Discrete Electronic Spectrum Research Articles

Defeating broken symmetry with doping: Symmetric resonant tunneling in noncentrosymetric heterostructures

Resonant tunneling transport in polar heterostructures is intimately connected to the polarization fields emerging from the geometric Berry-phase. In these structures, quantum confinement results not only in a discrete electronic spectrum, but also in built-in polarization charges exhibiting a broken inversion symmetry along the transport direction. Thus, electrons undergo highly asymmetric quantum interference effects with respect to the direction of current flow. By employing doping to counter the broken symmetry, we deterministically control the resonant transmission through GaN/AlN resonant tunneling diodes and experimentally demonstrate the recovery of symmetric resonant tunneling injection across the noncentrosymmetric double-barrier potential.

I–V characteristics and conductance of strained SWCNTs

We present a new procedure to investigate the I–V characteristics and the conductance for strained SWCNTs. These electronic transport properties have been studied theoretically at zero temperature for zig-zag, armchair and chiral SWCNTs under the effect of the uniaxial tension and torsional strain. The analytical expression of the energy spectrum in the tight binding approximation has been used to calculate the induced current and the conductance through Landauer–Büttiker formalism. It is shown that the conductance for unstrained CNTs at initial values of the voltage can take discrete values which are equal to zero and 4 (e2/h) for semiconducting and conducting SWCNTs respectively. The emergence of the kinks in the I–V characteristics is due to the discrete electronic spectrum in the SWCNTs. The location and number of kinks are changeable under the effect of strain process. The conductance in a strained armchair (5,5) CNT decreases to zero under torsional strain, consequently, it will transform the conducting SWCNTs at a threshold value of strain to a semiconducting SWCNT. In contrast, by applying the uniaxial tension on the armchair (5,5) CNT, the conductance does not change absolutely. There is a different behavior can be observed by applying the strain on zig-zag (10,0) CNT, where the conductance decreases rapidly and slightly under the influence of uniaxial tension and torsional strain, respectively. We found that the conductance of chiral (10,9) CNT is not significantly affected by applying the strain under consideration. More interestingly, the band structure of chiral (10,9) CNT under uniaxial tension and torsional strain have been investigated within the tight binding approximation.

Quantum dots microstructure by XAFS spectroscopy: GaN/AlN system depending on preparation conditions

GaK EXAFS spectra of GaN/AlN heterostructures were measured. Microstructure parameters of GaN/AlN heterosystems with discrete electronic spectra largely influenced by the elastic deformation at the boundaries of the nanoclusters and substrate was detected by the direct method. The local structure parameters determined by EXAFS spectroscopy are linked to preparation conditions and nanostructures morphology and adequate models are suggested and discussed.

Designable electron transport features in one-dimensional arrays of metallic nanoparticles: Monte Carlo study of the relation between shape and transport

We study the current and shot noise in a linear array of metallic nanoparticles taking explicitly into consideration their discrete electronic spectra. Phonon assisted tunneling and dissipative effects on single nanoparticles are incorporated as well. The capacitance matrix which determines the classical Coulomb interaction within the capacitance model is calculated numerically from a realistic geometry. A Monte Carlo algorithm which self-adapts to the size of the system allows us to simulate the single-electron transport properties within a semiclassical framework. We present several effects that are related to the geometry and the one-electron level spacing like e.g. a negative differential conductance (NDC) effect. Consequently these effects are designable by the choice of the size and arrangement of the nanoparticles.

Electronic excitation spectrum of metallic carbon nanotubes

We have studied the discrete electronic spectrum of closed metallic nanotube quantum dots. At low temperatures, the stability diagrams show a very regular four-fold pattern that allows for the determination of the electron addition and excitation energies. The measured nanotube spectra are in excellent agreement with theoretical predictions based on the nanotube band structure. Our results permit the complete identification of the electron quantum states in nanotube quantum dots.

Microscopic parameters of materials containing GaN/AlN and InAs/AlAs heterostructures

EXAFS spectra of A IIIB v heterostructures have been measured at the European Synchrotron Radiation Facility (ESRF, Grenoble, France), DUBBLE beam-line. It has been found that the first shell R Ga−N interatomic distance in heterostructure GaN/AlN is equal to 1.91 Å, which is 0.04 Å smaller compared to crystalline GaN. For the second Ga–Ga shell an interatomic distance R Ga−Ga of 3.13 Å was found, which is 0.06 Å smaller than in crystalline GaN. The coordination number N Ga−Ga was found to be 6.0. Our results suggest that this heterostructure with discrete electronic spectra contains two-dimentional islands with strong elastic strains. The first shell interatomic distance R In−As for the heterostructure containing InAs quantum dots (QDs) is 0.04 Å lower in comparison with those for the bulk InAs and is 2.58 Å. The second shell interatomic distance R In−In is 3.99 Å, i.e. 0.29 Å smaller compared to the bulk InAs. The Debye–Waller factor was found to be 0.022 Å 2, the coordination number N In−In∼2.0. The results obtained suggest that InAs/AlAs heterostructure with discrete electronic spectra contains three-dimentional islands with unhomogeneity of microstructure due to elastic strain relaxation.

Semi-Classical Study of a Hydrogenic Atom near a Rigid Wall

A semi-classical calculation of the discrete electronic spectrum for a hydrogenic atom located near a rigid wall, and the corresponding graphics of some of the energy levels as function of the nucleus–wall distance are presented. Calculations are based on the exact analytic solution of Newton equations of motion within a model which considers elastic collisions (EC) at the wall, followed by a primitive WKB quantization. This system can be used as a model for 2D and 3D quantum devices, such as shallow state of an impurity atom or Wannier-Mott exciton near to interfaces.

Semi-Classical Study of a Hydrogenic Atom near a Rigid Wall

A semi-classical calculation of the discrete electronic spectrum for a hydrogenic atom located near a rigid wall, and the corresponding graphics of some of the energy levels as function of the nucleus–wall distance are presented. Calculations are based on the exact analytic solution of Newton equations of motion within a model which considers elastic collisions (EC) at the wall, followed by a primitive WKB quantization. This system can be used as a model for 2D and 3D quantum devices, such as shallow state of an impurity atom or Wannier-Mott exciton near to interfaces.

Shell effects in small metal particles

By assuming periodic discrete electronic spectra, the properties of small metal particles are analyzed. The canonical partition function is obtained exactly. The heat capacity and the electronic magnetic susceptibility are calculated in the presence of a static magnetic field. These results are an extension of the calculations for an equally spaced spectrum. Preliminary considerations of the statistical theory of spectra are included.

The vibrational line shape of diatomic adsorbates on metal clusters

A decrease of at least an order of magnitude in the vibrational relaxation time T1 has been measured for CO bonded to Rh and Co clusters when the size of the cluster increases from 5 to 35 Å. We propose that this effect is mainly due to the coupling of the molecular vibration ω0 with the electron-hole excitations in the cluster. This is described via a model Hamiltonian. The finite size of the clusters give rise to a discrete electronic spectrum, and hence to a discrete pair excitation spectrum. This effect is measured in terms of D, the mean spacing between nearest-neighbor levels in the conduction band of the cluster. We find that: (1) the proposed mechanism starts to contribute to T1 only when D<ℏω0; (2) T1 is at least several hundred ps for clusters less than 15 Å in size; (3) there is a sharp decrease of T1 to about 10 ps as the cluster size increases from 15 to 40 Å; (4) T1 decreases smoothly towards the bulk value for larger clusters.

Theory of the resonances of the LoSurdo-Stark effect.

When an atom or a molecule is exposed to an electric field, the discrete electronic spectrum turns into a spectrum of resonances with complex energies due to the mixing of the bound wave function of each unperturbed stationary state with the asymptotic form of the Airy function. The complex energies are eigenvalues of a non-Hermitian Schr\"odinger equation whose solutions have a special outgoing-wave asymptotic form, which is derived rigorously. At least three coordinate transformations (rotation, translation, and a combination of these) regularize the dc-field-induced resonance function, the most efficient one being the long-honored rotation, f(x)=${\mathit{xe}}^{\mathit{i}\mathrm{\ensuremath{\theta}}}$, which causes the function to dissipate asymptotically as ${\mathit{e}}^{\mathrm{\ensuremath{-}}\ensuremath{\gamma}\mathit{x}3/2}$. This finding, obtained from first principles, explains previous results that have been obtained either via trial computations or via elaborate mathematical analyses of the spectrum. The theory is further developed toward the efficient computation of such resonances with ${\mathit{scrL}}^{2}$ functions. Starting from the resonance-wave-function form ${\mathrm{\ensuremath{\Psi}}}^{\mathrm{res}}$=a${\mathrm{\ensuremath{\Psi}}}_{0}$+${\mathit{bX}}_{\mathrm{as}}$, the computation of the localized ${\mathrm{\ensuremath{\Psi}}}_{0}$ is carried out on the real axis, and only the free-electron function belonging to ${\mathit{X}}_{\mathrm{as}}$ is rotated and optimized in the complex plane. Two applications are presented. The first involves a numerically solvable one-dimensional model of a shape resonance in a dc field for a large range of field strengths.The second involves the hydrogen atom in its ground as well as in its first excited state. In the first example, ${\mathrm{\ensuremath{\Psi}}}_{0}$ is obtained numerically in an explicitly constructed effective potential containing partly the effect of the field. To this ``dressed'' ${\mathrm{\ensuremath{\Psi}}}_{0}$, the asymptotic part ${\mathit{X}}_{\mathrm{as}}$ is then added as a sum of an only ten back-rotated complex Slater-type orbitals (STO's), whose coefficients and nonlinear parameter are optimized from the diagonalization of the full Hamiltonian until stability of the complex eigenvalue is achieved. In the second example, ${\mathrm{\ensuremath{\Psi}}}_{0}$ was chosen as the exact 1s for the ground state and as the two roots 2s\ifmmode\pm\else\textpm\fi{}2${\mathit{p}}_{0}$ of the total Hamiltonian for the excited state. ${\mathit{X}}_{\mathrm{as}}$ was expressed in terms of angular momentum symmetry blocks up to l=8, with each symmetry expanded in terms of ten complex STO's. No optimization of \ensuremath{\theta} or other nonlinear parameters was done. Comparison with the exact results for the model potential and with published ones for the H atom shows very good agreement, thereby demonstrating the efficiency and reliability of the theory as well as its potential for treating N-electron systems.

Quantum properties of a hydrogen-like particle near a hard wall

An exact solution of the Schrödinger equation for a hydrogen-like atom near a hard wall given by us previously [Kovalenko et al., Phys. Status Solidi (B) 155, 549 (1989)] is used for an investigation of the discrete electronic spectrum, the atom dipole moment and oscillator strengths dependent on the distance from the wall. A hydrogen-like molecular near a hard wall is considered in the framework of the Heitler—London method.

Electronic States of a Hydrogen Atom Near a Hard Wall

AbstractAn exact solution of the Schrödinger equation for a hydrogenic atom located near a hard wall is found. The discrete electronic spectrum and the set of semi‐bounded hydrogenic wave functions are obtained. The atom dipole moment which arises due to the presence of the wall is calculated.

A theory of electrode reactions through bridge transition states; bridges with a discrete electronic spectrum

A theory has been developed for outer-sphere non-adiabatic electron transfer reactions at electrodes, to or from which an electron is transferred via ionic or molecular bridge species adsorbed on the electrode surface. Assuming a discrete energy spectrum for the discharging species and for the bridge, and neglecting interaction between adsorbed bridges, current-voltage relationships have been calculated for all overvoltages, and it is shown that for suitable relative positions of the electronic terms, the rate of the bridge-assisted electron transfer is higher than that of the direct electron transfer. Experimental data for various systems have been considered, and a semiquantitative agreement with the theory is found for the reduction of [Fe(CN) 6 ] 3− .

A theory of electrode reactions through bridge transition states; bridges with a discrete electronic spectrum

Summary A theory has been developed for outer-sphere non-adiabatic electron transfer reactions at electrodes, to or from which an electron is transferred via ionic or molecular bridge species adsorbed on the electrode surface. Assuming a discrete energy spectrum for the discharging species and for the bridge, and neglecting interaction between adsorbed bridges, current-voltage relationships have been calculated for all overvoltages, and it is shown that for suitable relative positions of the electronic terms, the rate of the bridge-assisted electron transfer is higher than that of the direct electron transfer. Experimental data for various systems have been considered, and a semiquantitative agreement with the theory is found for the reduction of [Fe(CN) 6 ] 3− .

A prediction of the discrete electronic transition 2 pπu-3 dσg of H 2+

The potential curves of the 2 pπ u and 3 dσ g electronic states of H 2 + have been calculated in the Born-Oppenheimer approximation. A small hump (≊30 cm −1) has been found in the 2 pπ u state at large internuclear separations. A number of the vibrational levels of both states have been determined and a discrete electronic spectrum is predicted to occur in the near infrared region. The calculated spectroscopic constants of the two states are unusually small for diatomic hydrogen. A brief discussion of one possible observation of this spectrum is given.

The absorption spectra of the halogen acids in the vacuum ultra-violet

Although the halogen acids have long been known to Possess regions of continuous absorption, no discrete electronic spectra have previously been reported for the neutral molecules. Their emission spectra occurring between 2800 and 4000 A really belong to the molecular ions. In the work to be described here, new absorption spectra of the halogen acids, which consist of very intense system of relatively discrete bands, have been dis-covered in the Schumann region. The spectra are essentially in the nature of strong resonance bands and are very similar in this respect to corresponding bands of the alkyl halides (price 1936). Extensive absorption systems of I 2 , Br 2 and Cl 2 have also been found in the same region. These will be described in a later publication. The continuous background against which the bands were observed was provided by the Lyman continuum. Other experimental details have been reported previously (Collins and Price 1934). The absorption spectrum of hydrogen iodide is shown in fig. 1 a (Plate 11). This particular photograph corresponds to a pressure of about 0·01 mm. in a path length of 50 cm. The most striking feature of the spectrum is the presence of a large number of bands with strong sharp Q branches accompanied on either side by weaker P and R branches (fig. 1 a, b, c ), the rotational structures of allied are only slightly degraded. This indicates that a relatively non-bonding electron is being excited, a fact which is also substantiated by the absence of any pronounced vibrational progressions. For example, the first strong band at 1762 A is unaccompanied by any vibrational bands, there doing a transparent region more than 5000 cm. -1 wide to the short wave-length side of it. Though the rotational structures of the P and R branches of this band are diffuse, the sharp nature of the Q branch is easily discernible (see fig. 1 a, c). The spectra of HBr and HCl each begin with a very similar band occurring at 1491 A for HBr (fig. 1 d ) and at 1331A for HCl (fig. 1 e ). It will be shown that these bands are related to one another and are analogous to the B bands of the alkyl halides. The next strong bands on the short wave-length side of them can further be linked with the C bands of the alkyl halides. Because of certain peculiarities which the above bands of the halogen acids (fig. 1 c, d, e ) exhibit, they will be discussed together in a later paragraph.