| 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 |
- Core Challenge: The universal T-linear resistivity (Planckian dissipation) observed in strange metals (e.g., high-Tc superconductors, graphene) is challenging to attribute to a specific microscopic theory using only bulk measurements.
- Value Proposition: This work proposes that local imaging techniques, such as Nitrogen Vacancy Center Magnetometry (NVCM) or Scanning Single-Electron Transistors (SET), can reveal unique spatial current flow patterns (âfingerprintsâ) indicative of quantum critical transport.
- Theoretical Framework: A minimal holographic model (AdS/CFT duality) for a strange metal in two spatial dimensions was used to predict current flow through a constriction (slit) geometry.
- Quantum Critical Signature: The predicted current profile in the quantum critical regime is approximately sinusoidal, peaking strongly in the center of the constriction, contrasting sharply with the edge-peaked profile of Ohmic transport or the semi-circular profile of viscous hydrodynamic flow.
- Crossover Mechanism: The transition between Ohmic/Viscous and Quantum Critical transport is governed by the ratio of the constriction width (Wx) to the Planckian length scale (lqc ~ h*vF/kBT).
- Experimental Validation: The model successfully fits existing experimental data on charge-neutral graphene at 128 K and 297 K, providing a quantitative estimate for the dimensionless constant C â 0.18, consistent with prior bulk measurements.
- Future Testing: Measuring the conductance dependence on constriction width (Wx) (scaling as log Wx for Ohmic vs. exp(-α/Wx) for quantum critical) offers a simpler, non-imaging method to distinguish regimes.
| Parameter | Value | Unit | Context |
|---|
| Experimental Temperature (High) | 297 | K | Graphene transport data used for fitting |
| Experimental Temperature (Low) | 128 | K | Graphene transport data used for fitting |
| Simulated Constriction Width (Wx) | 3 | ”m | Standard width used in simulations and experimental comparison |
| Simulated Constriction Height (Wy) | 0.04 | ”m | Standard height used in simulations |
| Proposed Future Constriction Width | 600 | nm | Width suggested for clear distinction between Fermi liquid and quantum critical flow at T ~ 100 K |
| Fermi Velocity (vF) | 106 | m/s | Effective speed of light in the Dirac fluid (graphene) |
| Dimensionless Constant (C) | ~ 0.18 | None | Fitted parameter relating Planckian length (lqc) to temperature |
| Planckian Length Scale (lqc) | ~ hvF/(CkBT) | Length | Governing scale for quantum critical transport |
| Kinetic Fit lee (128 K) | ~ 80 | nm | Momentum-conserving scattering length (Boltzmann model fit) |
| Kinetic Fit lmr (128 K) | ~ 1300 | nm | Momentum-relaxing scattering length (Boltzmann model fit) |
| Holographic Model Dimension | 2 + 1 | None | Spatial dimensions of the boundary field theory (CFT) |
- Holographic Model Setup: The study utilizes the Einstein-Maxwell theory in 4 bulk spacetime dimensions (AdS4-RN geometry) to model a 2+1 dimensional conformal field theory (CFT) with a global U(1) symmetry at finite temperature T.
- Non-Local Conductivity Calculation: The momentum-dependent conductivity Ï(k) is calculated via the holographic correspondence by analyzing the Fourier transform of the retarded Greenâs function (GRJ J) of the current operator, derived from bulk gauge field fluctuations.
- Transport Simulation Framework: Current flow Ji(x) in the constriction geometry is calculated using a non-local transport equation: Ji(x) = â« d2xâ Ïij(x - xâ)Ej(xâ).
- Boundary Condition Implementation: The effect of the hard walls (where current cannot flow, Ji = 0) is modeled by introducing an effective induced electric field (EÌi) within the non-conducting region, analogous to the method of image charges in electrostatics. The standard âno-slipâ boundary condition (λ = 0) is used for the main results.
- Regime Differentiation: The transport regimes are distinguished based on the k-dependence of the conductivity:
- Ohmic: Ï(k) is constant (long wavelength).
- Viscous/Hydrodynamic (Finite Density): Ï(k) includes a term proportional to 1/k2.
- Quantum Critical (Zero Density): Ï(k) decays exponentially with k (Ï(k) ~ exp(-ak/T)).
- Experimental Comparison: Simulated current profiles were fitted to NVCM data from charge-neutral graphene at two temperatures. A Gaussian filter was applied to the theoretical profiles to account for the limited spatial resolution of the experimental magnetometer (0.14 ”m).
| Industry/Sector | Relevance to Quantum Critical Transport |
|---|
| Quantum Materials Engineering | Provides a crucial diagnostic tool for characterizing strongly correlated electron systems, such as high-Tc cuprates and magic-angle twisted bilayer graphene, where strange metallic behavior is prevalent. |
| Nanoscale Device Design | The ability to locally image current flow (using NVCM or SET) is essential for optimizing transport in 2D materials, especially when device features approach the Planckian length scale (10 nm to 100 nm). |
| Fundamental Condensed Matter Physics | Offers a method to experimentally test theoretical models (like holographic duality) describing non-quasiparticle transport, helping to resolve the long-standing mystery of Planckian dissipation. |
| Advanced Sensing Technology | Drives the development and application of high-resolution local probes (NVCM) capable of operating at cryogenic temperatures necessary to observe quantum critical phenomena. |
| Thermoelectric Devices | Understanding the relationship between charge transport and momentum relaxation (viscous vs. quantum critical flow) is critical for designing efficient thermoelectric and energy conversion materials. |
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.