Resonant Inelastic Light Scattering from Quantum Hall Systems

Pinczuk, A.

doi:10.1002/9783527617258.ch8

Cited by 16 publications

(24 citation statements)

References 100 publications

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“…The latter drastically modifies the electronic spectrum by quantizing it into discrete and highly degenerate Landau levels (LLs). The inter-LL excitations, i.e., the electron excitations from filled to empty LL, are the collective electronic modes [7,8] in any two-dimensional system, and their understanding is fundamental for a variety of quantum Hall effect phenomena [9]. The anticipated effects [10][11][12][13][14] of electron-electron interaction on LL spectrum in graphene have so far been little explored experimentally [2,15].…”

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confidence: 99%

Landau Level Spectroscopy of Electron-Electron Interactions in Graphene

et al. 2015

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We present magneto-Raman scattering studies of electronic inter-Landau level excitations in quasineutral graphene samples with different strengths of Coulomb interaction. The band velocity associated with these excitations is found to depend on the dielectric environment, on the index of Landau level involved, and to vary as a function of the magnetic field. This contradicts the single-particle picture of noninteracting massless Dirac electrons but is accounted for by theory when the effect of electron-electron interaction is taken into account. Raman active, zero-momentum inter-Landau level excitations in graphene are sensitive to electron-electron interactions due to the nonapplicability of the Kohn theorem in this system, with a clearly nonparabolic dispersion relation.

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confidence: 99%

Landau Level Spectroscopy of Electron-Electron Interactions in Graphene

et al. 2015

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“…The integer quantized Hall effect is a generic behavior of two-dimensional electron systems in a strong perpendicular magnetic field [1][2][3][4] . The primary manifestation of the effect is a precise quantization of the Hall conductance σ xy to integer multiples of e 2 /h, with coefficient determined by the electron density.…”

Section: Introduction and Principal Resultsmentioning

confidence: 99%

Edge states of bilayer graphene in the quantum Hall regime

2011

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We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by nonlinear transformations to the spectra of quantum Hall edge-states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a hole-like edge state of one valley and a particle-like state of the other on the same edge, which may or may not cross depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends both on boundary conditions and the energies of the bulk states.

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“…Vortices play interesting roles in various aspects of present-day physics such as vortex matters (vortex lattices) in condensed matters [1,2], quantum Hall effects [3][4][5], various vortex patterns of non-neutral plasma [6][7][8][9] and Bose-Einstein gases [10][11][12][13][14]. Some fundamental properties and applications of vortices in quantum mechanics were examined by many authors [15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…We can, of course, apply the results in scattering processes where injected particles can be treated as individual particles. In the above-mentioned processes where vortices are observed [1][2][3][4][5][6][7][8][9][10][11][12][13][14], however, correlations among constituent particles cannot be ignored. We have to study whether such zero-energy flows appear in many particle systems.…”

Section: Introductionmentioning

confidence: 99%

Zero-Energy Flows and Vortex Patin Quantum Mechanics

Kobayashi

2004

Phys. Scr.

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We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zeroenergy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. We point out three interesting properties of the zero-energy flows; (i) the absolute economy as for the energy consumption, (ii) the infinite variety of the vortex patterns, and (iii) the absolute stability of the vortex patterns .Keywords: Zero-energy solutions, vortex creations and annihilations, quantum mechanics, Gel'fand triplets, * E-mail: kobayash@a.tsukuba-tech.ac.jp IntroductionVortices play interesting roles in various aspects of present-day physics such as vortex matters (vortex lattices) in condensed matters [1,2], quantum Hall effects [3][4][5], various vortex patterns of non-neutral plasma [6][7][8][9] and Bose-Einstein gases [10][11][12][13][14]. Some fundamental properties and applications of vortices in quantum mechanics were examined by many authors [15][16][17][18][19][20][21][22][23].Recently we have proposed a way to investigate vortex patterns in terms of zero-energy solutions of Schrödinger equations in 2-dimensions, which are infinitely degenerate and eigenfunctions in conjugate spaces of Gel'fand triplets (CSGT) [24,25]. It should be noted that the eigenfunctions in CSGT represent scattering states, and thus they are generally not normalizable [26]. Therefore, the probability density (|ψ| 2 ) and the probability current (j = Re[ψ * (−i ∇)ψ]/m) for the eigenfunction (ψ), which are defined in usual Hilbert spaces, cannot be introduced to the eigenfunctions in CSGT. Instead of the probability current, however, the velocity which is defined by v = j/|ψ| 2 can have a well-defined meaning, because the ambiguity due to the normalization of the eigenfunctions disappears in the definition of the velocity. Actually we have shown that many interesting objects used in hydrodynamics such as the complex velocity potential can be introduced in the 2-dimensions of CSGT [27]. We can expect that the hydrodynamical approach is a quite hopeful framework in the investigation of phenomena described in CSGT. One should pay attention to two important facts obtained in the early works [24,25]. One is the fact that the zero-energy solutions are common over the two-dimensional central potentials such that V a (ρ) = −a 2 g a ρ 2(a−1) with ρ = x 2 + y 2 except a = 0 and then similar vortex patters described by the zero-energy solutions appear in all such potentials. Actually zeroenergy solutions for a definite number of a can be transformed to solutions for arbitrary number of a by conformal transformations [24,25]. The oth...

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Resonant Inelastic Light Scattering from Quantum Hall Systems

Cited by 16 publications

References 100 publications

Landau Level Spectroscopy of Electron-Electron Interactions in Graphene

Landau Level Spectroscopy of Electron-Electron Interactions in Graphene

Edge states of bilayer graphene in the quantum Hall regime

Zero-Energy Flows and Vortex Patin Quantum Mechanics

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