Average Energy Level Spacing Research Articles

Suppression of the superconducting transition temperature and magnetic-field-induced quantum critical behavior in three-dimensional polycrystalline niobium films

We have investigated the superconducting transition temperature T c depression and magnetic-field-induced quantum critical behavior in three-dimensional (3D) polycrystalline niobium (Nb) films. For superconducting films with 26.8 nm 72.9 nm, the T c value increases from ∼4.94 to ∼8.74 K. Through comparing our experimental data with proximity effect and weak localization effect, the T c depression can be explained by the proximity effect predicted by Cooper. Pure size effect could not induce T c depression because the average energy level spacing of grains is much smaller than the bulk Nb superconducting energy gap. The reason for the proximity effect is the metallic niobium monoxide NbO surrounding Nb grains. The superconductor-insulator transition (SIT) induced by magnetic field has been observed in T s 433 and 523 K films. The critical field B c in SIT satisfies a scaling relationship, similar to that caused by quantum phase transition in a two-dimensional (2D) cleaning system. The reason for that is the average polycrystalline grain size is smaller than the bulk Nb coherence length. The quantum effect is probably related to the Nb oxides.

Particle Number Dependence of Size and Energy Quantities in Sodium Clusters

The effective radial electronic potentials for neutral sodium clusters, which were determined by Ekardt on the basis of the local density approximation and the jellium model, are parametrized by means of the (symmetrized) Woods-Saxon and "Wine-Bottle" symmetrized Woods-Saxon potentials with the aim of investigating the dependence of size and energy quantities on the cluster particle number. The potential parameters are determined by vari­ous least-squares fitting procedures. It is found that for the radius R of the above potentials, complex expressions are more appropriate than the stan­dard one R = r0N^{1/3} for relatively small values of N. Furthermore, N-power expansions are derived for those complex expressions of R, as well as for the r.m.s. radius of the potential. It is also found that improved results in these cases are obtained with an expression of the form R = r0N^{1/3}+b, which is still very simple. There is also investigated the variation of energy quan­tities, such as the single particle energies of the 1s and 1p states, the level spacing |E1p-E1s| and the average energy level spacing, with respect to the particle number N. Expressions for the first three of these quantities with N-dependent terms of the form aN^{2/3} + βΝ^{-1} give good results.

Investigation of electron wave function hybridization in Ga0.25In0.75As/InP arrays

We present a measurement technique for quantifying coupling between semiconductor quantum dots in an array. This technique employs magnetoconductance fluctuations to probe the decrease in the average spacing of the quantum energy levels as the electron wave functions in the dots undergo hybridization. Focusing on Ga0.25In0.75As dots, we investigate hybridization as the coupling strength is varied and the number of dots in the array is increased. Our technique reveals a significant drop in the average energy level spacing for multiple dot arrays, which is strong evidence for wave function hybridization.

Nonlinear characteristics in the magnetoconductance of electron billiards

Abstract The effect of an applied bias on transport through an electron billiard is studied by analysis of magnetoconductance fluctuations. It is shown that at low bias, nonlinear effects are well-described by electron heating alone, while at higher bias ( V > 2 mV, or approximately 5% of the electron Fermi energy) non-equilibrium effects become significant. We chart this behavior by examining the effective electron temperature plotted against the empirical parameter Q (average energy level spacing over energy level broadening) and the spectral scaling exponent α . The high bias data shows a departure from a curve composed of lattice temperature data for the same device, which indicates a change in electron dynamics within the billiard.

A novel quantum interference probe of the energy spectrum of coupled nanodevices

Abstract Quantum transport of an array of quantum billiards is investigated as a function of the coupling strength of the quantum point contacts that connect the individual billiards. A fractal analysis of the measured magneto-conductance fluctuations is used as a novel non-invasive probe of two characteristic energy scales of the energy level spectrum—the average energy level spacing and average energy level broadening. This analysis reveals a marked transition in the coherent area of the array as the coupling between the billiards is increased and the array evolves into a combined quantum system.

Local quantum size effect as seen by room-temperature 195Pt NMR in octanethiol-protected Pt nanoparticles

The average energy level spacing δ at the Fermi level has been almost exclusively used as a global indicator for predicting quantum size effect in metal nanoparticles and its detailed local characteristics have usually been neglected. Here, we report new 195Pt NMR evidence obtained on octanethiol-protected Pt nanoparticles with an average particle size of 1.0 ± 0.3 nm at room temperature which shows that the local characteristics of δ can be discerned and are directly related to the local variations of electronic properties of the system in its ‘bulk’ metallic state.

Bouncing states in quantum dots

We observe sequences of asymmetric Coulomb blockade resonances in the conductance of a closed quantum dot. Around a symmetric peak at the center of such a sequence, several asymmetric resonances with a steep flank facing the central peak are found. This effect occurs for an average coupling of the quantum dot states to the leads which is of the order of both their average energy level spacing as well as of the thermal energy. These observations are interpreted in terms of a single state (``bouncing state'') that couples particularly well to the leads. Such a state can influence the line shapes of several neighboring Coulomb blockade resonances.

Effect of quantum diffusion on hopping transport

We present a study of quantum diffusion effect in granular metals, in the limit where Δ E c⪢Δ ε, with Δ ε the average energy level spacing and Δ E C the charging energy fluctuation. This effect results from the reduction, due to quantum diffusion, in the probability of a coherent hopping process, and is shown to affect the temperature dependence of hopping conductivity. To study the effect, we employ a numerical percolation calculation which includes up to the third nearest-neighbor hoppings. The effect is sizable in the low temperature range where the transport is dominated by long-range hoppings.

Particle number dependence of size and energy quantities in sodium clusters

The effective radial electronic potentials for neutral sodium clusters, which were determined by Ekardt on the basis of the local density approximation and the jellium model, are parameterized by means of the (symmetrized) Woods-Saxon and “wine-bottle”-symmetrized Woods-Saxon potentials with the aim of investigating the dependence of size and energy quantities on the cluster particle number. The potential parameters are determined by various least-squares fitting procedures. It is found that for the radius R of the above potentials, complex expressions are more appropriate than the standard one R = r 0N 1 3 for relatively small values of N. Furthermore, N-power expansions are derived for those complex expressions of R, as well as for the rms radius of the potential. It is also found that improved results in these cases are obtained with an expression of the form R=R 0N 1 3 + b , which is still very simple. There is also investigated the variation of energy quantities, such as the single-particle energies of the 1s and 1p states, the level spacing | E 1p − E 1s| and the average energy-level spacing, with respect to the particle number N. Expressions for the first three of these quantities with N-dependent terms of the form aN t-2 3 + βN −1 give good results. Finally, the total energy per particle is considered with the aim of deriving its asymptotic expression for large values of the particle number.

Single electron and hole quantum dot transistors operating above 110 K

Both single electron and hole quantum dot transistors in silicon-on-insulator were fabricated and characterized. The quantum dots were formed using electron-beam nanolithography and reactive ion etching. The single electron quantum dot transistors show the oscillation of the drain current as a function of the gate voltage at temperatures up to 170 K and drain biases up to 80 mV. The oscillation is due to electron tunneling through the discrete energy levels inside the quantum dot. The average energy level spacing is ∼60 meV. Data analysis shows that the discrete energy levels are caused by Coulomb interaction as well as quantum size effects. The single hole quantum dot transistors show similar oscillations up to 110 K and drain biases up to 50 mV. The average energy level spacing is ∼36 meV.

Single hole quantum dot transistors in silicon

Novel p-channel quantum-dot transistors were fabricated in silicon-on-insulator. Strong oscillations in the drain current as a function of the gate voltage have been observed at temperatures over 81 K and drain biases over 66 mV. The oscillations are attributed to holes tunneling through the discrete single hole energy levels in the quantum dot. Measurements show that the average energy level spacing is ∼35 meV. Simple modeling indicates that about two thirds of the energy level spacing come from the Coulomb interaction between holes (i.e., hole Coulomb blockade) and one third from the quantum confinement effect. The realization of single hole quantum-dot transistors opens new possibilities for innovative circuits that utilize complementary pairs of quantum-dot transistors.

Size Effect on the Width of Plasma Resonance Absorption of Silver Island Films

The size dependence of the half width of the optical plasma resonance absorption of silver island films has been investigated at 293 K. Below a diameter of about 14 A the deviation from the classical prediction was observed. Considering the average energy level spacing and the level broadening due to scatterings, this deviation was attributed to the quantum size-effect. The level broadening estimated from electron-electron scattering in the optical region was of the order of the average energy level spacing of the particle of about 20 A in diameter. Furthermore, the half width was not changed from 293 to 85 K, which agrees with the prediction based on the temperature dependence of this scattering. Therefore, it was concluded that the conduction band is continuous down to diameters of about 20 A because of the level broadening due to electron-electron scattering.