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The plateau-plateau transition in the integer quantum Hall effect is studied in three Hall bars with different widths. The slopes of the Hall resistance as a function of magnetic field follow the scaling power law as expected in the plateau-plateau transition, and saturate at the low temperature limit. Surprisingly, the saturation temperature is irrelevant with the Hall bar size, which suggests that the saturation of the coherence length is intrinsic.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have a range of unique physics properties and could be used in the development of electronics, photonics, spintronics and quantum computing devices. The mechanical exfoliation technique of micro-size TMD flakes has attracted particular interest due to its simplicity and cost effectiveness. However, for most applications, large area and high quality films are preferred. Furthermore, when the thickness of crystalline films is down to the 2D limit (monolayer), exotic properties can be expected due to the quantum confinement and symmetry breaking. In this paper, we have successfully prepared macro-size atomically flat monolayer NbSe2 films on bilayer graphene terminated surface of 6H-SiC(0001) substrates by molecular beam epitaxy (MBE) method. The films exhibit an onset superconducting critical transition temperature above 6 K, 2 times higher than that of mechanical exfoliated NbSe2 flakes. Simultaneously, the transport measurements at high magnetic fields reveal that the parallel characteristic field Bc// is at least 4.5 times higher than the paramagnetic limiting field, consistent with Zeeman-protected Ising superconductivity mechanism. Besides, by ultralow temperature electrical transport measurements, the monolayer NbSe2 film shows the signature of quantum Griffiths singularity when approaching the zero-temperature quantum critical point.

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state, but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state, but also for the design of future topological quantum computation devices.

The behavior of phase coherence is studied in two-dimensional hole gas through the integer quantum Hall plateau-to-plateau transition. From the plateau transition as a function of temperature, scaling properties of multiple transitions are analyzed. Our results are in good agreement with the assumption of the zero-point fluctuations of the coherent holes, and support the intrinsic saturation of the coherence time at low temperature limit. The critical exponent $p$ can also be determined under the scheme of the zero-point fluctuations. The similarity and difference in experimental observations between quantum Griffiths singularity and plateau transition is discussed. The spin-orbit coupling effect's influence on the plateau transition is explored by comparing the results from different transitions.