Landau quantization

About: Landau quantization is a research topic. Over the lifetime, 9588 publications have been published within this topic receiving 180530 citations. The topic is also known as: Landau level.

The quantized Hall effect

Abstract: tory since one may come to the conclusion that such a complicated system like a semiconuctor is not useful for very fundamental discoveries. Indeed, most of the experimental data in solid state physics are analyzed on the basis of simplified theories, and very often the properties of a semiconductor device is described by empirical formulas since the microscopic details are too complicated. Up to 1980 nobody expected that there exists an effect like the Quantized Hall Effect, which depends exclusively on fundamental constants and is not affected by irregularitie s in the semiconductor like impurities or interface effects. The discovery of the Quantized Hall Effect (QHE) was the result of systematic measurements on silicon field effect transistors-the most important device in microelectron ics. Such devices are not only important for applications but also for basic research. The pioneering work by Fowler, Fang, Howard and Stiles [l] has shown that new quantum phenomena become visible if the electrons of a conductor are confined within a typical length of 10 nm. Their discoveries opened the field of two-dimension al electron systems which since 1975 is the subject of a conference series [2]. It has been demonstrated that this field is important for the description of nearly all optical and electrical properties of microelectron ic devices. A two-dimensiona l electron gas is absolutely necessary for the observation of the Quantized Hall Effect, and the realization and properties of such a system will be discussed in section 2. In addition to the quantum phenomena connected with the confinement of electrons within a two-dimensional layer, another quantization - the Landau quantization of the electron motion in a strong magnetic field - is essential for the interpretation of the Quantized Hall Effect (section 3). Some experimental results will be summarized in section 4 and the application of the QHE in metrology is the subject of section 5.

Scaling theory of the integer quantum Hall effect

Abstract: A brief review is given of the present understanding of the transitions between integer quantized plateaus of the Hall conductivity in two-dimensional disordered systems in a strong magnetic field. The similarity to continuous thermodynamic phase transitions is emphasized. Results of numerical simulations for non-interacting electrons are presented and compared to experiment. The role of the Coulomb interactions at the integer quantum Hall transitions is studied.

Nearly flatbands with nontrivial topology.

Abstract: We report the theoretical discovery of a class of 2D tight-binding models containing nearly flatbands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Because of the similarity with 2D continuum Landau levels, these topologically nontrivial nearly flatbands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flatband aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.

Theory of Quantum Transport in a Two-Dimensional Electron System under Magnetic Fields. I. Characteristics of Level Broadening and Transport under Strong Fields

Abstract: Characteristics of level broadening and transverse conductivity of a two-dimensional electron system under extremely strong fields have been theoretically investigated in the simplest approximation without the difficulty of divergence, i e. in the so-called damping theoretical one. Those of various cases of short- and long-ranged scatterers have been obtained. To see the dependence on the range explicitly, numerical calculation has been performed for the system with scatterers with the Gaussian potential. Especially in case of short-ranged ones the peak value of the transverse conductivity has been shown to be \((N+1/2)e^{2}/\pi^{2}\hbar\) which depends only on the natural constants and the Landau level index. It has been argued from general point of view that this fact is approximately true without reference to kinds of approximations. Such characteristic of the conductivity was confirmed experimentally, but there still remain some problems as to the absolute value of the level width.

Single-Layer Behavior and Its Breakdown in Twisted Graphene Layers

Abstract: We report high magnetic field scanning tunneling microscopy and Landau level spectroscopy of twisted graphene layers grown by chemical vapor deposition For twist angles exceeding ~3° the low energy carriers exhibit Landau level spectra characteristic of massless Dirac fermions Above 20° the layers effectively decouple and the electronic properties are indistinguishable from those in single-layer graphene, while for smaller angles we observe a slowdown of the carrier velocity which is strongly angle dependent At the smallest angles the spectra are dominated by twist-induced van Hove singularities and the Dirac fermions eventually become localized An unexpected electron-hole asymmetry is observed which is substantially larger than the asymmetry in either single or untwisted bilayer graphene