On a Degenerate Parabolic Problem in Holder Spaces

In this paper, we study some degenerate parabolic equation with Cauchy-Dirichlet boundary conditions. This problem is considered in little Holder spaces. The optimal regularity of the solution v is obtained and is specified in terms of those of the second member when some conditions upon the Holder exponent with respect to the degeneracy are satisfied. The proofs mainly use the sum theory of linear operators with or without density of domains and the results of smoothness obtained in the study of some abstract linear differential equations of elliptic type.

Polaronic correction to the first excited electronic energy level in an anisotropic semiconductor quantum dot

Within the framework of second-order Rayleigh-Schrodinger perturbation theory, the polaronic correction to the first excited state energy of an electron in an quantum dot with anisotropic parabolic confinements is presented. Compared with isotropic confinements, anisotropic confinements will make the degeneracy of the excited states to be totally or partly lifted. On the basis of a three-dimensional Frohlich's Hamiltonian with anisotropic confinements, the first excited state properties in two-dimensional quantum dots as well as quantum wells and wires can also be easily obtained by taking special limits. Calculations show that the first excited polaronic effect can be considerable in small quantum dots.

Raman spectroscopic investigation of pure and ytterbium-doped rare earth silicate crystals

Raman spectroscopy was used to study the molecular structure of a series of selected rare earth (RE) silicate crystals including Y2SiO5 (YSO), LU2SiO5 (LSO), (Lu0.5Y0.5)(2)SiO5 (LYSO) and their ytterbium-doped samples. Raman spectra show resolved bands below 500 cm(-1) region assigned to the modes of SiO4 and oxygen vibrations. Multiple bands indicate the nonequivalence of the RE-O bonds and the lifting of the degeneracy of the RE ion vibration. Low intensity bands below 500 cm(-1) are an indication of impurities. The (SiO4)(4-) tetrahedra are characterized by bands near 200 cm(-1) which show a separation of the components of nu(4) and nu(2), in the 500-700 cm(-1) region which are attributed to the distorting bending vibration and in the 880-1000 cm(-1) region which are attributed to the symmetric and antisymmetric stretching vibrational modes. The majority of the bands in the 300-610 cm(-1) region of Re2SiO5 were found to arise from vibrations involving both Si and RE ions, indicating that there is considerable mixing of Si displacements with Si-O bending modes and RE-0 stretching modes. The Raman spectra of RE silicate crystals were analyzed in terms of the molecular structure of the crystals, which enabled separation of the bands attributed to distinct vibrational units. Copyright (C) 2007 John Wiley & Sons, Ltd.

Electronic structure of a hydrogenic acceptor impurity in semiconductor nano-structures

The electronic structure and binding energy of a hydrogenic acceptor impurity in 2, 1, and 0-dimensional semiconductor nano-structures (i.e. quantum well (QW), quantum well wire (QWW), and quantum dot (QD)) are studied in the framework of effective-mass envelope-function theory. The results show that (1) the energy levels monotonically decrease as the quantum confinement sizes increase; (2) the impurity energy levels decrease more slowly for QWWs and QDs as their sizes increase than for QWs; (3) the changes of the acceptor binding energies are very complex as the quantum confinement size increases; (4) the binding energies monotonically decrease as the acceptor moves away from the nano-structures' center; (5) as the symmetry decreases, the degeneracy is lifted, and the first binding energy level in the QD splits into two branches. Our calculated results are useful for the application of semiconductor nano-structures in electronic and photoelectric devices.

High Polarization Single Mode Photonic Crystal Microlaser

Generally, dipole mode is a doubly degenerate mode. Theoretical calculations have indicated that the single dipole mode of two-dimensional photonic crystal single point defect cavity shows high polarization property. We present a structure with elongated lattice, which only supports a single y-dipole mode. With this structure we can eliminate the degeneracy, control the lasing action of the cavity and demonstrate the high polarization property of the single dipole mode. In our experiment, the polarization extinction ratio of the y-dipole mode is as high as 51 1.

Symmetry and optical transition rule for low-dimensional semiconductor system with spin-orbit interaction and magnetic field

Starting from effective mass Hamiltonian, we systematically investigate the symmetry of low-dimensional structures with spin-orbit interaction and transverse magnetic field. The position-dependent potentials are assumed to be space symmetric, which is ever-present in theory and experiment research. By group theory, we analyze degeneracy in different cases. Spin-orbit interaction makes the transition between Zeeman sub-levels possible, which is originally forbidden within dipole approximation. However, a transition rule given in this paper for the first time shows that the transition between some levels is forbidden for space symmetric potentials. (C) 2009 Elsevier Ltd. All rights reserved.

Binding energy of a hydrogenic donor impurity in a rectangular parallelepiped-shaped quantum dot: Quantum confinement and Stark effects

We calculate the binding energy of a hydrogenic donor impurity in a rectangular parallelepiped-shaped quantum dot (QD) in the framework of effective-mass envelope-function theory using the plane wave basis. The variation of the binding energy with edge length, position of the impurity, and external electric field is studied in detail. A finite potential model is adopted in our calculations. Compared with the infinite potential model [C. I. Mendoza , Phys. Rev. B 71, 075330 (2005)], the following results are found: (1) if the impurity is located in the interior of the QD, our results give a smaller binding energy than the infinite potential model; (2) the binding energies are more sensitively dependent on the applied electric field in the finite potential model; (3) the infinite potential model cannot give correct results for a small QD edge length for any location of the impurity in the QD; (4) some degeneracy is lifted when the dot is no longer cubic. (C) 2007 American Institute of Physics.

Energy spectra of two-electron two-dimensional quantum dots confined by elliptical and bowl-like potentials

The laterally confining potential of quantum dots (QDs) fabricated in semiconductor heterostructures is approximated by an elliptical two-dimensional harmonic-oscillator well or a bowl-like circular well. The energy spectrum of two interacting electrons in these potentials is calculated in the effective-mass approximation as a function of dot size and characteristic frequency of the confining potential by the exact diagonalization method. Energy level crossover is displayed according to the ratio of the characteristic frequencies of the elliptical confinement potential along the y axis and that along the x axis. Investigating the rovibrational spectrum with pair-correlation function and conditional probability distribution, we could see the violation of circular symmetry. However, there are still some symmetries left in the elliptical QDs. When the QDs are confined by a "bowl-like" potential, the removal of the degeneracy in the energy levels of QDs is found. The distribution of energy levels is different for the different heights of the barriers. (C) 2003 American Institute of Physics.

Single dipole mode photonic crystal laser on InGaAsP/InP QW waveguide slab - art. no. 698436

Single point defect microcavity possesses only the degenerate dipole modes under certain photonic crystal structure parameters. By deforming lattice structure, the degeneracy of the dipole modes has been broken. Theoretical simulation shows the large splitting of 65nm between the splitted x-mode and y-mode, approximate to the luminescent gain spectrum, which benefits for the single mode lasing. Experimentally the single dipole mode lasing, y-mode, is achieved in the deformed microcavity.

Temperature-dependent modulation characteristics for 1.3 mu m InAs/GaAs quantum dot lasers

Temperature-dependent modulation characteristics of 1.3 mu m InAs/GaAs quantum dot (QD) lasers under small signals have been carefully studied at various bias currents. Based on experimental observations, it is found that the modulation bandwidth significantly increases when excited state (ES) lasing emerges at high temperature. This is attributed to additional photons emitted by ES lasing which contribute to the modulation response. A rate equation model including two discrete electron energy levels and the level of wetting layer has been used to investigate the temperature-dependent dynamic behavior of the QD lasers. Numerical investigations confirm that the significant jump for the small signal modulation response is indeed caused by ES photons. Furthermore, we identify how the electron occupation probabilities of the two discrete energy levels can influence the photon density of different states and finally the modulation rate. Both experiments and numerical analysis show that the modulation bandwidth of QD lasers at high temperature can be increased by injecting more carriers into the ES that has larger electron state degeneracy and faster carrier's relaxation time than the ground state.

Kondo Effect in Carbon Nanotube Quantum Dots with Spin-Orbit Coupling

Motivated by recent experimental observation of spin-orbit coupling in carbon nanotube quantum dots [F. Kuemmeth , Nature (London) 452, 448 (2008)], we investigate in detail its influence on the Kondo effect. The spin-orbit coupling intrinsically lifts out the fourfold degeneracy of a single electron in the dot, thereby breaking the SU(4) symmetry and splitting the Kondo resonance even at zero magnetic field. When the field is applied, the Kondo resonance further splits and exhibits fine multipeak structures resulting from the interplay of spin-orbit coupling and the Zeeman effect. A microscopic cotunneling process for each peak can be uniquely identified. Finally, a purely orbital Kondo effect in the two-electron regime is also predicted.

Ab initio study on the electronic, magnetic, and mechanical properties of CaCu3V4O12

The electronic, magnetic, and mechanical properties of CaCu3V4O12 are investigated by use of the density functional theory method. The calculated results indicate that CaCu3V4O12 is a half-metallic and ferrimagnetic compound. The magnetic coupling for Cu-V is antiferromagnetic, while those for Cu-Cu and V-V are ferromagnetic. The obtained elastic constants suggest that the compound is mechanically stable. The calculated oxidation states and density of states reveal the existence of a mixed valence for Cu and V. This supports the experimental observation of the mixed valence in Ca2+Cu2+Cu2+(V25+V24+)O-12.

Structural stability and magnetic coupling in CaCu3Co4O12 from first principles

The structural, electronic and magnetic properties of CaCu3Co4O12 were studied by use of the full-potential linearized augmented plane wave method. The calculated results indicate that CaCu3Co4O12 is stable both thermodynamically and mechanically. Both GGA (generalized gradient approximation) and GGA + U methods predict that CaCu3Co4O12 is metallic. The ferromagnetic configuration is only slightly more stable in energy compared with the non-magnetic configuration (3.7 meV), suggesting that they are competitive for being the ground state. Co is in the low spin state (S = 1/2).

Ferrimagnetic and half-metallic CaCu3Fe4O12: Prediction from first principles investigation

The structural stability and physical properties of CaCu3Fe4O12 were studied by the use of the full-potential linearized augmented plane wave method. The authors' calculated result indicates that the title compound is stable both thermodynamically and mechanically. It is ferrimagnetic and half-metallic. The calculated magnetic structure reveals that the coupling of Cu-Fe is antiferromagnetic, while those of Cu-Cu and Fe-Fe are ferromagnetic.

Magnetic and electronic properties of CaCu3Cr4O12 and CaCu3Cr2Sb2O12 by first-principles density functional calculation

The electronic and magnetic properties of CaCu3Cr4O12 and CaCu3Cr2Sb2O12 are investigated by the use of the full-potential linearized augumented plane wave (FPLAPW) method. The calculated results indicate that CaCu3- Cr4O12 is a ferrimagnetic and half-metallic compound, in good agreement with previous theoretical studies. CaCu3- Cr2Sb2O12 is a ferrimagnetic semiconductor with a small gap of 0.136 eV. In both compounds, because Cr4+ 3d (d(2)) and Cr3+ 3d (d(3)) orbitals are less than half filled, the coupling between Cr-Cu is antiferromagnetic, whereas that between Cu-Cu and Cr-Cr is ferromagnetic. The total net spin moment is 5.0 and 3.0 mu(B) for CaCu3Cr4O12 and CaCu3Cr2Sb2O12, respectively. In CaCu3Cr4O12, the 3d electrons of Cr4+ are delocalized, which strengthens the Cr-Cr ferromagnetic coupling. For CaCu3Cr2Sb2O12, the doping of nonmagnetic ion Sb5+ reduces the Cr-Cr ferromagnetic coupling, and the half-filled Cr3+ t(2g) (t(2g)(3)) makes the chromium 3d electrons localized. In addition, the ordering arrangement of the octahedral chromium and antimony ions also prevents the delocalization of electrons. Hence, CaCu3Cr2Sb2O12 shows insulating behavior, in agreement with the experimental observation.