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This paper begins with a summary of a powerful formalism for the study of electronic states in condensed matter physics called "Gauge Theory of States/Phases of Matter." The chiral anomaly, which plays quite a prominent role in that…
Under general assumptions, we present a low-energy effective action for the quantum Hall state when edges exist. It is shown that the chiral edge current is necessary to make the effective action to be gauge invariant. However the chiral…
Quantized Hall conductance is a generic feature of two dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is…
The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…
Recent experimental progress in condensed matter physics enables the observation of signatures of the parity anomaly in two-dimensional Dirac-like materials. Using effective field theories and analyzing band structures in external…
A two-layer system coupled via tunneling and with different carrier masses in each layer is investigated in the integer quantum Hall regime. Striking deviations of the one-layer Hall conductivity from the usual quantization are found, if…
Quantum anomalous Hall (QAH) effect in magnetic topological insulator (TI) is a novel transport phenomenon in which the Hall resistance reaches the quantum plateau in the absence of external magnetic field. Recently, this exotic effect has…
Quantum anomalous Hall (QAH) effect provides dissipationless chiral channels for spin transport, expected as an outstanding candidate in future low-power quantum computation. The spin-splitting band structure is vital for obtaining QAH…
We reexamine the problem of delocalization of two-dimensional electrons in the presence of random magnetic field. By introducing spatial correlations among random fluxes, a well-defined metal-insulator transition characterized by a…
We consider magnetotransport in high-mobility 2D electron gas in a non-quantizing magnetic field. We employ a weakly chiral network model to test numerically the prediction of the scaling theory that the transition from an Anderson to a…
We report the observation of TEMPERATURE-INDUCED transitions between insulator, metal, and quantum-Hall behaviors for transport coefficients in the very dilute high mobility two-dimensional electron system in silicon. We consider the…
Ferromagnetic topological insulators in the quantum anomalous Hall (QAH) regime host chiral, dissipationless edge states whose propagation direction is determined by the internal magnetization. Under suitable conditions, a strong electrical…
The use of ultra-low temperature cooling and of high hydrostatic pressure techniques has significantly expanded our understanding of the two-dimensional electron gas confined to GaAs/AlGaAs structures. This chapter reviews a selected set of…
Interlayer exchange coupling (IEC) between two magnetic layers sandwiched by a nonmagnetic spacer layer plays a critical role in shaping the magnetic properties of such heterostructures. The quantum anomalous Hall (QAH) effect has been…
Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting…
The quantum anomalous Hall effect (QAHE) is a topological state of matter with a quantized Hall resistance. It has been observed in some two-dimensional insulating materials such as magnetic topological insulator films and twisted bilayer…
The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, non-unitary conformal field theories with logarithmic correlations. The nature and the physical…
The quantum Hall transition is one of the simplest and most studied quantum phase transitions. Nevertheless, the experimental observation of a new phase in this regime, the quantum Hall insulator, still remains a puzzle since the first…
We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the…
In an earlier work, Damle and the author (Phys. Rev. B in press; cond-mat/9705206) demonstrated the central role played by incoherent, inelastic processes in transport near two-dimensional quantum critical points. This paper extends these…