Electronic Impurity States Research Articles

Legendre transformation in hubbard and anderson models

The previously derived variational-derivative equations for the Hubbard model and for the single-impurity Anderson model after the Legendre transformation are represented in the form of a set of two nonlinear integral equations. The one-particle propagators of the number of particles and of the momentum that are defined by these equations exhibit a regular behavior in three limiting cases. First, for both models in the limit of the zero width of the conduction band (W/U = 0) there is obtained a result known as the atomic limit. Second, it has been shown that in the limit of U/W ≪ 1 the Pauli principle in the form of an additional coupling equation excludes from the perturbation-theory series some class of diagrams that are present in the standard expansion. Finally, for the case of U = ∞ and Ne = Nat − 1 in the framework of the Hubbard model there has been obtained an equation that agrees with the exact Nagaoka statement on the saturated ferromagnetism. A calculation has been performed of the density of impurity electron states in the symmetrical Anderson model in the paramagnetic phase for various values of the parameters of the Coulomb interaction U/πΓ and temperature T/Γ, where Γ is the width of the localized impurity level. The calculation results are in good agreement with the results obtained by other methods.

External electric field effects on the electronic and hydrogenic impurity states in ellipsoidal and semi-ellipsoidal quantum dots

In the effective mass approximation, energy eigenvalues of an electron confined in ellipsoidal and semi-ellipsoidal quantum dots, with and without hydrogenic impurity, under the influence of an external electric field have been investigated, using the matrix diagonalization method. The lower-laying states of the electron as functions of the electric field strength, the dot size and its geometry are calculated. Our results show that the electronic states are strongly affected by the applied electric field, the size and the geometry of the dot.

Determination of effective magnetic moments of the hybridized electronic states of impurities from the concentration dependence of the Curie constant

The concentration dependence of the Curie constant in the magnetic susceptibility of impurities of transition elements in a nonmagnetic matrix is considered for the case where the energy level of an impurity electron falls into the conduction band and hybridized states arise. As a result of an analysis of the new experimental data on the magnetic susceptibility of the iron impurity in crystals of mercury selenide, a substantiation of the earlier proposed simple formula that describes the linear dependence of the Curie constant on the concentration of impurities with allowance for the hybridization of states is given. The application of this formula to the description of the temperature dependence of the magnetic susceptibility of the cobalt impurities allowed us, on the basis of the formulated ideas about the arrangement of the energy levels of d electrons and of the available data on the Hall concentration of electrons, to find the effective spin of the hybridized electronic states at the impurity cobalt and the resonance value of the concentration of donor electrons.

Low-temperature manifestations of hybridized electronic states of iron impurities in the thermoelectric power of mercury selenide

The temperature dependence of the Seebeck coefficient (thermoelectric power) of mercury selenide with iron and cobalt impurities is investigated at low temperatures. In crystals with iron impurities at concentrations close to those corresponding to the concentration maximum of the electron mobility, an anomalously strong decrease of the thermoelectric power is observed in a temperature interval below 25K. This decrease is attributed to a manifestation of resonance scattering of electrons in hybridized states at the iron donor impurities. A fitting of the theoretical temperature dependence to the experimental data permits a quantitative interpretation of the experimental results and yields values of the parameters of the hybridized states which agree with those found from investigations of other effects. In crystals with cobalt impurities no anomalies due to manifestations of hybridized electronic states are observed. This finding is in agreement with the conductivity data and implies a lower value of the resonance energy for the cobalt impurities as compared to the iron.

Effect of different effective mass and electric field on the electronic structure in GaN/AlxGa1-xN spherical quantum dot

In this paper，we have calculated the impurity electronic states and the binding energy with the variation of the quantum dot radius and Al content in GaN/AlxGa1-xN spherical quantum dot (QD) using the plane wave method. The modification of the energy states is discussed when the difference in effective electron mass in GaN and AlxGa1-xN is taken into account. The results show that the difference in effective mass can not be neglected when Al content is large. In addition，with the consideration of the difference in effective mass，we investigate the binding energy as function of quantum dot radius, impurity position and external electric field. The results are meaningful and can be widely applied in the design of optoelectronic devices.

Impurity states of electrons in quantum dots in external magnetic fields

The influence of isolated impurity atoms on the electron energy spectrum in a parabolic quantum dot in quantizing magnetic field is studied. The impurity potential is approximated by a Gaussian separable operator which allows one to obtain the exact solution of the problem. We demonstrate that in the electron energy spectrum there is a set of local levels which are split from the Landau zone boundaries in the upward or downward direction depending on the impurity type. We have calculated the local level positions, the wave functions of electrons in bound states, and the residues of the electron scattering amplitudes by impurity atoms at the poles.

Influence of the hybridization of impurity electron states on the quantum magneto-oscillation phenomena in mercury selenide with iron impurities

Experimental study of the concentration dependence of the parameters of the Shubnikov–de Haas and de Haas–van Alphen oscillations in mercury selenide crystals containing iron impurities under conditions where the donor resonance energy level of the impurities falls into the conduction band and hybridization of the electronic states occurs. The observed concentration dependence of the Dingle temperature and g factor of the electrons exhibit minima correlated in position with the maximum of the electronic mobility. It is shown that the observed anomalies can be explained on the basis of a previously developed theory of hybridization effects.

Resonant effects in the manifestation of hybridized electronic states of iron impurities in the temperature dependences of the absorption coefficient and velocity of ultrasound propagation in mercury selenide

The temperature dependences of the absorption coefficient and phase velocity of 52-MHz ultrasonic waves in iron-doped mercury selenide crystals are studied. The presence of impurities in concentrations of about 1019 cm−3 is found to initiate the appearance of a resonance peak in the absorption coefficient at a temperature of about 5 K and the corresponding anomaly in the velocity of the slow transverse wave propagating in the 〈110〉 direction. It is shown that the observed effects can be accounted for by the interaction of ultrasound with electrons in the states created in hybridization of the iron impurity donor states with the conduction band states of the crystal. A straightforward theoretical description and quantitative interpretation of these effects are proposed and used to derive data on the hybridized states, which conform with the earlier treatment of the temperature and concentration anomalies of conductivity in the crystals under study.

Entanglement of electronic states of impurities in a nanocrystal

It is shown that the dynamics of electronic states of impurities in a nanocrystal embedded in a bulk matrix can be described with the help of the model of a single-mode microcavity with quasi-resonant atoms and losses at the mirrors. In the proposed model, the dynamics of impurities is similar to the collective decay of atoms in a common bath. In the case of a nanocrystal, matrix phonons represent this bath. Impurities interact with the localized phonon mode of the nanocrystal owing to the electron-phonon interaction. The localized phonon mode is coupled with bath phonons at the nanocrystal boundary. In the dispersive limit, the standard model of collective relaxation appears, within the framework of which, different types of many-particle entangled electronic states of impurities are described. In the case of exact resonance, similar entangled states also appear, which are discussed for two impurities in a nanocrystal.

Donors in Semiconductors - are they Understood in Electronic Era?

The physics of semiconductors and contemporary electronics cannot be understood without impurities. The hydrogen-like shallow donor (and acceptor) state of electron (hole) bound by Coulomb electrostatic force of excess charge of impurity is used to control conductivity of semiconductors and construct semiconductor diodes, transistors and numerous types of semiconductor electronic and optoelectronic devices, including lasers.Recently, surprisingly, the physics of impurity donors appeared to be much reacher. Experimental evidence has been provided for universal existence of other types of electronic states of the same donor impurity:i) mysterious, deep, DX-type state resulting in metastability -- slow hysteresis phenomena - understood as two-electron, acceptor-like state of donor impurity, formed upon large lattice distortion or rearrangement arround impurity and accompanying capture of second electron, resulting in negative electron correlation energy U;ii) deep, localized, fully symmetric, A1, one-electron donor state of substitutional impurity.The latter state can be formed from the "ordinary" shallow hydrogen-like state in the process of strong localization of electron by short range, local potential of impurity core, preserving full (A1) symmetry of the substitutional impurity in the host lattice. The "anticrossing" of the two A1(shallow hydrogenic and deep localized) energy levels upon transformation is observed.All types of electronic states of impurity can be universally observed for the same donor impurity and mutual transformation between different states occur upon changing experimental conditions.The knowledge about existence and properties of these "new", molecular type, donor states in semiconductors seems still await general recognition and positive application in contemporary material and device science and engineering.

Electronic states of a hydrogenic donor impurity in semiconductor nano-structures

We propose a method for uniformly calculating the electronic states of a hydrogenic donor impurity in low-dimensional semiconductor nano-structures in the framework of effective-mass envelope-function theory, and we study the electronic structures of this systems. Compared to previous methods, our method has the following merits: (a) It can be widely applied in the calculation of the electronic states of hydrogenic donor impurities in nano-structures of various shapes; (b) It can easily be extended to study the effects of external fields and other complex cases; (c) The excited states are more easily calculated than with the variational method; (d) It is convenient to calculate the change of the electronic states with the position of a hydrogenic donor impurity in nano-structures; (e) The binding energy can be calculated explicitly. (c) 2007 Elsevier B.V. All rights reserved.

Ionization energy of donor and acceptor impurities in semiconductor nanowires: Importance of dielectric confinement

Calculations of the electronic states of donor and acceptor impurities in nanowires show that the ionization energy of the impurities is strongly enhanced with respect to the bulk, above all when the wires are embedded in a material with a low dielectric constant. In free-standing nanowires with diameter below $10\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, the ionization of the impurities at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is strongly reduced and heavy doping is necessary to obtain conductive systems. These results imply that the critical density for metal-nonmetal transitions is not the same as in the bulk. Experiments are proposed to test the predictions.

Electronic states of Mn impurities and magnetic coupling between Mn spins in diluted magnetic semiconductors

Electronic states and magnetic properties of single $Mn$ impurity and dimer doped in narrow-gap and wide-gap $III$-$V$ semiconductors have been studied systematically. It has been found that in the ground state for single $Mn$ impurity, $Mn$-$As(N)$ complex is antiferromagnetic (AFM) coupling when $p$-$d$ hybridization $V_{pd}$ is large and both the hole level $E_{v}$ and the impurity level $E_{d}$ are close to the midgap; or very weak ferromagnetic (FM) when $V_{pd}$ is small and both $E_{v}$ and $E_d$ are deep in the valence band. In $Mn$ dimer situation, the $Mn$ spins are AFM coupling for half-filled or full-filled $p$ orbits; on the contrast, the Mn spins are double-exchange-like FM coupling for any $p$-orbits away from half-filling. We propose the strong {\it p-d} hybridized double exchange mechanism is responsible for the FM order in diluted $III$-$V$ semiconductors.

Electronic and Shallow Impurity States in Semiconductor Heterostructures Under an Applied Electric Field**The projectsupported by the Natural Science Foundation of Shanghai Municipal Commission ofEducation under Grant No. 99QF55

With the use of variational method to solve the effective mass equation, wehave studied the electronic and shallow impurity states in semiconductorheterostructures under an applied electric field. The electron energy levelsare calculated exactly and the impurity binding energies are calculated withthe variational approach. It is found that the behaviors of electronic andshallow impurity states in heterostructures under an applied electric fieldare analogous to that of quantum wells. Our results show that with theincreasing strength of electric field, the electron confinement energiesincrease, and the impurity binding energy increases also when the impurityis on the surface, while the impurity binding energy increases at first, toa peak value, then decreases to a value which is related to the impurityposition when the impurity is away from the surface. In the absence ofelectric field, the result tends to the Levine's ground state energy(-1/4 effective Rydberg) when the impurity is on the surface, and the groundimpurity binding energy tends to that in the bulk when the impurity is faraway from the surface. The dependence of the impurity binding energy on theimpurity position for different electric fieldis also discussed.

Electronic structure and impurity states in GaN quantum dots

We study the electronic structure of spherical GaN quantum dots (QD's) with a substitutional acceptor impurity at the center. The size-dependent energy spectra are calculated within the sp 3 s* tight-binding model, which yields a good agreement with the confinement-induced blue shifts observed in undoped QD's. The acceptor binding energy is strongly enhanced in a QD and decreases with increasing size following a scaling law that extrapolates to the bulk experimental value. The size-dependent average radius of the hole orbit is also calculated. The results are in agreement with the available experimental data for Mg impurity in bulk GaN.

Ultrafast optical generation of coherent phonons inCdTe1−xSexquantum dots

We report on the impulsive generation of coherent optical phonons in CdTe0.68Se0.32 nanocrystallites embedded in a glass matrix. Pump probe experiments using femtosecond laser pulses were performed by tuning the laser central energy to resonate with the absorption edge of the nanocrystals. We identify two longitudinal optical phonons, one longitudinal acoustic phonon and a fourth mode of a mixed longitudinal-transverse nature. The amplitude of the optical phonons as a function of the laser central energy exhibits a resonance that is well described by a model based on impulsive stimulated Raman scattering. The phases of the coherent phonons reveal coupling between different modes. At low power density excitations, the frequency of the optical coherent phonons deviates from values obtained from spontaneous Raman scattering. This behavior is ascribed to the presence of electronic impurity states which modify the nanocrystal dielectric function and, thereby, the frequency of the infrared-active phonons.

Decoherence in a spin–spin-bath model with environmental self-interaction

A low-temperature model system consisting of a central spin coupled to a spin-bath is studied to determine whether interaction among bath spins has an effect on central spin dynamics. In the absence of intra-environmental coupling, decoherence of the central spin is fast and irreversible. Strong intra-environmental interaction results in an effective decoupling of the central spin from the bath and suppression of decoherence. Weaker intra-environmental coupling reduces but does not eliminate decoherence. We argue that similar suppression of decoherence should be observed for electronic states of He impurities in silicon or diamond.

Wannier-like equation for the resonant cavity modes of locally perturbed photonic crystals

In analogy to the Wannier equation for localized electronic impurity states in crystalline materials, a wave equation for the envelope of the resonant optical modes of local defects within two-dimensional periodic dielectric structures is derived. In the case of degenerate satellite extrema, this is generalized to a set of coupled Wannier-like equations for a multienvelope system. The localized Wannier envelope solutions are then used in conjunction with a group theoretical symmetry analysis to determine an approximate form for donor and acceptor modes in a hexagonal photonic crystal. For an effective harmonic potential formed by varying the filling fraction of the lattice, the localized resonant modes are explicitly calculated using the Wannier equation and symmetry analysis, and a comparison to exact numerically computed modes is presented.

STARK EFFECT IN A FINITE REGION FOR A 1D COULOMB POTENTIAL

We calculate the states of a one-dimensional hydrogen atom under the effect of an electric field (Stark effect) in the strong field regime being the field confined in a finite region of width 2a (capacitor region). We find numerically the solution inside the capacitor and match it to an analytical solution outside the capacitor. Although the electric field tends to separate the two opposite charges particles, the total energy of the system decreases with increasing electric field strength. Our results are useful as a guideline to study strong electric field effects in electronic states of impurities or excitons in 1D systems.

Effect of quantum entanglement on Aharonov-Bohm oscillations, spin-polarized transport and current magnification effect

We present a simple model of transmission across a metallic mesoscopic ring. In one of its arm an electron interacts with a single magnetic impurity via an exchange coupling. We show that entanglement between electron and spin impurity states leads to reduction of Aharonov-Bohm oscillations in the transmission coefficient. The spin-conductance is asymmetric in the flux reversal as opposed to the two-probe electrical conductance which is symmetric. In the same model, in contradiction to the naive expectation of a current magnification effect, we observe enhancement as well as suppression of this effect depending on the system parameters. The limitations of this model to the general notion of dephasing or decoherence in quantum systems are pointed out.