A recently developed technique of transmission-mode microwave impedance microscopy (T-MIM) has greatly extended the capabilities of standard reflection-mode MIM to novel applications, such as the in operando study of nanoscale electro-acoustic devices. As is common for new techniques, systematic design principles for boosting sensitivity and balancing bandwidth are lacking. Here, we show numerically and analytically that the T-MIM signal is proportional to the reflection-mode voltage enhancement factor η of the circuit, as long as the output impedance of the local voltage source is properly treated. We show that this proportionality holds in the currently achievable "weak sampling"regime and beyond, for which we demonstrate a realistic path with commercially available superconducting components and critically coupled impedance matching networks. We demonstrate that for these next-generation designs, the sensitivity is generally maximized at a slightly different frequency from the unloaded S11 resonance, which can be explained by the maximum power transfer theorem.

Microwave impedance microscopy (MIM) is an emerging scanning probe technique that measures the local complex dielectric function using near-field microwave. Although it has made significant impacts in diverse fields, a systematic, quantitative understanding of the signal's dependence on various important design parameters is lacking. Here, we show that for a wide range of MIM implementations, given a complex tip-sample admittance change Δ Y, the MIM signal - the amplified change in the reflected microwave amplitude - is - G · Δ Y / 2 Y 0 · η 2 · V in, where η is the ratio of the microwave voltage at the probe to the incident microwave amplitude, Y0 is the system admittance, and G is the total voltage gain. For linear circuits, η is determined by the circuit design and does not depend on V in. We show that the maximum achievable signal for different designs scales with η 2 or η when limited by input power or sample perturbation, respectively. This universal scaling provides guidance on diverse design goals, including maximizing narrow-band signal for imaging and balancing bandwidth and signal strength for spectroscopy.

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.

Over 50 years ago, Anderson and Blount proposed that ferroelectric-like structural phase transitions may occur in metals, despite the expected screening of the Coulomb interactions that often drive polar transitions. Recently, theoretical treatments have suggested that such transitions require the itinerant electrons be decoupled from the soft transverse optical phonons responsible for polar order. However, this decoupled electron mechanism (DEM) has yet to be experimentally observed. Here we utilize ultrafast spectroscopy to uncover evidence of the DEM in LiOsO_3, the first known band metal to undergo a thermally driven polar phase transition (T_c ≈ 140 K). We demonstrate that intra-band photo-carriers relax by selectively coupling to only a subset of the phonon spectrum, leaving as much as 60% of the lattice heat capacity decoupled. This decoupled heat capacity is shown to be consistent with a previously undetected and partially displacive TO polar mode, indicating the DEM in LiOsO₃.