Electron–phonon interaction in fan-shaped quantum dot and quantum wire

The optical phonon modes and electron–optical-phonon interaction in fan-shaped quantum dot and quantum wire are studied with the dielectric continuum (DC) model and separation of variables. The explicit expressions for the longitudinal optical (LO) and interface optical (IO) phonon eigenmodes are deduced. It is found that there exist two types of IO phonon modes: top interface optical (TIO) phonon mode and arc interface optical (AIO) phonon mode, in a fan-shaped quantum dot. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron–phonon interaction. The potential applications of these results are also discussed.     

Energy levels of the Fröhlich polaron in a spherical quantum dot

The one-phonon variational state is suitably applied to describe the ground state and excited states of the Fröhlich polaron bound to a quantum dot. A general analytical expression for the electronic energy spectra and the polaron binding energy for different electronic subband bound states in a quantum dot is presented and discussed with reference to the parameters of a real solid.     

Impurity states in a cylindrical quantum dot with the modified Pöschl-Teller potential

We study impurity states in a cylindrical quantum dot with two confining potentials: in the direction of cylinder axis modified Pöschl-Teller potential and in radial direction parabolic potential. Studies of impurity states are performed in the frames of variational method and by using numerical methods, the dependences of the particle energy on the geometrical parameters of the cylindrical quantum dot are derived. Dependences of the electron binding energy on the half-width and depth of the potential wall are revealed.     

Electron–hole two-stream instability in a quantum semiconductor plasma with exchange-correlation effects

The electron–hole two-stream instability in a quantum semiconductor plasma has been studied including electrons and holes quantum recoil effects, exchange-correlation potentials, and degenerate pressures of the plasma species. Typical values of GaAs and GaSb semiconductors are used to estimate the growth rate of the two-stream instability. The effects of electron– and hole–phonon collision, quantum recoil effects, the streaming velocities, and the corresponding threshold on the growth rate are investigated numerically. Considering the phonon susceptibility allows the acoustic mode to exist and the collisional instability arises in combination with drift of the holes.     

Electronic states in a cylindrical quantum dot with the modified Pöschl-Teller potential in the presence of external magnetic field

Energy levels of an electron in a cylindrical quantum dot with a modified Pöschl-Teller potential in the presence of external homogeneous magnetic field are studied. Analytical expressions for the wave function and energy of the particle are obtained. Different regimes of magnetic quantization are considered and peculiarities of behavior of the electron energy spectrum depending on the value of applied magnetic field are revealed.     

Enhancement of the shot noise of a quantum dot–Luttinger lead system

We investigate the joint effects of the intralead electron interaction and Coulombic dot–lead interaction on the shot noise of a quantum dot coupled to Luttinger liquid leads. A formula of the shot noise is derived by applying the nonequilibrium Green function technique. The shot noise is enhanced by the dot–lead interaction. For a weak or moderately strong interaction the differential shot noise demonstrates resonant-like behavior as a function of bias and gate voltages. In the limit of strong interaction resonant behavior disappears and the differential shot noise and Fano factor scale as a power law in bias voltage. Under some parameters, the differential shot noise may become negative around resonant peaks, and the physical reason is analyzed.     

On a relation of the angular frequency to the Aharonov–Casher geometric phase in a quantum dot

By analysing the behaviour of a neutral particle with permanent magnetic dipole moment confined to a quantum dot in the presence of a radial electric field, Coulomb-type and linear confining potentials, then, an Aharonov–Bohm-type effect for bound states and a dependence of the angular frequency of the system on the Aharonov–Casher geometric phase and the quantum numbers associated with the radial modes, the angular momentum and the spin are obtained. In particular, the possible values of the angular frequency and the persistent spin currents associated with the ground state are investigated in two different cases.     

The quantum nonthermal effect of a nonstationary Kerr－Newman black hole and the average range of the effective particles

We have found that the nonthermal radiation of a nonstationary Kerr－Newman black hole is affected by interstellar materials. In particular, the interstellar gas deeply influences the average range of nonthermal radiation particles, while the average range depends on the maximum energy of the radiation and the energy extent of the radiation.     

Tricritical point in quantum phase transitions of the Coleman–Weinberg model at Higgs mass

The tricritical point, which separates first and second order phase transitions in three-dimensional superconductors, is studied in the four-dimensional Coleman–Weinberg model, and the similarities as well as the differences with respect to the three-dimensional result are exhibited. The position of the tricritical point in the Coleman–Weinberg model is derived and found to be in agreement with the Thomas–Fermi approximation in the three-dimensional Ginzburg–Landau theory. From this we deduce a special role of the tricritical point for the Standard Model Higgs sector in the scope of the latest experimental results, which suggests the unexpected relevance of tricritical behavior in the electroweak interactions.     

Consequences of the center–of–mass correction in nuclear mean–field models

We study the influence of the scheme for the correction for spurious center–of–mass motion on the fit of effective interactions for self–consistent nuclear mean–field calculations. We find that interactions with very simple center–of–mass correction have significantly larger surface coefficients than interactions for which the center–of–mass correction was calculated for the actual many–body state during the fit. The reason for that is that the effective interaction has to counteract the wrong trends with nucleon number of all simplified schemes for center–of–mass correction which puts a wrong trend with mass number into the effective interaction itself. The effect becomes clearly visible when looking at the deformation energy of largely deformed systems, e.g. superdeformed states or fission barriers of heavy nuclei. Received: 6 September 1999     

Impact of heavy hole–light hole coupling on the exciton fine structure in quantum dots

We present analytical results which describe the properties of the exciton ground state in a single semiconductor quantum dot (QD). Calculations are performed within the Luttinger–Kohn and Bir–Pikus Hamiltonian theory. We show in an explicit form that an interplay of the exchange interaction and the heavy hole–light hole coupling, which is due to the in-plane asymmetries of the dot shape and the strain distribution, plays an essential role. For both the bright and dark exciton, this combined effect leads to a dependence of the fine structure splitting and polarizations on the main anisotropy axis direction relative to the dot orientation. Basing on the obtained analytical expressions, we discuss some special cases in details.     

Resonant transfer of one- and two-photon excitations in quantum dot–bacteriorhodopsin complexes

Light-sensitive protein bacteriorhodopsin (BR), which is capable of electrical response upon exposure to light, is a promising material for photovoltaics and optoelectronics. However, the rather narrow absorption spectrum of BR does not allow achieving efficient conversion of the light energy in the blue and infrared spectral regions. This paper summarizes the results of studies showing the possibility of extending the spectral region of the BR function by means of the Förster resonance energy transfer (FRET) from CdSe/ZnS quantum dots (QDs), which have a broad spectrum of one-photon absorption and a large twophoton absorption cross section (TPACS), to BR upon one- and two-photon excitation. In particular, it is shown that, on the basis of QDs and BR-containing purple membranes, it is possible to create electrostatically associated bio-nano hybrid systems in which FRET is implemented. In addition, the large TPACS of QDs, which is two orders of magnitude larger than those of BR and organic dyes, opens up a means for selective two-photon excitation of synthesized bio-nano hybrid complexes. On the basis of the results of this work, the spectral region in which BR converts the light energy into electrical energy can be extended from the UV to near-IR region, creating new opportunities for the use of this material in photovoltaics and optoelectronics.     

Charged and neutral biexciton–exciton cascade in a single quantum dot within a photonic bandgap

We investigate the recombination dynamics of positively charged and neutral biexcitons and excitons in a single InAs/GaAs quantum dot (QD) within a two-dimensional (2D) photonic bandgap (PBG). The 2D PBG makes the exciton lifetime four times longer and enhances photon-extraction efficiency compared to those without the PBG. Photon cross-correlation measurements demonstrate the cascade emissions of both charged and neutral biexcitons–excitons from the same QD. In the charged case, a hole in the p-shell relaxes into the s-shell between the cascade, and the corresponding transition is confirmed based on the spin configuration. The long exciton lifetime with the PBG helps us to reveal the spin dynamics that did not clearly appear in intrinsic QDs.     

A study of an exciton in a quantum dot with Woods–Saxon potential

A theoretical study of an exciton confined in a quantum dot with the Woods–Saxon potential is presented. The great advantage of our methodology is that it enables confinement regimes by varying two parameters in the model potential. Calculations are made by using the method of the numerical diagonalization of the Hamiltonian matrix within the effective-mass approximation. The binding energies of the ground (L=0$L=0$) and first excited (L=1$L=1$) states are obtained as functions of the dot radius. Based on the computed energies and wave functions, the linear, the third-order nonlinear and the total optical absorption coefficients have been examined between the ground and the first excited states. The results are presented as a function of the incident photon energy for the different values of the dot radius and the barrier slope. It is found that the binding energy and the optical properties of the excitons in a quantum dot are strongly affected by the dot radius and the barrier slope of the confinement potential.     

Sum frequency generation in the spherical quantum dots in the presence of applied electric field and spin–orbit interaction

The sum-frequency generation (SFG) is theoretically studied in a quantum dot (QD) through the framework of the effective-mass approximation and compact density matrix approach. QD is spherical with the parabolic potential confinement, under applied electric field and in the presence of Rashba spin-orbit interaction (SOI). Using the computed energies and eigenkets, the second-order susceptibility of SFG has been also calculated as a function of radius of QD, spin–orbit interaction strength and the applied electric field. The effects of Rashba SOI strength, radius of QD and the applied electric field on the second-order of susceptibility coefficient are considered.     

Electric field induced nonlinear optical properties of a confined exciton in a ZnO/Zn1−xMgxO strained quantum dot

Electric field induced exciton binding energy as a function of dot radius in a ZnO/Zn_1−xMg_xO quantum dot is investigated. The interband emission as a function of dot radius is obtained in the presence of electric field strength. The Stark effect on the exciton as a function of the dot radius is discussed. The effects of strain, including the hydrostatic and the biaxial strain and the internal electric field, induced by spontaneous and piezoelectric polarization are taken into consideration in all the calculations. Numerical calculations are performed using variational procedure within the single band effective mass approximation. Some nonlinear optical properties are investigated for various electric field strengths in a ZnO/Zn_1−xMg_xO quantum dot taking into account the strain-induced piezoelectric effects. Our results show that the nonlinear optical properties strongly depend on the effects of electric field strength and the geometrical confinement.     

The generalization of the Mermin–Wagner theorem and the possibility of long-range order in the isotropic discrete one-dimensional quantum Heisenberg model

The problem of existence of long-range order in the isotropic quantum Heisenberg model on the D=1 lattice is reconsidered in view of the possibility of sufficiently slow decaying exchange interaction with infinite effective radius. It is shown that the macrosopic arguments given by Landau and Lifshitz and then supported microscopically by Mermin and Wagner fail for this case so that the non-zero spontaneous magnetization may yet exist. This result was anticipated by Thouless on the grounds of phenomenological analysis, and we give its microscopic foundation, which amounts to the generalization of Mermin–Wagner theorem for the case of the infinite second moment of the exchange interaction. Two well known in lattice statistics models – i.e., Kac-I and Kac-II – illustrate our results.     

Fine structure of the emission spectrum of a two-dimensional electron–hole liquid in SiGe/Si quantum wells

The fine structure of the emission spectrum of a quasi-two-dimensional electron–hole liquid in shallow SiGe/Si quantum wells is observed experimentally. This fine structure is explained by the occurrence of steps in the density of states resulting from the coexistence of light and heavy holes in the liquid phase and by the interaction of charge carriers with charge-density oscillations in the liquid.