Research Projects

Modern quantum condensed matter physics is driven by two fundamental concepts: topology and strong correlations. A topological phase of matter is characterized by the quantization of a few physical quantities, whose values are robust against local perturbation. For example, the quantum Hall (QH) effect and the quantum anomalous Hall (QAH) effect are the topological phases, characterized by a quantized Hall conductance. In contrast, a strongly correlated state is determined by the local interactions between electrons, giving rise to unconventional transport and energy landscape. For example, a Mott insulator is an insulating state emerges due to the strong Coulomb interaction. These two concepts (strong correlation and topology) combine in the recent revolutionary physics platform of two-dimensional (2D) materials. More interesting phenomena occur when these 2D materials are stacked together in a homo-bilayer or hetero-bilayer structures with a relative angle (twist) between them. For example, gate-tunable strongly correlated insulating states and superconductivity emerge in twisted bilayer graphene devices with a twist angle of ~1⁰. In transition metal dichalcogenides (TMDCs), a hetero-bilayer formed of MoTe2 and WSe2 exhibits an electrically tunable transition from a Mott insulating phase to a metal at 0 ° twist angle, while at a relative 60 ° twist angle, it exhibits a transition from a Mott insulating phase to a QAH state. Furthermore, integer and fractional Chern insulators, integer and fractional (IQAH and FQAH) insulators, and magnetic correlated states with gate-tunable moiré structure emerge in the case of the homo-bilayer structure of twisted MoTe2. More recently, IQAH and FQAH states have also been observed in pentalayer graphene devices. This extremely nontrivial combination of topology and electronic correlations in a 2D material opens a gateway to studying complicated physical models, such as extended Hubbard models, previously mainly accessed through engineered quantum systems, such as cold atoms. While these transitions were observed in transport measurements, the information obtained in such measurements is limited and usually does not tell the whole story. While transport measurements are useful in the initial identification of the phases, measurements of thermodynamic quantities, such as electronic compressibility, offer direct access to the electron-electron interaction strength, correlations, and energy gap. Although transport measurements provide some estimates of the gap size, the true intrinsic thermodynamic gap is masked due to the presence of disorder and various scattering mechanisms. Furthermore, thermodynamic measurements provide information about the pair-correlation functions that can be calculated theoretically directly. Therefore, we propose a project titled “Development of cryogenic charge sensors for probing thermodynamic properties of emergent electronic phases in novel quantum materials”. In this project, we plan to develop two kinds of charge sensors: (a) Single electron transistor (SET) quantum charge sensor on the tip of diameter ~30-100 nm, capable of highly sensitive charge detection at nanoscale. (b) A graphene-based van der Waals charge sensor, which will be separated by a thin hexagonal boron nitride (hBN) spacer from the two-dimensional sample of interest and can provide the global average thermodynamic response. Using these charge sensors, we aim to measure the thermodynamic quantities, such as electronic compressibility, chemical potential, and entropy of the emergent phases in novel quantum materials. The few listed examples are: (1) Measurement of thermodynamic energy gap, chemical potential, and entropy of integer and fractional quantum anomalous Hall (QAH) states in pentalyer graphene and twisted MoTe2 samples. (2) Thermodynamic sensing of generalized Wigner states in twisted TMDCs systems. (3) Imaging of the local Hall potential and current distribution in QAH states.