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Quantum Hall Effects
TL;DR: In this paper, an introduction to quantum Hall effects both for non-relativistic and relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and electrons in graphene is given.
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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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Citations
Quantum Phase Transitions
TL;DR: In this paper, the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems is discussed.
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Electronic properties of graphene in a strong magnetic field
TL;DR: In this paper, the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field are reviewed, and the role of electron-electron interactions both in the weak coupling limit, where the electron-hole excitations are determined by collective modes, and in the strong coupling regime of partially filled relativistic Landau levels, where exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states.
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Incompressibility Estimates for the Laughlin Phase
TL;DR: In this paper, the authors consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level and obtain estimates indicating that there is a universal bound on the maximum local density of these states in the limit of large particle number.
Phase transitions in hexagonal, graphene-like lattice sheets and nanotubes under the influence of external conditions
TL;DR: In this article, the authors considered a class of (2+1)D schematic models with four-fermion interactions that are effectively used in studying condensed-matter systems with planar crystal structure, and especially graphene.
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Rigidity of the Laughlin liquid
TL;DR: In this article, the authors consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor $1/\ell$ and an analytic function of the N variables.
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