On the direct insulator-quantum Hall transition in two-dimensional electron systems in the vicinity of nanoscaled scatterers

Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi_{2}Te_{4}

In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators MnBi_{2}Te_{4}. Nevertheless, whether the nonzero Chern number (C≠0) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed C=2 phase [Deng et al., Science 367, 895 (2020)SCIEAS0036-807510.1126/science.aax8156]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered MnBi_{2}Te_{4}. Rather good consistency between the experimental and numerical results confirms that the bulk states are localized in the absence of a magnetic field and a QAH edge state emerges with C=1. However, under a strong magnetic field, the lowest Landau band formed with the localized bulk states, survives disorder, together with the QAH edge state, leading to a C=2 phase. Eventually, we present a phase diagram of a disordered MnBi_{2}Te_{4} which indicates more coexistence states of QAH and QH to be verified by future experiments.

Dirac fermion heating, current scaling, and direct insulator-quantum Hall transition in multilayer epitaxial graphene

We have performed magnetotransport measurements on multilayer epitaxial graphene. By increasing the driving current I through our graphene devices while keeping the bath temperature fixed, we are able to study Dirac fermion heating and current scaling in such devices. Using zero-field resistivity as a self thermometer, we are able to determine the effective Dirac fermion temperature (TDF) at various driving currents. At zero field, it is found that TDF ∝ I≈1/2. Such results are consistent with electron heating in conventional two-dimensional systems in the plateau-plateau transition regime. With increasing magnetic field B, we observe an I-independent point in the measured longitudinal resistivity ρxx which is equivalent to the direct insulator-quantum Hall (I-QH) transition characterized by a temperature-independent point in ρxx. Together with recent experimental evidence for direct I-QH transition, our new data suggest that such a transition is a universal effect in graphene, albeit further studies are required to obtain a thorough understanding of such an effect.

Insulating to relativistic quantum Hall transition in disordered graphene

Quasi-particle excitations in graphene exhibit a unique behavior concerning two key phenomena of mesoscopic physics: electron localization and the quantum Hall effect. A direct transition between these two states has been found in disordered two-dimensional electron gases at low magnetic field. It has been suggested that it is a quantum phase transition, but the nature of the transition is still debated. Despite the large number of works studying either the localization or the quantum Hall regime in graphene, such a transition has not been investigated for Dirac fermions. Here we discuss measurements on low-mobility graphene where the localized state at low magnetic fields and a quantum Hall state at higher fields are observed. We find that the system undergoes a direct transition from the insulating to the Hall conductor regime. Remarkably, the transverse magneto-conductance shows a temperature independent crossing point, pointing to the existence of a genuine quantum phase transition.

Experimental evidence for direct insulator-quantum Hall transition in multi-layer graphene

We have performed magnetotransport measurements on a multi-layer graphene flake. At the crossing magnetic field Bc, an approximately temperature-independent point in the measured longitudinal resistivity ρxx, which is ascribed to the direct insulator-quantum Hall (I-QH) transition, is observed. By analyzing the amplitudes of the magnetoresistivity oscillations, we are able to measure the quantum mobility μq of our device. It is found that at the direct I-QH transition, μqBc ≈ 0.37 which is considerably smaller than 1. In contrast, at Bc, ρxx is close to the Hall resistivity ρxy, i.e., the classical mobility μBc is ≈ 1. Therefore, our results suggest that different mobilities need to be introduced for the direct I-QH transition observed in multi-layered graphene. Combined with existing experimental results obtained in various material systems, our data obtained on graphene suggest that the direct I-QH transition is a universal effect in 2D.

Direct measurement of the spin gaps in a gated GaAs two-dimensional electron gas

We have performed magnetotransport measurements on gated GaAs two-dimensional electron gases in which electrons are confined in a layer of the nanoscale. From the slopes of a pair of spin-split Landau levels (LLs) in the energy-magnetic field plane, we can perform direct measurements of the spin gap for different LLs. The measured g-factor g is greatly enhanced over its bulk value in GaAs (0.44) due to electron-electron (e-e) interactions. Our results suggest that both the spin gap and g determined from conventional activation energy studies can be very different from those obtained by direct measurements.