Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots

Genkin, Michael; Lindroth, Eva

doi:10.1103/physrevb.81.125315

Cited by 32 publications

(26 citation statements)

References 41 publications

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“…In the next sections, we shall apply the result of theorem 2 to study the possible quasi-exact analytic solutions for the d-dimension Schrödinger equation (3) for unconstrained and constrained Coulomb plus harmonic oscillator potential (4). We shall also apply AIM, theorem 1, to obtain accurate approximations for arbitrary potential parameters, again, for the unconstrained and constrained d-dimensional Schrödinger equation (3).…”

Section: The Asymptotic Iteration Methods and Some Related Resultsmentioning

confidence: 99%

Soft and hard confinement of a two-electron quantum system

2014

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A model physical problem is studied in which a system of two electrons is subject either to soft confinement by means of attractive oscillator potentials or by entrapment within an impenetrable spherical box of finite radius R. When hard confinement is present the oscillators can be switched off. Exact analytical solutions are found for special parameter sets, and highly accurate numerical solutions (18 decimal places) are obtained for general cases. Some interesting degeneracy questions are discussed at length.

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Section: The Asymptotic Iteration Methods and Some Related Resultsmentioning

confidence: 99%

Soft and hard confinement of a two-electron quantum system

2014

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“…Comprehensive reviews are now available on this topic. Theoretically, different types of confinement models can be realized for different physical situations, for example, atoms under plasma environment, endohedrally confined atoms and molecules in fullerene cages, impurities in quantum dots or nano crystals, matter under extreme pressure in zeolite sieves, or in the walls of nuclear reactors, and so forth. Moreover, the confined atom models assume contemporary significance in understanding the cores of Jovian planets such as Jupiter and Saturn .…”

Section: Introductionmentioning

confidence: 99%

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Saha

Bhattacharyya²,

Mukherjee³

2016

Int J of Quantum Chemistry

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A detailed analysis on the effect of spherical impenetrable confinement on the structural properties of two-electron ions in S2 states has been performed. The energy values of 1sns [n5224] ( 3 S e ) states of helium-like ions (Z5125) are estimated within the framework of Ritz variational method using explicitly correlated Hylleraas-type basis sets. The correlated wave functions used here are consistent with the finite boundary conditions due to spherical confinement. A comparative study between the singlet and triplet states originating from a particular electronic configuration shows incidental degeneracy and the subsequent level-crossing phenomena. The thermodynamic pressure felt by the ion inside the sphere pushes the energy levels toward continuum. Critical pressures for the transition to strong confinement regime (where the singly excited two-electron energy levels cross the corresponding one-electron threshold) as well as for the complete destabilization are also estimated.correlation, pressure confinement, two-electron atom, variational method | I N T R O D U C T I O NStudies on the subject of confined atomic systems have started soon after the advent of quantum mechanics. In recent years, a paradigm shift in the facility for doing controlled experiment on confined atom and modern high-speed computational resources open up a new horizon for this subject. The modifications of the structural and spectral properties of the atom or the molecule depending on the number and degree of confining parameters is the interesting aspect of the problem. Comprehensive reviews [1][2][3] are now available on this topic. Theoretically, different types of confinement models can be realized for different physical situations, for example, atoms under plasma environment, [4,5] endohedrally confined atoms and molecules in fullerene cages, [6] impurities in quantum dots or nano crystals, [7,8] matter under extreme pressure in zeolite sieves, [9] or in the walls of nuclear reactors, [10] and so forth. Moreover, the confined atom models assume contemporary significance in understanding the cores of Jovian planets such as Jupiter and Saturn. [11] Nonspherical confinement models [12][13][14][15] are also assumed to deal with important quantum mechanical problems. Vast applicability of the outcomes from such studies in different branches of science and technology makes the subject a topic of immense interest in the recent times. [16][17][18] Hydrogen atom confined in impenetrable spherical cavity was first studied by Michels et al. [19] to model the effects of pressure on its energy and polarizability. Subsequently, many workers [20][21][22][23][24][25][26] have addressed this problem from different angles to develop a comprehensive understanding about such confined systems. Helium atom confined by such spherical cavity is a much complicated numerical problem as compared to the hydrogen-like ions for obvious reasons. For ions having two or more electrons, the effect of electron correlation plays an important role in the str...

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“…It is also imperative to limit the number of electrons -or, in other words, to specify the quantum numbers n, l, and m -while computing the optical (or magneto-optical) absorption in the system [see, e.g., Eqs. (28) or (30)]. This is equivalent to truncating the ∞ × ∞ matrix in the band structure computation in solid state physics by limiting, for example, the number of plane waves.…”

Section: Illustrative Examplesmentioning

confidence: 99%

Magneto-optical absorption in semiconducting spherical quantum dots: Influence of the dot-size, confining potential, and magnetic field

Kushwaha

2014

AIP Advances

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Semiconducting quantum dots -more fancifully dubbed artificial atoms -are quasi-zero dimensional, tiny, manmade systems with charge carriers completely confined in all three dimensions. The scientific quest behind the synthesis of quantum dots is to create and control future electronic and optical nanostructures engineered through tailoring size, shape, and composition. The complete confinement -or the lack of any degree of freedom for the electrons (and/or holes) -in quantum dots limits the exploration of spatially localized elementary excitations such as plasmons to direct rather than reciprocal space. Here we embark on a thorough investigation of the magnetooptical absorption in semiconducting spherical quantum dots characterized by a confining harmonic potential and an applied magnetic field in the symmetric gauge. This is done within the framework of Bohm-Pines' randomphase approximation that enables us to derive and discuss the full Dyson equation that takes proper account of the Coulomb interactions. As an application of our theoretical strategy, we compute various single-particle and many-particle phenomena such as the Fock-Darwin spectrum; Fermi energy; magneto-optical transitions; probability distribution; and the magneto-optical absorption in the quantum dots. It is observed that the role of an applied magnetic field on the absorption spectrum is comparable to that of a confining potential. Increasing (decreasing) the strength of the magnetic field or the confining potential is found to be analogous to shrinking (expanding) the size of the quantum dots: resulting into a blue (red) shift in the absorption spectrum. The Fermi energy diminishes with both increasing magnetic-field and dot-size; and exhibits saw-tooth-like oscillations at large values of field or dot-size. Unlike laterally confined quantum dots, both (upper and lower) magneto-optical transitions survive even in the extreme instances. However, the intra-Landau level transitions are seen to be forbidden. The spherical quantum dots have an edge over the strictly two-dimensional quantum dots in that the additional (magnetic) quantum number makes the physics richer (but complex). A deeper grasp of the Coulomb blockade, quantum coherence, and entanglement can lead to a better insight into promising applications involving lasers, detectors, storage devices, and quantum computing.

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Effects of screened Coulomb impurities on autoionizing two-electron resonances in spherical quantum dots

Cited by 32 publications

References 41 publications

Soft and hard confinement of a two-electron quantum system

Soft and hard confinement of a two-electron quantum system

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Magneto-optical absorption in semiconducting spherical quantum dots: Influence of the dot-size, confining potential, and magnetic field

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