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We study the phase structure and Hall conductance quantization in weakly coupled multi-layer electron systems in the integer quantum Hall regime. We derive an effective field theory and perform a two-loop renormalization group calculation.…
We study the critical properties of the in-plane magnetic field-induced quantum anomalous Hall (QAH) plateau transition in axion insulators. Take even septuple layer film MnBi$_2$Te$_4$ as a concrete example, we find the mirror symmetry…
The mapping between the metal-insulator transition of the quantum Hall system and a superfluid-to-insulator transition is revisited based on a disordered anyon model. The one-parameter scaling of the superfluid-to-insulator transition is…
The nature of a metal-insulator transition tuned by external gates in quantum Hall (QH) systems with point constrictions, as reported in recent experiments of Roddaro et al [1], is examined. We attribute this phenomenon to a splitting of…
We review some elementary aspects of the critical properties of the series of metal-insulator transitions that constitute the integer quantum Hall effect. Numerical work has proven essential in charting out this phenomenon. Without being…
The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility…
We present a new theoretical approach for the integer quantum Hall effect, which is able to describe the inter-plateau transitions as well as the transition to the Hall insulator. We find two regimes (metallic and insulator like) of the top…
The two-dimensional surface of a coupled multilayer integer quantum Hall system consists of an anisotropic chiral metal. This unusual metal is characterized by ballistic motion transverse and diffusive motion parallel (\hat{z}) to the…
We report in this paper results of experimental and theoretical studies of transitions between different integer quantum Hall phases, as well as transition between the insulating phase and quantum Hall phases at high magnetic fields. We…
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator (TI) films. However, the universal…
The quantum anomalous Hall effect refers to the quantization of Hall effect in the absence of applied magnetic field. The quantum anomalous Hall effect is of topological nature and well suited for field-free resistance metrology and…
We study the possible phase transitions between (2+1)-dimensional abelian Chern-Simons theories. We show that they may be described by non-unitary rational conformal field theories with c_eff = 1. As an example we choose the fractional…
The quantum anomalous Hall (QAH) effect holds fundamental importance in topological physics and technological promise for electronics. It is generally believed that the QAH effect can only be realized in insulators. In this Letter, we…
The quantum Hall effect is studied numerically in modulated two-dimensional electron systems in the presence of disorder. Based on the scaling property of the Hall conductivity as well as the localization length, the critical energies where…
For more than a decade it was widely accepted that two-dimensional electrons are insulating at zero temperature and at zero magnetic-field. Experimentally it was demonstrated that, when placed in a strong perpendicular magnetic field, the…
The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states through either sweeping the magnetic field or tuning the carrier density. The recent…
The quantum anomalous Hall effect is a intriguing topological nontrivial phase arising from spontaneous magnetization and spin-orbit coupling. However, the tremendously harsh realizing requirements of the quantum anomalous Hall effects in…
The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are…
Metal--insulator transitions and transitions between different quantum Hall liquids are used to describe the physical ideas forming the basis of quantum phase transitions and the methods of application of theoretical results in processing…
We report a continuous phase transition between quantum-anomalous-Hall and trivial-insulator phases in a magnetic topological insulator upon magnetization rotation. The Hall conductivity transits from one plateau of quantized Hall…