Microwave impedance microscopy (MIM) is a near-field imaging technique that has been used to visualize the local conductivity of materials with nanoscale resolution across the GHz regime. In recent years, MIM has shown great promise for the investigation of topological states of matter, correlated electronic states, and emergent phenomena in quantum materials. To explore these low-energy phenomena, many of which are only detectable in the milliKelvin regime, we have developed a novel low-temperature MIM incorporated into a dilution refrigerator. This setup, which consists of a tuning-fork-based atomic force microscope with microwave reflectometry capabilities, is capable of reaching temperatures down to 70 mK during imaging and magnetic fields up to 9 T. To test the performance of this microscope, we demonstrate microwave imaging of the conductivity contrast between graphite and silicon dioxide at cryogenic temperatures and discuss the resolution and noise observed in these results. We extend this methodology to visualize edge conduction in Dirac semi-metal cadmium arsenide in the quantum Hall regime.
A key aspect of how the brain learns and enables decision-making processes is through synaptic interactions. Electrical transmission and communication in a network of synapses are modulated by extracellular fields generated by ionic chemical gradients. Emulating such spatial interactions in synthetic networks can be of potential use for neuromorphic learning and the hardware implementation of artificial intelligence. Here, we demonstrate that in a network of hydrogen-doped perovskite nickelate devices, electric bias across a single junction can tune the coupling strength between the neighboring cells. Electrical transport measurements and spatially resolved diffraction and nanoprobe X-ray and scanning microwave impedance spectroscopic studies suggest that graded proton distribution in the inhomogeneous medium of hydrogen-doped nickelate film enables this behavior. We further demonstrate signal integration through the coupling of various junctions.
Electron surface states in solids are typically confined to the outermost atomic layers and, due to surface disorder, have negligible impact on electronic transport. Here, we demonstrate a very different behavior for surface states in graphene. We probe the wavelike character of these states by Fabry-Perot (FP) interferometry and find that, in contrast to theoretical predictions, these states can propagate ballistically over micron-scale distances. This is achieved by embedding a graphene resonator formed by gate-defined p-n junctions within a graphene superconductor-normal-superconductor structure. By combining superconducting Aharanov-Bohm interferometry with Fourier methods, we visualize spatially resolved current flow and image FP resonances due to p-n-p cavity modes. The coherence of the standing-wave edge states is revealed by observing a new family of FP resonances, which coexist with the bulk resonances. The edge resonances have periodicity distinct from that of the bulk states manifest in a repeated spatial redistribution of current on and off the FP resonances. This behavior is accompanied by a modulation of the multiple Andreev reflection amplitude on-and-off resonance, indicating that electrons propagate ballistically in a fully coherent fashion. These results, which were not anticipated by theory, provide a practical route to developing electron analog of optical FP resonators at the graphene edge.
