Quantum Hall Effect at Finite Temperatures

These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The interaction physics in the extreme quantum limit which is responsible for the fractional quantum Hall effect is discussed at length and from an elementary point of view.

We theoretically consider disorder and temperature effects on the integer quantum Hall effect (IQHE) using a variety of distinct and complementary analytical and numerical techniques. In particular, we address simple, physical, and experimentally relevant questions: How does disorder and/or temperature affect the IQHE plateau width? Does the plateau width increase or decrease with disorder and/or temperature? What happens to the peak in the longitudinal conductance with incre...

We report on numerical studies into the interplay of disorder and electron-electron interactions within the integer quantum Hall regime, where the presence of a strong magnetic field and two-dimensional confinement of the electronic system profoundly affects thermodynamic and transport properties. We emphasise the behaviour of the electronic compressibility, the local density of states, and the Kubo conductivity. Our treatment of the electron-electron interactions relies on t...

A short review paper for the quantum anomalous Hall effect. A substantially extended one is published as Adv. Phys. 64, 227 (2015).

Recent developments in the scaling theory of the integer quantum Hall effect are discussed. In particular, the influence of electron-electron interactions on the critical behavior are studied. It is further argued that recent experiments on the disappearance of the quantum Hall effect at low magnetic fields support rather than disprove the scaling theory, when interpreted properly.

We study quantum Hall systems (mainly the integer case) at finite temperatures and show that there is a novel temperature dependence even for a pure system, thanks to the `anomalous' nature of generators of translation. The deviation of Hall conductivity from its zero temperature value is controlled by a parameter $T_0 =\pi \rho /m^\ast N$ which is sample specific and hence the universality of quantization is lost at finite temperatures.

The local electron temperature distribution is calculated considering a two dimensional electron system in the integer quantum Hall regime in presence of disorder and uniform perpendicular magnetic fields. We solve thermal-hydrodynamical equations to obtain the spatial distribution of the local electron temperature in the linear-response regime. It is observed that, the variations of electron temperature exhibit an antisymmetry regarding the center of the sample in accordance...

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 disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered system...

The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. In recent years, quantum anomalous Hall effect has been proposed theoretically and realized experimentally. In this review article, we provide a systematic overview of the theoretica...

We numerically investigate how electron-electron interactions influence the transport properties of disordered electrons in two dimensions. Our study is based on the quantum Coulomb glass model appropriately generalized to include the spin degrees of freedom. In order to obtain the low-energy properties of this model we employ the Hartree-Fock based diagonalization, an efficient numerical method similar to the configuration interaction approach in quantum chemistry. We calcul...