Lifshitz tails for alloy-type models in a constant magnetic field

Klopp, Frédéric

doi:10.1088/1751-8113/43/47/474029

Cited by 6 publications

(23 citation statements)

References 8 publications

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“…IV, where we compare the results with the results in Ref. 19. We then investigate the energy dependence on the collapse of the axes within the framework of Palmer and study the trion wave functions and their dependence on the dimension of the system.…”

Section: Introductionmentioning

confidence: 78%

“…We found that the fractional D dimensional model provided accurate predictions of the trion binding energy on the surface of a cylinder. 19,20 Other authors have demonstrated that this model also predicts exciton binding energies in quantum wells and carbon nanotubes very accurately. [12][13][14][15][16]21 Thus, the model is applicable to a wide variety of systems.…”

Section: Introductionmentioning

confidence: 89%

“…Two years later, F. H. Stillinger gave a more detailed description of the mathematical foundation of the model. 18 We have recently reported on the binding energy of charged excitons (trions) in fractional D dimensional space 19 using the model proposed by Herrick and Stillinger. In the calculations we approximated the Hamiltonian by first removing the centerof-mass motion, expressing the Hamiltonian of relative motion in Hylleraas coordinates and finally neglecting the angle dependence of the kinetic operator. We found that the fractional D dimensional model provided accurate predictions of the trion binding energy on the surface of a cylinder.…”

Section: Introductionmentioning

confidence: 99%

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Variational quantum Monte Carlo study of charged excitons in fractional dimensional space

et al. 2011

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In this article we study excitons and trions in fractional dimensional spaces using the model suggested by C. Palmer [J. Phys. A: Math. Gen. 37, 6987 (2004)] through variational quantum Monte Carlo. We present a direct approach for estimating the exciton binding energy and discuss the von Neumann rejection-and Metropolis sampling methods. A simple variational estimate of trions is presented which shows good agreement with previous calculations done within the fractional dimensional model presented by D. R. Herrick and F. H. Stillinger [Phys. Rev. A 11, 42 (1975) and J. Math. Phys. 18, 1224Phys. 18, (1977]. We explain the spatial physics of the positive and negative trions by investigating angular and inter-atomic distances. We then examine the wave function and explain the differences between the positive and negative trions with heavy holes. As applications of the fractional dimensional model we study three systems: First we apply the model to estimate the energy of the hydrogen molecular ion H + 2 . Then we estimate trion binding energies in GaAs-based quantum wells and we demonstrate a good agreement with other theoretical work as well as experimentally observed binding energies. Finally, we apply the results to carbon nanotubes. We find good agreement with recently observed binding energies of the positively charged trion.

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Section: Introductionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Variational quantum Monte Carlo study of charged excitons in fractional dimensional space

et al. 2011

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“…The behaviour (1.9) is known as Lifshitz tails (for more details, see part IV.9.A of [19]) and the exponent −d/2 is called the Lifshitz exponent of the operator. The principal results known on Lifshitz tails are mainly shown for Schrödinger operators, in both continuous and discrete cases (see [7,8,11,14,18,22] and others) and for Schrödinger operators with magnetic fields (see [12,15] ).…”

Section: A Particular Modelmentioning

confidence: 99%

Lifshitz Tails for Continuous Matrix-Valued Anderson Models

Boumaza

Najar

2015

J Stat Phys

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This paper is devoted to the study of Lifshitz tails for a continuous matrix-valued Anderson-type model H ω acting on L 2 (R d ) ⊗ C D , for arbitrary d ≥ 1 and D ≥ 1.We prove that the integrated density of states of H ω has a Lifshitz behavior at the bottom of the spectrum. We obtain a Lifshitz exponent equal to −d/2 and this exponent is independent of D. It shows that the behaviour of the integrated density of states at the bottom of the spectrum of a quasi-d-dimensional Anderson model is the same as its behaviour for a d-dimensional Anderson model. * boumaza@math.univ-paris13.fr † hatem.najar@ipeim.rnu.tn; Research supported by CMCU project 09/G-15-04.

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“…See [33,40,44,53,63], etc. for random alloy-type models, [2,12,13,19,20,27,38,43,51,70], etc. for random Landau Hamiltonians and [42,57], etc.…”

Section: Introductionmentioning

confidence: 99%

Existence, uniqueness and anisotropic-decay-caused Lifshitz tails of the integrated density of surface states for random surface models

Shen

2014

Random Operators and Stochastic Equations

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The current paper is devoted to the study of existence, uniqueness and Lifshitz tails of the integrated density of surface states (IDSS) for Schrödinger operators with alloy type random surface potentials. We prove the existence and uniqueness of the IDSS for negative energies, which is de ned as the thermodynamic limit of the normalized eigenvalue counting functions of localized operators on strips with sections being special cuboids. Under the additional assumption that the single-site impurity potential decays anisotropically, we also prove that the IDSS for negative energies exhibits Lifshitz tails near the bottom of the almost sure spectrum in the following three regimes: the quantum regime, the quantum-classical/classical-quantum regime and the classical regime. We point out that the quantum-classical/classical-quantum regime is new for random surface models.

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Lifshitz tails for alloy-type models in a constant magnetic field

Cited by 6 publications

References 8 publications

Variational quantum Monte Carlo study of charged excitons in fractional dimensional space

Variational quantum Monte Carlo study of charged excitons in fractional dimensional space

Lifshitz Tails for Continuous Matrix-Valued Anderson Models

Existence, uniqueness and anisotropic-decay-caused Lifshitz tails of the integrated density of surface states for random surface models

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