Development and applications of microwave impedance microscopy for imaging emergent properties in quantum materials

Near-field scanning microwave microscopy (NSMM) detects local physical properties of materials through electromagnetic interaction between the tip and the sample at a length scale much smaller than the freespace wavelength of the microwave radiation. However, previous implementations of NSMM have suffered from poor resolutions, low sensitivity, and unreliable tip-sample contact conditions. In this dissertation, I will first briefly review the prior research of NSMM (Chapter 1) and then naturally move on to the main theme — the basic principles and technical details of the recently developed microwave impedance microscope (MIM) (Chapter 2). I will present the development of MIM instrumentation including quantitative measurement with tuning-fork-based probes, broadband impedance microcopy, and implementation in cryogenic environment (Chapter 3), which are utilized in research described in the following chapters. The application of MIM will be demonstrated by a number of scientific studies in two general categories, emergent phenomena at ferroelectric domain walls and electrical inhomogeneity in nanodevices. Chapter 4 describes the discovery of low-energy structural dynamics of ferroelectric domain walls in hexagonal rare-earth manganites (h-RMnO₃) by broadband impedance microscopy. Chapter 5 includes direct visualization of sketched conductive nanostructures at the LaAlO₃/SrTiO₃ heterostructure and nanoscale conductance evolution in ion-gel-gated oxide transistors, demonstrating the capability of MIM to image buried structures. I will conclude the dissertation with a short summary and outlook for the future.