Tuning quantum non-local effects in graphene plasmonics

Abstract: The response of an electron system to electromagnetic fields with sharp spatial variations is strongly dependent on quantum electronic properties, even in ambient conditions, but difficult to access experimentally. We use propagating graphene plasmons, together with an engineered dielectric-metallic environment, to probe the graphene electron liquid and unveil its detailed electronic response at short wavelengths.The near-field imaging experiments reveal a parameter-free match with the full theoretical quantum description of the massless Dirac electron gas, in which we identify three types of quantum effects as keys to understanding the experimental response of graphene to short-ranged terahertz electric fields. The first type is of single-particle nature and is related to shape deformations of the Fermi surface during a plasmon oscillations. The second and third types are a many-body effect controlled by the inertia and compressibility of the interacting electron liquid in graphene. We demonstrate how, in principle, our experimental approach can determine the full spatiotemporal response of an electron system.

• The paper demonstrates precise tuning of non-local plasmon effects via near-field microscopy in graphene-hBN-metal heterostructures.
• It employs a full quantum model capturing Fermi surface deformations, many-body corrections, and compressibility dynamics.
• Results reveal a strong match between experimental observations and theory, highlighting tunable electron velocity renormalization and plasmon dispersion.

Tuning Quantum Non-Local Effects in Graphene Plasmonics

The paper "Tuning Quantum Non-Local Effects in Graphene Plasmonics" explores the intricate quantum mechanical behaviors of electron systems in graphene when subjected to sharp spatial variations in electromagnetic fields. Leveraging the unique properties of graphene plasmons and the customizability of the surrounding dielectric-metallic environment, the authors aim to elucidate the non-local electronic response, a domain traditionally challenging to probe with standard optical and transport techniques.

Key Contributions

Experimental Methodology

The authors deploy a sophisticated near-field optical microscopy technique to visualize and quantify the behavior of propagating plasmons in high-quality graphene-hBN-metal heterostructures. The plasmon propagation is distinctly manipulated by adjusting the electron carrier density and the dielectric spacing, enabling a broad investigation of non-local effects. This configuration allows them to match experimental data with the full theoretical quantum description of the Dirac electron gas without fitting parameters. This novel alignment between experiment and theory enables an intricate dissection of quantum effects in graphene's plasmonic behavior.

Theoretical Framework

Central to the study is the quantum theoretical model that accounts for multiple layers of electron interactions. The paper identifies three primary quantum effects contributing to these observations:

1. Single-Particle Fermi Surface Deformations: Introducing non-local behavior by observing the modifications in the Fermi surface during plasmon oscillations. This effect prominently features in the random phase approximation (RPA) model, which the authors use to explain the variance in conductivity with wave vector $q$.
2. Many-Body Effects: The phenomenon associated with the inertia and fine details like compressibility within the electron system. These are modeled using corrections to the RPA to account for real electronic interactions occurring in graphene, emphasizing velocity renormalization and compressibility corrections.
3. Inertial and Compressibility Dynamics: These attributes provide insights into the dynamical conductivity of graphene as a function of frequency and wavevector, $\sigma(\omega,q)$. The tunable capacitance of the dielectric-metal environment heavily influences these dynamics, as revealed by Eq. $(1)$ in the paper, which defines the self-oscillation conditions adjusted by experimental setup parameters.

Results and Implications

The numerical results demonstrate strong consistency between the theoretical predictions and experimental observations across devices with varying dielectric thicknesses and carrier densities. Notably, the paper identifies the significant influence of electron velocity renormalization on the measurements. Velocity renormalization effects, that cause the observed Fermi velocity to exceed nominal values at low densities, are rigorously modeled, showcasing the necessity of incorporating interactions and compressibility into the theoretical framework.

Graphene plasmons can be tuned to low phase velocities, nearly matching the Fermi velocity itself, leading to non-local effects becoming significant—a feature unusable in typical 2D electron gas systems. The findings present a compelling case for utilizing spatially confined plasmons to probe electron correlations, a method transferable to studying other exotic electron systems like fractional quantum Hall states or superconductors.

Future Directions

This study opens avenues for detailed spatial spectroscopy of other complex electron systems, challenging traditional models and paving the way for enhanced quantum characterization techniques. Further work can explore finer control over plasmon dispersion relations and density-dependent electron interactions. The successfully achieved parameter-free match with theoretical predictions suggests highly precise models applicable to various nanoscale materials and electronic phenomena.

In conclusion, this paper provides a robust framework for interpreting and harnessing quantum non-local effects in graphene, advocating the importance of incorporating full quantum mechanical descriptions in plasmonic research and opening new paths for probing quantum electron systems.