scale up device fabrication and integration of NVCM systems.
- Precision Polishing: Achieving high-quality NV centers and ensuring clean interfaces for 2D materials (like graphene) requires exceptional surface finish. 6CCVD guarantees Ra < 1 nm on SCD surfaces.
- Advanced Metalization: The creation of electrical contacts for the constriction devices (e.g., Ti/Pt/Au) is a standard internal capability. We offer custom deposition of Au, Pt, Pd, Ti, W, and Cu stacks to meet specific experimental needs.
- Micro- and Nano-Structuring: For defining the constriction geometry or integrating NV layers, 6CCVD offers custom laser cutting and etching services to achieve the precise dimensions ($W_x$, $W_y$) required for probing Planckian length scales.
Engineering Support
Section titled âEngineering SupportâThe transition from theoretical prediction to experimental validation requires deep material and device expertise. 6CCVDâs in-house PhD team specializes in diamond growth, processing, and surface engineering for quantum applications.
We offer consultation on:
- Material Selection: Optimizing SCD purity and orientation for maximum NV center coherence time and density.
- Interface Engineering: Developing optimal diamond surface terminations to ensure high-quality integration with 2D materials (graphene, MATBG) necessary for Quantum Critical Transport projects.
- Thermal Management: Designing diamond substrates to maintain the precise low temperatures (T $\sim$ 100 K) required to observe the quantum critical crossover.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Understanding electrical transport in strange metals, including the seeming universality of Planckian T-linear resistivity, remains a longstanding challenge in condensed matter physics. We propose that local imaging techniques, such as nitrogen vacancy center magnetometry, can locally identify signatures of quantum critical response which are invisible in measurements of a bulk electrical resistivity. As an illustrative example, we use a minimal holographic model for a strange metal in two spatial dimensions to predict how electrical current will flow in regimes dominated by quantum critical dynamics on the Planckian length scale. We describe the crossover between quantum critical transport and hydrodynamic transport (including Ohmic regimes), both in charge neutral and finite density systems. We compare our holographic predictions to experiments on charge neutral graphene, finding quantitative agreement with available data; we suggest further experiments which may determine the relevance of our framework to transport on Planckian scales in this material. More broadly, we propose that locally imaged transport be used to test the universality (or lack thereof) of microscopic dynamics in the diverse set of quantum materials exhibiting T-linear resistivity.