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“Electronic structure of the valence band in cylindrical strained InP/InGaP quantum dots in an external magnetic field”. Tadic, Peeters FM, Physica. E: Low-dimensional systems and nanostructures
T2 –, 14th International Conference on the Electronic Properties of, Two-Dimensional Systems, July 30-August 03, 2001, Prague, Czech Republic 12, 880 (2002). http://doi.org/10.1016/S1386-9477(01)00445-3
Abstract: The multiband effective-mass model of cylindrical self-assembled quantum dots in a magnetic field normal to the layer of the quantum dots is presented. The strain distribution is computed by the valence force field method. The strain-dependent multiband Hamiltonian is modified into an axially symmetric form, which commutes with the total angular momentum F-2 = fh. where f denotes the total magnetic quantum number. The heavy hole and the light hole parts in the mixed hole state are resolved. It is found that the heavy hole component dominates in the ground states for both f = 1/2 and 3/2. The electronic structure exhibits numerous anticrossings between the hole levels. The Zeeman splitting between the +\f\ and -\f\ states is also computed. (C) 2002 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.221
Times cited: 1
DOI: 10.1016/S1386-9477(01)00445-3
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“Even-odd transition in the Shubnikov-de Haas oscillations in a two-dimensional electron gas subjected to periodic magnetic and electric modulations”. Shi J, Peeters FM, Edmonds KW, Gallagher BL, Physical review : B : condensed matter and materials physics 66, 035328 (2002). http://doi.org/10.1103/PhysRevB.66.035328
Abstract: We investigate low-temperature magnetotransport of high-mobility two-dimensional electron gases subjected to one-dimensional periodic magnetic and electric modulations. Our previous quantum perturbation theory is extended to lower temperatures and the energy broadening due to impurity scattering is incorporated. Numerical calculations are made for situations where several Landau bands overlap. We find that the Shubnikov-de Haas (SdH) oscillations are dominated by collisional resistance. The amplitudes of the SdH oscillations are strongly modulated and the positions of the SdH minima switch between even and odd Landau-level filling factors, in the resistance both parallel and perpendicular to the one-dimensional modulation. This is a consequence of the internal structure (i.e., smeared out van Hove singularities) of overlapping Landau bands. Our theoretical results are in good agreement with recent experiments.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 32
DOI: 10.1103/PhysRevB.66.035328
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“Exciton trapping in a periodically modulated magnetic field”. Freire JAK, Freire VN, Farias GA, Peeters FM, Brazilian journal of physics 32, 310 (2002). http://doi.org/10.1590/S0103-97332002000200016
Abstract: The behavior of excitons in spatially modulated magnetic fields is described taking into account the exciton spin contribution. The results show that the exciton trapping in periodic magnetic fields is possible and dependent on the modulation profile.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 0.732
Times cited: 1
DOI: 10.1590/S0103-97332002000200016
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“Fractional and negative flux penetration in mesoscopic superconducting disks”. Peeters FM, Schweigert VA, Baelus BJ, Physica: C : superconductivity 369, 158 (2002). http://doi.org/10.1016/S0921-4534(01)01234-5
Abstract: The one vortex entry in a superconducting disk is investigated within the non-linear Ginzburg-Landau theory near the first critical field. We find that in mesoscopic superconducting disks the magnetic flux enters with fractions of one flux quantum phi(0) = ch/2e. For disks with a very smooth surface it is possible to drive the Meissner state so far into the metastable region that at the vortex entry a net amount of flux is expelled from the superconductor. We show that the magnetic field for flux entry is very sensitive to indentations of the disk surface and only weakly to bulges. On the other hand the flux exit field is practically insensitive to such geometrical surface defects. Our results are in agreement with recent experimental findings. (C) 2001 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.404
Times cited: 11
DOI: 10.1016/S0921-4534(01)01234-5
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“Geometry induced defects in a confined Wigner lattice”. Peeters FM, Kong M, Partoens B, , 192 (2002)
Keywords: P1 Proceeding; Condensed Matter Theory (CMT)
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“Giant vortices in small mesoscopic disks : an approximate description”. Yampolskii SV, Peeters FM, Physica: C : superconductivity 369, 347 (2002). http://doi.org/10.1016/S0921-4534(01)01274-6
Abstract: We present an approximate description of the giant vortex state in a thin mesoscopic superconducting disk within the phenomenological Ginzburg-Landau approach. Analytical asymptotic expressions for the energies of the states with fixed vorticity are obtained when a small magnetic flux is accumulated in the disk. The spectrum of the lowest Landau levels of such a disk is also discussed. (C) 2001 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.404
DOI: 10.1016/S0921-4534(01)01274-6
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“Joule heat in a two-dimensional electron gas exposed to a normal non-homogeneous magnetic field of a 'chess' configuration”. Badalyan SM, Peeters FM, Physica: B : condensed matter 316, 216 (2002). http://doi.org/10.1016/S0921-4526(02)00462-3
Abstract: We have calculated analytically the spatial distribution of the electric field and current density, and obtained the Joule heat generation rate in a two-dimensional electron gas (2DEG) subjected to a non-homogeneous magnetic field of a 'chess' configuration. The generation of the Joule heat from the 2DEG is mainly concentrated near the singular corners of each 'chess' field and tends to zero in other corners. (C) 2002 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.386
DOI: 10.1016/S0921-4526(02)00462-3
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“Magnetic confinement of electrons into quantum wires and dots on a liquid helium surface”. Freire JAK, Studart N, Peeters FM, Farias GA, Freire VN, Physica. E: Low-dimensional systems and nanostructures
T2 –, 14th International Conference on the Electronic Properties of, Two-Dimensional Systems, July 30-August 03, 2001, Prague, Czech Republic 12, 946 (2002). http://doi.org/10.1016/S1386-9477(01)00416-7
Abstract: We investigate the possibility to laterally confine surface electrons on a liquid helium surface by inserting magnetic discs and stripes which generate nonhomogeneous magnetic field profiles. (C) 2002 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.221
Times cited: 2
DOI: 10.1016/S1386-9477(01)00416-7
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“Magnetic coupling between mesoscopic superconducting rings”. Baelus BJ, Yampolskii SV, Peeters FM, Physica: C : superconductivity 369, 366 (2002). http://doi.org/10.1016/S0921-4534(01)01278-3
Abstract: Using the nonlinear Ginzburg-Landau theory we investigated the dependence of the magnetic coupling between two concentric mesoscopic superconducting rings on their thickness. The size of this magnetic coupling increases with the thickness of the rings. (C) 2001 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.404
Times cited: 1
DOI: 10.1016/S0921-4534(01)01278-3
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“Magnetic pinning of vortices in a superconducting film: the (anti)vortex-magnetic dipole interaction energy in the London approximation”. Milošević, MV, Yampolskii SV, Peeters FM, Physical review : B : condensed matter and materials physics 66, 174519 (2002). http://doi.org/10.1103/PhysRevB.66.174519
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 76
DOI: 10.1103/PhysRevB.66.174519
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“Magneto-exciton in single and coupled type II quantum dots”. Janssens KL, Partoens B, Peeters FM, Physica status solidi: A: applied research 190, 571 (2002). http://doi.org/10.1002/1521-396X(200204)190:2<571::AID-PSSA571>3.0.CO;2-K
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
DOI: 10.1002/1521-396X(200204)190:2<571::AID-PSSA571>3.0.CO;2-K
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“Molecular terms and optical transitions of C60n+/- molecular ions”. Nikolaev AV, Michel KH, AIP conference proceedings
T2 –, 16th International Winterschool on Electronic Properties of Novel, Materials, MAR 02-09, 2002, KIRCHBERG, AUSTRIA , 417 (2002)
Abstract: We have studied the molecular energy terms of the hole configurations (h(u)(+))(m), m=2,3,4,5 of C-60(m+) cations and the electronic configurations (t(1u))(n) n=2,3,4, as well as (t(1u))(n-1)t(1g) of the C-60(n-) anions. The lowest terms (within an energy span of 0.03 eV) for C-60(2+) are three triplets T-3(1g), (3)G(g), T-3(2g) and for C-60(3+) are three quartets T-4(1u), (4)G(u), T-4(2u), which favor Jahn-Teller distortions. For the ground state of C-60(2-) we find a triplet T-3(1g) in agreement with Hund's rules. Our method takes into account intramolecular direct and exchange multipolar Coulomb interactions.
Keywords: P1 Proceeding; Condensed Matter Theory (CMT)
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“Multi-vortex states of a thin superconducting disk in a step-like external magnetic field”. Milošević, MV, Yampolskii SV, Peeters FM, Physica: C : superconductivity 369, 343 (2002). http://doi.org/10.1016/S0921-4534(01)01273-4
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.404
Times cited: 5
DOI: 10.1016/S0921-4534(01)01273-4
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“Quantum-confined magneto-Stark effect in diluted magnetic semiconductor coupled quantum wells”. Chang K, Xia JB, Wu HB, Feng SL, Peeters FM, Applied physics letters 80, 1788 (2002). http://doi.org/10.1063/1.1459491
Abstract: The magneto-Stark effect in a diluted magnetic semiconductor (DMS) coupled quantum well (CQW) induced by an in-plane magnetic field is investigate theoretically. Unlike the usual electro-Stark effects, in a DMS CQW the Lorenz force leads to a spatially separated exciton. The in-plane magnetic field can shift the ground state of the magnetoexciton from a zero in-plane center of mass (CM)/momentum to a finite CM momentum, and render the ground state of magnetoexciton stable against radiative recombination due to momentum conservation. (C) 2002 American Institute of Physics.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.411
Times cited: 8
DOI: 10.1063/1.1459491
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“Quenching of the Hall effect in localised high magnetic field regions”. Novoselov KS, Geim AK, Dubonos SV, Cornelissens YG, Peeters FM, Maan JC, Physica. E: Low-dimensional systems and nanostructures 12, 244 (2002). http://doi.org/10.1016/S1386-9477(01)00364-2
Abstract: We report the suppression of the Hall effect in a mesoscopic Hall cross with a strong magnetic field only in the centre and vanishingly small outside, The local magnetic field is produced by placing Dy pillar on top of a structure with a high-mobility two-dimensional electron gas. The effect is found to be due to a sharp increase of the number of back-scattered and quasi-localised electron orbits. The possibility of localising electrons inside the magnetic inhomogeneity region is discussed. (C) 2002 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.221
Times cited: 3
DOI: 10.1016/S1386-9477(01)00364-2
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“Response function of a Hall magnetosensor in the diffusive regime”. Cornelissens YG, Peeters FM, Journal of applied physics 92, 2006 (2002). http://doi.org/10.1063/1.1487909
Abstract: Two-dimensional electron gas systems patterned into micrometer Hall bars can be used as Hall magnetosensors. In this way, ballistic Hall probes have already been studied and used successfully. Here, the response function of a Hall sensor is determined in the diffusive regime, which allows this device to be used as a magnetosensor for the determination of inhomogeneous magnetic field distributions. Furthermore, the influence of the geometry of the Hall bar on this response function, such as circular corners and asymmetry in the probes, is also investigated and appears to be non-negligible. (C) 2002 American Institute of Physics.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.068
Times cited: 24
DOI: 10.1063/1.1487909
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“Scattering of ballistic electrons at a mesoscopic spot of strong magnetic field”. Novoselov KS, Geim AK, Dubonos SV, Cornelissens YG, Peeters FM, Maan JC, Physical review : B : condensed matter and materials physics 65, 233312 (2002). http://doi.org/10.1103/PhysRevB.65.233312
Abstract: We report quenching of the Hall effect with increasing magnetic field confined in a micron-sized spot. Such fields were created by placing tall ferromagnetic pillars on top of a two-dimensional electron gas, which allowed us to achieve the field strength up to 0.4 T under the pillars in the absence of external field. The quenching is accompanied by an anomalous increase in resistance and occurs when the cyclotron diameter matches the size of the magnetic spot. The results are explained by a rapid increase in the number of electrons that are scattered or quasilocalized by the magnetic region.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 38
DOI: 10.1103/PhysRevB.65.233312
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“Single and coupled type II quantum dots in magnetic and electric fields”. Janssens KL, Partoens B, Peeters FM, Physicalia magazine 24, 211 (2002)
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
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“Single and vertically coupled type-II quantum dots in a perpendicular magnetic field: exciton ground-state properties”. Janssens KL, Partoens B, Peeters FM, Physical review : B : condensed matter and materials physics 66, 075314 (2002). http://doi.org/10.1103/PhysRevB.66.075314
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 38
DOI: 10.1103/PhysRevB.66.075314
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“Spin-current modulation and square-wave transmission through periodically stubbed electron waveguides”. Wang XF, Vasilopoulos P, Peeters FM, Physical review : B : condensed matter and materials physics 65, 165217 (2002). http://doi.org/10.1103/PhysRevB.65.165217
Abstract: Ballistic spin transport through waveguides, with symmetric or asymmetric double stubs attached to them periodically, is studied systematically in the presence of a weak spin-orbit coupling that makes the electrons precess. By an appropriate choice of the waveguide length and of the stub parameters injected spin-polarized electrons can be blocked completely and the transmission shows a periodic and nearly-square-type behavior, with values 1 and 0, with wide gaps when only one mode is allowed to propagate in the waveguide. A similar behavior is possible for a certain range of the stub parameters even when two modes can propagate in the waveguide and the conductance is doubled. Such a structure is a good candidate for establishing a realistic spin transistor. A further modulation of the spin current can be achieved by inserting defects in a finite-number stub superlattice. Finite-temperature effects on the spin conductance are also considered.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 112
DOI: 10.1103/PhysRevB.65.165217
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“Spin-engineered quantum dots”. Fleurov V, Ivanov VA, Peeters FM, Vagner ID, Physica. E: Low-dimensional systems and nanostructures 14, 361 (2002). http://doi.org/10.1016/S1386-9477(01)00487-8
Abstract: Spatially nonhomogeneously spin polarized nuclei are proposed as a new mechanism to monitor electron states in a nanostructure, or as a means to create and, if necessary, reshape such nanostructures in the course of the experiment. We found that a polarization of nuclear spins may lift the spin polarization of the electron states in a nanostructure and, if sufficiently strong, leads to a polarization of the electron spins. Polarized nuclear spins may form an energy landscape capable of binding electrons with energy up to several meV and the localization radius > 100 Angstrom. (C) 2002 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Engineering sciences. Technology; Condensed Matter Theory (CMT)
Impact Factor: 2.221
Times cited: 12
DOI: 10.1016/S1386-9477(01)00487-8
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“Stark shift in single and vertically coupled type-I and type-II quantum dots”. Janssens KL, Partoens B, Peeters FM, Physical review : B : condensed matter and materials physics 65, 233301 (2002). http://doi.org/10.1103/PhysRevB.65.233301
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 43
DOI: 10.1103/PhysRevB.65.233301
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“Stationary-phase slip state in quasi-one-dimensional rings”. Vodolazov DY, Baelus BJ, Peeters FM, Physical review : B : condensed matter and materials physics 66, 054531 (2002). http://doi.org/10.1103/PhysRevB.66.054531
Abstract: The nonuniform superconducting state in a ring in which the order parameter vanishing at one point is studied. This state is characterized by a jump of the phase by pi at the point where the order parameter becomes zero. In uniform rings such a state is a saddle-point state and consequently unstable. However, for nonuniform rings with, e.g., variations of geometrical or physical parameters or with attached wires this state can be stabilized and may be realized experimentally.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 29
DOI: 10.1103/PhysRevB.66.054531
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“Strain and band edges in single and coupled cylindrical InAs/GaAs and InP/InGaP self-assembled quantum dots”. Tadić, M, Peeters FM, Janssens KL, Korkusinski M, Hawrylak P, Journal of applied physics 92, 5819 (2002). http://doi.org/10.1063/1.1510167
Abstract: A comparative study is made of the strain distribution in cylindrical InAs/GaAs and InP/InGaP self-assembled quantum dots as obtained from isotropic elasticity theory, the anisotropic continuum mechanical model, and from atomistic calculations. For the isotropic case, the recently proposed approach [J. H. Davies, J. Appl. Phys. 84, 1358 (1998)] is used, while the finite-element method, the valence force field method, and Stillinger-Weber potentials are employed to calculate the strain in anisotropic structures. We found that all four methods result in strain distributions of similar shapes, but with notable quantitative differences inside the dot and near the disk-matrix boundary. The variations of the diagonal strains with the height of the quantum dot, with fixed radius, as calculated from all models, are almost linear. Furthermore, the energies of the band edges in the two types of quantum dots are extracted from the multiband effective-mass theory by inserting the strain distributions as obtained by the four models. We demonstrated that all strain models produce effective potentials for the heavy and light holes which agree very well inside the dot. A negligible anisotropy of all normal strains in the (x,y) plane is found, which, providing the axial symmetry of the kinetic part of the multiband effective-mass Hamiltonian, justifies the use of the axial approximation. Strain propagation along the vertical direction is also considered with the aim to study the influence of strain on the electron coupling in stacks of quantum dots. We found that the interaction between the strain fields of the individual quantum dots makes the effective quantum wells for the electrons in the conduction band shallower, thereby counteracting the quantum mechanical coupling. (C) 2002 American Institute of Physics.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.068
Times cited: 73
DOI: 10.1063/1.1510167
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“Structural transitions in a classical two-dimensional molecule system”. Ferreira WP, Farias GA, Carmona HA, Peeters FM, Solid state communications 122, 665 (2002). http://doi.org/10.1016/S0038-1098(02)00157-6
Abstract: The ground state of a classical two-dimensional (2D) system with a finite number of charge particles, trapped by two positive impurity charges localized at a distance (z(0)) from the. 2D plane and separated from each other by a distance chi(p) are obtained. The impurities are allowed to carry more than one positive charge. This classical system can form a 2D-like classical molecule that exhibits structural transitions and spontaneous symmetry breaking as function of the separation between the positive charges before it transforms into two 2D-like classical atoms. We also observe structural transitions as a function of the dielectric constant of the substrate which supports the charged particles, in addition to broken symmetry states and unbinding of particles. (C) 2002 Elsevier Science Ltd. All rights reserved.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.554
Times cited: 3
DOI: 10.1016/S0038-1098(02)00157-6
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“Superconducting properties of mesoscopic cylinders with enhanced surface superconductivity”. Baelus BJ, Yampolskii SV, Peeters FM, Montevecchi E, Indekeu JO, Physical review : B : condensed matter and materials physics 65, 024510 (2002). http://doi.org/10.1103/PhysRevB.65.024510
Abstract: The superconducting state of an infinitely long superconducting cylinder surrounded by a medium which enhances its superconductivity near the boundary is studied within the nonlinear Ginzburg-Landau theory. This enhancement can be due to the proximity of another superconductor or due to surface treatment. Quantities such as the free energy, the magnetization and the Cooper-pair density are calculated. Phase diagrams are obtained to investigate how the critical field and the critical temperature depend on this surface enhancement for different values of the Ginzburg-Landau parameter kappa. Increasing the superconductivity near the surface leads to higher critical fields and critical temperatures. For small cylinder diameters only giant vortex states nucleate, while for larger cylinders multivortices can nucleate. The stability of these multivortex states also depends on the surface enhancement. For type-I superconductors we found the remarkable result that for a range of values of the surface extrapolation length the superconductor can transit from the Meissner state into superconducting states with vorticity L > 1. Such a behavior is not found for the case of large kappa, i.e., type-II superconductivity,
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 13
DOI: 10.1103/PhysRevB.65.024510
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“The pinning effect in a parabolic quantum dot”. Mukhopadhyay S, Peeters FM, Journal of physics : condensed matter 14, 8005 (2002). http://doi.org/10.1088/0953-8984/14/34/319
Abstract: Using improved Wigner-Brillouin perturbation theory we study resonant electron-phonon interaction in a semiconductor quantum dot. We predict pinning of the excited energy levels to the ground state level plus one optical phonon as a function of the strength of the confinement potential. This effect should be observable through optical spectroscopic measurements.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.649
Times cited: 4
DOI: 10.1088/0953-8984/14/34/319
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“Theoretical model for the structural phase transition at the metal-insulator transition in polymerized KC60”. Verberck B, Nikolaev AV, Michel KH, Physical Review B 66, 165425 (2002). http://doi.org/10.1103/PhysRevB.66.165425
Abstract: The recently discovered structural transition in polymerized KC60 at about 50 K results in a doubling of the unit cell volume and accompanies the metal-insulator transition. Here we show that the ((a) over right arrow+(c) over right arrow,(b) over right arrow,(a) over right arrow-(c) over right arrow) superstructure results from small orientational charge density waves along the polymer chains and concomitant displacements of the surrounding K+ ions. The effect is specific for the space group Pmnn of KC60 and is absent in RbC60 and CsC60 (space group I2/m). The mechanism is relevant for the metal-insulator transition.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 10
DOI: 10.1103/PhysRevB.66.165425
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“Theory of trions in quantum wells”. Riva C, Peeters FM, Varga K, Physica. E: Low-dimensional systems and nanostructures
T2 –, 14th International Conference on the Electronic Properties of, Two-Dimensional Systems, JUL 30-AUG 03, 2001, PRAGUE, CZECH REPUBLIC 12, 543 (2002). http://doi.org/10.1016/S1386-9477(01)00484-2
Abstract: We investigate the energy levels of the negatively and positively charged excitons (also called trions) in a 200 Angstrom wide GaAs quantum well in the presence of a perpendicular magnetic field. A comparison is made with the experimental results of Glasberg et al. (Phys. Rev. B. 59 (1999) R10 425) and of Yusa et al. (cond-mat/0103505). (C) 2002 Elsevier Science B.V. All rights reserved.
Keywords: A1 Journal article; Engineering sciences. Technology; Condensed Matter Theory (CMT)
Impact Factor: 2.221
Times cited: 2
DOI: 10.1016/S1386-9477(01)00484-2
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“Transition between ground state and metastable states in classical two-dimensional atoms”. Kong M, Partoens B, Peeters FM, Physical review : E : statistical physics, plasmas, fluids, and related interdisciplinary topics 65, 046602 (2002). http://doi.org/10.1103/PhysRevE.65.046602
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.366
Times cited: 51
DOI: 10.1103/PhysRevE.65.046602
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