Two-dimensional electron gas has various novel properties. This kind of electronic system like two-dimensional semiconducting transition metal dichalcogenides (TMDCs) and graphene are discovered with novel physical phenomena like valley Hall effect, Ising superconductivity and circular dichroism etc. In this thesis, the negative capacitance and inverse compressibility was studied on atomically thin molybdenum disulfide (MoS₂) based capacitance devices. And another technique to detect the quantum capacitance so called capacitance bridge was developed in our experiment through studying the graphene capacitance under large perpendicular magnetic field in cryogenic system.

Introduction was to illustrate the basic lattice structure and electronic structure for both of our experimental mate...[ Read more ]

Two-dimensional electron gas has various novel properties. This kind of electronic system like two-dimensional semiconducting transition metal dichalcogenides (TMDCs) and graphene are discovered with novel physical phenomena like valley Hall effect, Ising superconductivity and circular dichroism etc. In this thesis, the negative capacitance and inverse compressibility was studied on atomically thin molybdenum disulfide (MoS₂) based capacitance devices. And another technique to detect the quantum capacitance so called capacitance bridge was developed in our experiment through studying the graphene capacitance under large perpendicular magnetic field in cryogenic system.

Introduction was to illustrate the basic lattice structure and electronic structure for both of our experimental materials. Electronic structure includes the energy dispersion and the density of states. Meanwhile several typical experiments were given to prove the existence of strong electron-electron interaction and negative compressibility in two-dimensional electron systems. In the end of the introduction, a brief explanation about Hartree-Fock approximation was described and showed how dimension will affect the exchange energy in electron system then induce such kind of negative capacitance.

Some basic experiment and characteristic methods were given in chapter 2 and 3. To conduct the experiments, high quality of BN-materials-BN structure samples were fabricated by the try transfer method.

In chapter 4, the negative capacitance effect which is induced by strong e-e interaction is focused. Our data showed how frequency and chemical potential will affect this effect. Then the penetration field data was shown and I gave my own suggest on the odd data.

The last chapter shows the basic principle of capacitance bridge measurement. Then the 4-fold degeneracy of LL=0 Landau level was observed both by precise LCR meter and our homemade capacitance bridge.