Quantum Dots In Magnetic Field Research Articles

Effects of Aharonov–Bohm flux and gap on graphene quantum dots in magnetic field

Effects of Aharonov–Bohm flux and gap on graphene quantum dots in magnetic field

Polarized photoluminescence and g-factor in an inhomogeneous ensemble of quantum dots in magnetic fields

In this work, polarized photoluminescence caused by quasi-equilibrium spin orientation of excitons at Zeeman sublevels in an ensemble of quantum dots of different sizes is studied theoretically. The following unexpected results are found: (i) the splitting of photoluminescence bands in a magnetic field in an ensemble of quantum dots is much larger than the Zeeman splitting of exciton levels in a single dot, (ii) contrary to the Boltzmann distribution the low-energy luminescence band has a lower intensity than the high-energy band, (iii) the sign of the circular polarization of photoluminescence changes along the contour of the bands, (iv) a universal formula for the dependence of the exciton g-factor on the quantum dot size is obtained. All of the above features of the polarized luminescence spectra are explained by variations of the exciton g-factor when its quantization energy changes. The results obtained are applicable not only to ensembles of quantum dots, but also to any ensemble of localized states: excitons in quantum wells under conditions of well-width fluctuations, impurity states in quantum wells, etc.

Density-functional study of electronic structure of quantum dots in high magnetic fields

Density-functional theory is used to study the electronic structure of quantum dots in magnetic field. New series of magic numbers are found for the total angular momentum of electrons. The empirical formula for the plateau width is obtained. The effect of a charged impurity on the electronic structure of a quantum dot has been studied.

Biexciton in 2D parabolic quantum dot in magnetic fields

We theoretically study biexciton, exciton and charged excitons confined in 2D parabolic quantum dots in a magnetic field by using an unrestricted Hatree-Fork method. The energy and binding energy of exciton and biexciton are presented as a function of magnetic field which show their increase with increasing magnetic field, although small. Our results for the case of strong confinement in InAs/GaAs self-assembled quantum dots show that, while the binding energies of both exciton and negatively charged exciton are positive, the binding energies of the biexciton and positively charged exciton are negative indicating that biexcitons in this system are antibinding.

The heat capacity of a semiconductor quantum dot in magnetic fields

The heat capacity of a semiconductor quantum dot in magnetic fields

Fine Structure of Nearly Isotropic Bright Excitons in InP/ZnSe Colloidal Quantum Dots

The fine structure of exciton states in colloidal quantum dots (QDs) results from the compound effect of anisotropy and electron-hole exchange. By means of single-dot photoluminescence spectroscopy, we show that the emission of photoexcited InP/ZnSe QDs originates from radiative recombination of such fine structure exciton states. Depending on the excitation power, we identify a bright exciton doublet, a trion singlet, and a biexciton doublet line that all show pronounced polarization. Fluorescence line narrowing spectra of an ensemble of InP/ZnSe QDs in magnetic fields demonstrate that the bright exciton effectively consists of three states. The Zeeman splitting of these states is well described by an isotropic exciton model, where the fine structure is dominated by electron-hole exchange and shape anisotropy leads to only a minor splitting of the F = 1 triplet. We argue that excitons in InP-based QDs are nearly isotropic because the particular ratio of light and heavy hole masses in InP makes the exciton fine structure insensitive to shape anisotropy.

Electronic spectra and chemical potential of 2-D multi-electron quantum dots in magnetic field: exact multi-pole expansion of coulomb correlation

Two-dimensional superlattices, TMDCs and graphene family exhibit strong coulomb correlations among e–e, e–h, electron-phonon and etc. As the number of electron increases, confining gate voltage and transverse magnetic field are superseded by increasing coulomb interactions (N(N−1)/2 factors) that composes non-trivial Schrödinger equations. Representing such equations in Whittaker-M functions yields a modest alternate formalism, that accommodates integrals of coulomb (exchange) correlations in single-summed, finite and exact Lauricella functions via Chu-Vandermonde identity. For higher carrier density (N = 3, 4, 5, 6, ..), the multipole expansion is incurred as exact and finite-summed coulomb, coulomb-type and dipole-type integrals. Although, fermionic exchange symmetry of many electron systems could be included in terms of various two-electron integrals, for the sake of brevity we have aimed to reproduce experimental results without spin. Signature of interplay among gate voltage, magnetic field, dielectric constant, mass and density of carriers is examined in electronic spectra, magnetization, chemical potential for the systems spanning over wide range of materials (He, BN, GaAs and etc.). Interestingly, chemical potential and addition energy as a function of magnetic field and number of carriers monitor the statistics between strongly degenerate to weakly degenerate composite fermions, coulomb blockade and shell structure of 2-D superlattices. At the most, quadrapole and octapole suffice the convergence.

Binding energies and chemical potential of neutral and charged exciton-complexes of transition metal dichalcogenides/anisotropic 2-D quantum dots in magnetic field by exact multi-pole expansion of coulomb correlations

Anisotropy is inevitable fate of charged excitonic complexes due to difference in dielectric constants, effective masses, charges of carriers, magnetic field, applied gate voltage etc along in-plane and out-of-plane directions of transition metal dichalcogenides (TMDCs-MX2; M = Mo, W; X = S, Se, Te) as well as in anisotropic quantum dots. In the present paper, the multi-dynamic attractive and scattering interactions among neutral and charged exciton-complexes (N-excitonic, N = 2,3,4, ….) amongst the various charge carriers, i.e., e − h, e − e, h − h has been elegantly accounted for by the use of Lauricella functions and the subsequent application of Chu-vandermonde identity. An exact variational treatment for such complex and intertwined interactions in presence of anisotropy has been achieved by employing multi-pole expansion. The result of which emerges as a unique single-summed, finite, exact and absolutely terminating integrals. The calculated binding energies for various N-excitonic systems have been found to be consistent with the previous experimental and computational studies. A discussion of energy spectra, chemical potential (μ) and addition energy (Δμ) are presented. The results thus obtained indicate increase in binding energy and bosonic character of the multi-excitonic complexes with magnetic field. The effects of anisotropy are manifested through the interplay between many-body coulomb interactions resulting in the dissolution of degeneracy of excitonic states.

Addition energy and magnetization of 3-D multicarrier anisotropic quantum dots in magnetic field by exact multi-pole expansion of coulomb correlations

Coulomb interactions replicates in N(N − 1)∕2 terms for interacting 3-D N − e confined quantum dots leading to non-trivial Schrödinger equations. For the systems having N > 3, e − e interaction reciprocating to both lateral (electrical) and transverse (magnetic) confinements in moderate fields causes acute interplay in anisotropic quantum dots. As DFT, Hartree-Fock and other perturbative methods have certain limitations, recasting Schrödinger equations into self-adjoint Whittaker-M functions addresses coulomb (exchange) integrals as simplest, finite and single-summed analytical Lauricella functions (F2) via Chu-Vandermonde identity. In case of higher ′N′, expansion of coulomb correlations in terms of multi-pole expansion facilitates the convergences for bound states upto quadrapole and octopole terms. Although, fermionic exchange symmetry of many electron systems could be included in terms of various two-electron integrals, for the sake of brevity we have aimed to reproduce experimental results without spin. Level clustering/accidential degeneracies manifest on energy level spectra due to competitive role among anisotropic confinement strength, magnetic field, mass of the carrier and dielectric constant of the medium. It triggers orbital induced paramagnetism (T ∼ (0 − 1)K), signature of fractional quantum Hall effect (FQHE) in chemical potential cusps (μ) and formation of different ′shell structures′ in capacitive energy respectively, spanning over wide dielectric range of materials (atomic like quantum dots, ZnO, GaAs and PbSe (Lead Chalcogenide) etc).

The electronic states and magnetization of coupled AlGaAs/GaAs quantum dots in magnetic fields

We present a theoretical study of electronic states and magnetization of two interacting electrons confined in coupled quantum dots (CQDs) presented in a magnetic field. We obtain the eigenenergies of the CQD by solving the relative two-dimensional (2D) Hamiltonian using the combined variational–exact diagonalization method. The dependence of magnetization on temperature, magnetic field strength, confining frequency and barrier height has been investigated. We have shown the singlet–triplet transitions in the ground state of the CQD spectra and the corresponding jumps in the magnetization curves. The comparisons show that our results are in very good agreement with the reported works.

Strongly Correlated Excitons of Regular/Irregular Planar Quantum Dots in Magnetic Field: Size-Extensive Bi- and Triexciton (e-h-e-h and e-e-h/e-h-h) Systems by Multipole Expansion.

Excitons in parabolically confined planar quantum dots with a transverse magnetic field have been studied in various model systems. The correlations between e–h, e–e, and h–h have been incorporated in terms of exact, simply elegant, and absolutely terminating finite summed Lauricella functions which eliminate the secular divergence problem and pave way for a comprehensive understanding of certain exotic phenomena of various two-dimensional regular and irregular quantum dots. A simple yet highly accurate and exact variational wave function in terms of Whittaker-M function extensible to multiexcitonic systems has been propounded. We have also presented a formulation extending the size of the systems to triexcitonic (e–e–h/e–h–h), biexcitonic (e–h–e–h), and multiexcitonic (“N” e–h pair) planar dots by mono-, di-, quadru-, and octopole expansions. As a benchmark, we have examined the energy spectra, level-spacing statistics, heat capacities (Cv at 1 K), and magnetization (T ≈ 0–1 K) of He/SiO2/BN/GaAs model systems for different lateral confinements, magnetic fields, mass ratios of e–h, and dielectric constants (ϵ).

Magnetic Susceptibility of Coupled Double GaAs Quantum Dot in Magnetic Fields

Magnetic Susceptibility of Coupled Double GaAs Quantum Dot in Magnetic Fields

Magnetization of Coupled Double Quantum Dot in Magnetic Fields

Magnetization of Coupled Double Quantum Dot in Magnetic Fields

Multi-excitonic (N=1,2 and 3) quantum dots in magnetic field: Analytical mapping of correlations (exchange) by multipole expansion

The understanding of the physics of exciton, bi-exciton, tri-exciton and the subsequent insight into controlling the properties of mesoscopic systems holds the key to various exotic optical, electrical and magnetic phenomena like superconductivity, Mott insulation, Quantum Hall effect etc. Many of exciton properties are similar to atomic hydrogen that attracts researchers to explore electronic structure of exciton in quantum dots, but nontriviality arises due to coulombic interactions among electrons and holes. We propose an exact integral of coulomb (exchange) correlation in terms of finitely summed Lauricella functions to examine 3-D exciton of harmonic dots confined in zero and non-zero arbitrary magnetic field. The highlight of our work is the use of exact variational solution for coloumbic interaction between the hole and the electron and evaluation of the cross terms arising out of the coupling among centre-of-mass and relative coordinates. We also have extended the size of the system to generalized N-body problem with N=3,4 for tri-exciton (e-e-h/e-h-h) ▪ and biexciton (e-h-e-h) (e-h-e-h) ▪ respectively by multipole expansions. As a probe we have examined level spacing statistics, energy spectra, specific heat (Cv), magnetization and chemical potential (μ) at low temperatures.

Exact e–e (exchange) correlations of 2-D quantum dots in magnetic field: Size extensive [formula omitted]-electron systems via multi-pole expansion

Inclusion of coulomb interaction emerges with the complexity of either convergence of integrals or separation of variables of Schrödinger equations. For an N-electron system, interaction terms grow by N(N-1)/2 factors. Therefore, 2-e system stands as fundamental basic unit for generalized N-e systems. For the first time, we have evaluated e–e correlations in very simple and absolutely terminating finite summed hypergeometric series for 2-D double carrier parabolic quantum dot in both zero and arbitrary non-zero magnetic field (symmetric gauge) and have appraised these integrals in variational methods. The competitive role among confinement strength, magnetic field, mass of the carrier and dielectric constant of the medium on energy level diagram, level-spacing statistics, heat capacities (Cv at 1K) and magnetization (T∼(0–1)K) is studied on systems spanning over wide range of materials (GaAs,Ge,CdS,SiO2 and He, etc). We have also constructed an exact theory for generalized correlated N-e 2-D quantum dots via multi-pole expansion but for the sake of compactness of the article we refrain from data.

Two-Electron Spherical Quantum Dot in a Magnetic Field

We investigate three-dimensional, two-electron quantum dots in an external magnetic field B. Due to mixed spherical and cylindrical symmetry the Schrodinger equation is not completely separable. Highly accurate numerical solutions, for a wide range of B, have been obtained by the expansion of wavefunctions in double-power series and by imposing on the radial functions appropriate boundary conditions. The asymptotic limit of a very strong magnetic field and the 2D approach have been considered. Ground state properties of the two-electron semiconductor quantum dots are investigated using both the 3D and 2D models. Theoretical calculations have been compared with recent experimental results.

AA-stacked bilayer graphene quantum dots in magnetic field**Dedicated to Professor Dr Hachim A Yamani on the occasion of his 70th birthday.

By applying the infinite-mass boundary condition, we analytically calculate the confined states and the corresponding wave functions of AA-stacked bilayer graphene (BLG) quantum dots (QDs) in the presence of an uniform magnetic field B. It is found that the energy spectrum shows two set of levels, which are the double copies of the energy spectrum for single layer graphene, shifted up–down by and , respectively. However, the obtained spectrum exhibits different symmetries between the electron and hole states as well as the intervalley symmetries. It is noticed that, the applied magnetic field breaks all symmetries, except one related to the intervalley electron–hole symmetry, i.e. . Two different regimes of confinement are found: the first one is due to the infinite-mass barrier at weak B and the second is dominated by the magnetic field as long as B is large. We numerically investigated the basics features of the energy spectrum to show the main similarities and differences with respect to monolayer graphene, AB-stacked BLG and semiconductor QDs.

Variational calculations of the heat capacity of a semiconductor quantum dot in magnetic fields

The heat capacity of two interacting electrons confined in a quantum dot presented in a magnetic field had been calculated by solving the relative Hamiltonian using variational method. We had investigated the dependence of the heat capacity on temperature, magnetic field and confining frequency. The singlet triplet transitions in the ground state of the quantum dot spectra and the corresponding jumps in the heat capacity curves had been shown. The comparisons show that our results are in very good agreement with reported works.

Inelastic light and electron scattering in parabolic quantum dots in magnetic field: Implications of generalized Kohn's theorem

We investigate a one-component, quasi–zero-dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron energy loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron energy loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in diverse fields such as quantum computing and medical imaging.

Orbital and spin moments of one-electron states localized on quantum dots in a magnetic field

This paper discusses the behavior of single-electron states localized on quantum dots in an external magnetic field. Such states have a significant size of the electron cloud and can serve as a basis for implementing qubits with optical computation procedures. The orbital and spin “current” induced by a magnetic field in such states is calculated, along with the magnetic moments of these currents. It is shown that the magnetic susceptibility of the states of interest exceeds by several orders of magnitude the values that are characteristic of atomic physics, while the spin moment is determined only by the magnetic splitting factor of the semiconductor.