TL;DR
This paper provides a comprehensive introduction to quantum Hall effects, covering both non-relativistic and relativistic electrons, their quantisation, transport properties, and complex multicomponent systems like graphene.
Contribution
It offers a detailed, pedagogical overview of quantum Hall phenomena, including recent developments in multicomponent systems and graphene, not extensively covered in prior literature.
Findings
Quantisation of kinetic energy in strong magnetic fields
Transport characteristics of integer quantum Hall effect
Basic aspects of fractional quantum Hall effect
Abstract
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief historical overview in chapter 1, we discuss in detail the kinetic-energy quantisation of non-relativistic and the relativistic electrons in a strong magnetic field (chapter 2). Chapter 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in chapter 4. In chapter 5, we briefly discuss several multicomponent quantum Hall systems, namely the quantum Hall ferromagnetism, bilayer systems and graphene that may be viewed as a four-component system.
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