This thesis is composed of three projects including the AC magnetic susceptibility study of high-temperature superconductor YBa$2$Cu$3$O, the ionic-liquid gating study of the Mott insulator Sr$2$IrO$4$, and the single-electron study of quantum dot device with self-assembled nanocrystal PbS. Chapter 1 covers a general introduction to all three projects. The basic background and the motivation for each project are presented.

Project I is covered in Chapter 2, Chapter 3, and Chapter 4. The first part of Chapter 2 is a theoretical introduction to the Bardeen–Cooper–Schrieffer theory of superconductivity with its main conclusions presented. This chapter builds a basis for the use of high pressure technique to YBa$2$Cu$3$O in the later chapters. The rest of Chapter 2 reviews the work in the study of high-temperature superconductors, especially on YBa$2$Cu$3$O, on both experiments and theories and the possible applications of high-temperature superconductors. Chapter 3 introduces the YBa$2$Cu$3$O sample preparation process and the characterisation. A dry cryomagnetic equipment was employed for the measurement. The results and the discussion are presented in Chapter 4.

Project II is described in Chapter 5, Chapter 6, and Chapter 7. Chapter 5 firstly introduces the background knowledge of the gated material SrTiO$3$ and the technical details of the ionic-liquid gating technique. Then the sample growth and the characterisation are presented. The fabrication process of Sr$2$IrO$4$ and SrTiO$3$ (material for a control experiment) are described in Chapter 6. Chapter 7 covers the measurement and the result of the fabricated devices and related discussion.

Project III ranges from Chapter 8, and Chapter 9. A literature review of quantum-dot devices and self-assembled nanocrystals is presented in Chapter 8. The experimental design of this nanocrystal quantum dot device is also included. Following it, the fabrication process of quantum-dot devices and the techniques used for fabrication are introduced in the start of Chapter 9. Chapter 9 also gives a description of the probe-station for measurements. The results and discussion of the measurements are covered in the last section of Chapter 9.

Chapter 10 summarises and concludes the three projects stated above and gives some suggestions about the directions for future work.