Johnson-noise-limited cancellation-free microwave impedance microscopy with monolithic silicon cantilever probes.

Microwave impedance microscopy (MIM) is an emerging scanning probe technique for nanoscale complex permittivity mapping and has made significant impacts in diverse fields. To date, the most significant hurdles that limit its widespread use are the requirements of specialized microwave probes and high-precision cancellation circuits. Here, we show that forgoing both elements not only is feasible but also enhances performance. Using monolithic silicon cantilever probes and a cancellation-free architecture, we demonstrate Johnson-noise-limited, drift-free MIM operation with 15 nm spatial resolution, minimal topography crosstalk, and an unprecedented sensitivity of 0.26 zF/√Hz. We accomplish this by taking advantage of the high mechanical resonant frequency and spatial resolution of silicon probes, the inherent common-mode phase noise rejection of self-referenced homodyne detection, and the exceptional stability of the streamlined architecture. Our approach makes MIM drastically more accessible and paves the way for advanced operation modes as well as integration with complementary techniques.

The Reststrahlen Effect in the Optically Thin Limit: A Framework for Resonant Response in Thin Media.

Sharp resonances can strongly modify the electromagnetic response of matter. A classic example is the Reststrahlen effect - high reflectivity in the mid-infrared in many polar crystals near their optical phonon resonances. Although this effect in bulk materials has been studied extensively, a systematic treatment for finite thickness remains challenging. Here we describe, experimentally and theoretically, the Reststrahlen response in hexagonal boron nitride across more than 5 orders of magnitude in thickness, down to a monolayer. We find that the high reflectivity plateau of the Reststrahlen band evolves into a single peak as the material enters the optically thin limit, within which two distinct regimes emerge: a strong-response regime dominated by coherent radiative decay and a weak-response regime dominated by damping. We show that this evolution can be explained by a simple two-dimensional sheet model that can be applied to a wide range of thin media.

Unconventional Correlation between Quantum Hall Transport Quantization and Bulk State Filling in Gated Graphene Devices.

We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still conductive. This result points to a revised understanding of transport quantization when carriers are accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in graphene and related topological states in other two-dimensional electron systems.