Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field

Hoang, Ngoc-Tram D.; Nguyen, Duy-Anh P.; Hoang, Van-Hung; Le, Van-Hoang

doi:10.1016/j.physb.2016.04.038

Cited by 9 publications

(12 citation statements)

References 17 publications

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“…Present results agree with those of Szmytkowski [13] and not with those derived by other authors by means of the Levi-Civita transformation of the coordinates and the expression of the resulting two-dimensional Hamiltonian operator in terms of suitable creation-annihilation operators [10][11][12]. We have no doubt that their weak-field expansions do not agree with the actual ones.…”

Section: Discussionsupporting

confidence: 62%

“…The two-dimensional hydrogen-like atom in a uniform magnetic field perpendicular to the atomic plane has received considerable attention as a model for excitons in thin materials such as nano-scale multilayer semiconductor systems. The Schrödinger equation is separable in polar coordinates and has been solved approximately in many different ways [1][2][3][4][5][6][7][8][9][10][11][12][13]. Here we are interested in the application of perturbation theory that provides approximate solutions in terms of power series of the field strength that are suitable in the weak-field limit [3,8,[10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

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Two-dimensional hydrogen-like atom in a uniform magnetic field: Large-order perturbation theory

Fernández

2018

Eur. Phys. J. Plus

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The well known hypervirial perturbation method (HPM) based on hypervirial relations and the Hellmann-Feynman theorem is suitable for the calculation of perturbation corrections of large order for the twodimensional hydrogen-like atom in a uniform magnetic field. We show analytical results in terms of the quantum numbers and large order corrections for particular states. This approach appears to be simpler and more efficient than the recently proposed one based on Green functions. *

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Section: Discussionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Two-dimensional hydrogen-like atom in a uniform magnetic field: Large-order perturbation theory

Fernández

2018

Eur. Phys. J. Plus

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“…Properties of model two-dimensional hydrogenic systems immersed in a magnetic field have been investigated for several decades within the frameworks of nonrelativistic and relativistic [32][33][34][35][36][37][38][39][40][41][42][43] quantum mechanics. Besides of being interesting from a purely theoretical point of view, results of such studies are also important for understanding various aspects of physics of lowdimensional semiconductors [1][2][3][6][7][8]10,12,15,18,26] and of graphene [44][45][46][47][48][49][50][51]. The subject is still far from being exhausted, and further research in this area, especially the one based on the use of analytical methods, is certainly demanded.…”

Section: Introductionmentioning

confidence: 99%

Relativistic two-dimensional hydrogen-like atom in a weak magnetic field

Szmytkowski

2019

Annals of Physics

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A two-dimensional (2D) hydrogen-like atom with a relativistic Dirac electron, placed in a weak, static, uniform magnetic field perpendicular to the atomic plane, is considered. Closed forms of the first-and second-order Zeeman corrections to energy levels are calculated analytically, within the framework of the Rayleigh-Schrödinger perturbation theory, for an arbitrary electronic bound state. The second-order calculations are carried out with the use of the Sturmian expansion of the two-dimensional generalized radial Dirac-Coulomb Green function derived in the paper. It is found that, in contrast to the case of the three-dimensional atom [P. Stefańska, Phys. Rev. A 92 (2015) 032504], in two spatial dimensions atomic magnetizabilities (magnetic susceptibilities) are expressible in terms of elementary algebraic functions of a nuclear charge and electron quantum numbers. The problem considered here is related to the Coulomb impurity problem for graphene in a weak magnetic field.

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“…Sivalertporn et al used the wave functions of the electrons and holes as a complete set of functions for a Fourier‐like expansion to compute exciton states in the low‐dimensional system. Analytic solutions have also been obtained . For instance, González and Domínguez analyzed excitonic states proposing an exact solution by replacing the electron‐hole Coulomb interaction by a projective operator .…”

Section: Introductionmentioning

confidence: 99%

Exciton binding energy in coupled double zinc blende GaN/InGaN quantum well

Rojas-Briseño

Miranda-Pedraza

Martı́nez-Orozco

2016

Phys. Status Solidi B

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In this work, the study of the 1s‐like exciton states and binding energy is presented for coupled double zinc blende GaN/InGaN quantum wells. The effective mass approximation and a variational procedure are the key theoretical tools used. The significant role of the position‐dependent effective mass is highlighted. It is found that the correct inclusion of position‐dependent masses is the cause of a noticeable difference in exciton energies with respect to the use of constant effective mass. In addition, the influence of the interaction of electrons and holes with the central barrier, and the effect of its size are particularly discussed.

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Highly accurate analytical energy of a two-dimensional exciton in a constant magnetic field

Cited by 9 publications

References 17 publications

Two-dimensional hydrogen-like atom in a uniform magnetic field: Large-order perturbation theory

Two-dimensional hydrogen-like atom in a uniform magnetic field: Large-order perturbation theory

Relativistic two-dimensional hydrogen-like atom in a weak magnetic field

Exciton binding energy in coupled double zinc blende GaN/InGaN quantum well

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