Topic

# Landau quantization

About: Landau quantization is a(n) research topic. Over the lifetime, 9588 publication(s) have been published within this topic receiving 180530 citation(s). The topic is also known as: Landau level.

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TL;DR: A two-dimensional condensed-matter lattice model is presented which exhibits a nonzero quantization of the Hall conductance in the absence of an external magnetic field, and exhibits the so-called "parity anomaly" of (2+1)-dimensional field theories.

Abstract: A two-dimensional condensed-matter lattice model is presented which exhibits a nonzero quantization of the Hall conductance ${\ensuremath{\sigma}}^{\mathrm{xy}}$ in the absence of an external magnetic field. Massless fermions without spectral doubling occur at critical values of the model parameters, and exhibit the so-called "parity anomaly" of (2+1)-dimensional field theories.

3,679 citations

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10 Oct 2003-

Abstract: Introduction.- Band Structure of Semiconductors.- The Extended Kane Model.- Electron and Hole States in Quasi 2D Systems.- Origin of Spin-Orbit Coupling Effects.- Inversion Asymmetry Induced Spin Splitting.- Anisotropic Zeeman Splitting in Quasi 2D Systems.- Landau Levels and Cyclotron Resonance.- Anomalous Magneto-Oscillations.- Conclusions.- Notation and Symbols.- Quasi Degenerate Perturbation Theory.- The Extended Kane Model: Tables.- Band Structure Parameters.

1,763 citations

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Abstract: There are two known distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems1,2, and the other is its relativistic counterpart observed in graphene, where charge carriers mimic Dirac fermions characterized by Berry’s phase π, which results in shifted positions of the Hall plateaus3,4,5,6,7,8,9. Here we report a third type of the integer quantum Hall effect. Charge carriers in bilayer graphene have a parabolic energy spectrum but are chiral and show Berry’s phase 2π affecting their quantum dynamics. The Landau quantization of these fermions results in plateaus in Hall conductivity at standard integer positions, but the last (zero-level) plateau is missing. The zero-level anomaly is accompanied by metallic conductivity in the limit of low concentrations and high magnetic fields, in stark contrast to the conventional, insulating behaviour in this regime. The revealed chiral fermions have no known analogues and present an intriguing case for quantum-mechanical studies.

1,582 citations

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TL;DR: An effective two-dimensional Hamiltonian is derived to describe the low-energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase 2pi.

Abstract: We derive an effective two-dimensional Hamiltonian to describe the low-energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase $2\ensuremath{\pi}$. Its high-magnetic-field Landau-level spectrum consists of almost equidistant groups of fourfold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall conductivity dependence on carrier density, ${\ensuremath{\sigma}}_{xy}(N)$, which exhibits plateaus at integer values of $4{e}^{2}/h$ and has a double $8{e}^{2}/h$ step between the hole and electron gases across zero density, in contrast to $(4n+2){e}^{2}/h$ sequencing in a monolayer.

1,498 citations

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TL;DR: Experimental spectroscopic measurements by scanning tunneling microscopy of highly strained nanobubbles that form when graphene is grown on a platinum surface open the door to both the study of charge carriers in previously inaccessible high magnetic field regimes and deliberate mechanical control over electronic structure in graphene or so-called “strain engineering.”

Abstract: Recent theoretical proposals suggest that strain can be used to engineer graphene electronic states through the creation of a pseudo-magnetic field. This effect is unique to graphene because of its massless Dirac fermion-like band structure and particular lattice symmetry (C3v). Here, we present experimental spectroscopic measurements by scanning tunneling microscopy of highly strained nanobubbles that form when graphene is grown on a platinum (111) surface. The nanobubbles exhibit Landau levels that form in the presence of strain-induced pseudo-magnetic fields greater than 300 tesla. This demonstration of enormous pseudo-magnetic fields opens the door to both the study of charge carriers in previously inaccessible high magnetic field regimes and deliberate mechanical control over electronic structure in graphene or so-called "strain engineering."

1,234 citations