Extent Of Electron Wave Function Research Articles

The Transition to the Metallic State in Alkali and Low-Z Fluids

Abstract We review here experiments that investigate how the electronic properties of five chemically dissimilar fluid elements, hydrogen, nitrogen, oxygen, rubidium and caesium, vary with density beyond their critical points. Remarkably, all five elements in their metallic regime have essentially the same electrical conductivities, close to the predicted minimum metallic conductivity of a high-temperature, disordered metallic fluid. The large differences in their respective metal-nonmetal transition densities are rationalized in terms of each chemical element’s unique atomic properties of size (radial extent of electronic wave function, N.F.Mott) and electronic polarizability (K.F.Herzfeld and D.A.Goldhammer). These experiments thereby highlight the pivotal role of atomic properties in dictating the metallic or nonmetallic status of chemical elements of the periodic classification.

Localization-delocalization transition in quantum dots

Single-electron capacitance spectroscopy precisely measures the energies required to add individual electrons to a quantum dot. The spatial extent of electronic wave functions is probed by investigating the dependence of these energies on changes in the dot confining potential. For low electron densities, electrons occupy distinct spatial sites localized within the dot. At higher densities, the electrons become delocalized, and all wave functions are spread over the full dot area. Near the delocalization transition, the last remaining localized states exist at the perimeter of the dot. Unexpectedly, these electrons appear to bind with electrons in the dot center.

Tunneling spectroscopy of quantum dots using submicrometer-diameterAlxGa1−xAs-GaAs triple-barrier diodes

We have studied resonant tunneling (RT) through ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$ As-GaAs triple-barrier diodes with diameters between 0.2 and 10 \ensuremath{\mu}m. We have observed fine structures just above and below the RT threshold voltage ${\mathrm{V}}_{\mathrm{th}}$ in the current-voltage curve of a submicrometer diode at T=4 K. With a diameter of 0.4\char21{}0.8 \ensuremath{\mu}m, the magnetic-field dependence and the sample dependence of the structure unambiguously show that (1) fine structures above ${\mathrm{V}}_{\mathrm{th}}$ are caused by resonant tunneling (RT) through zero-dimensional (0D) states and coupled-0D states confined by the diode side-wall depletion region with a parabolic potential, and (2) fine structures below ${\mathrm{V}}_{\mathrm{th}}$ are caused by RT through shallow-donor-bound states. Energy spacings of side-wall confined states and shallow-donor-bound energy are estimated to be 6.5 and 15\char21{}20 meV, respectively, which are consistent with a simple model. The tunneling current through the side-wall confined state is found to be proportional to the degeneracy of the 0D level confined by the parabolic potential. With a diameter of 0.2\char21{}0.3 \ensuremath{\mu}m, fine structures superimposed on the steplike structure were observed. We consider that those interplay between the 0D tunneling and a Coulomb blockade. The radius of a quantum dot estimated from a Coulomb staircase of 14 nm is in reasonable agreement with the extent of electron wavefunction in a quantum dot of 12 nm.

Stark ladders in periodically Si- delta -doped GaAs.

We study theoretically the electronic structure of periodically Si delta-doped GaAs subject to a homogeneous electric field applied along the growth direction. The space-charge potential due to delta doping is obtained by means of the Thomas-Fermi approach. Analyzing the change in the density of states in the superlattice introduced in the electric field, we observe a set of equally-spaced sharp peaks corresponding to Stark-ladder resonances. Intrinsic broadening of resonances turns out to be smaller than the level spacing in the whole range of the electric field we consider. We use the inverse participation ratio to evaluate the spatial extent of electron wave functions, and we find that the Stark-ladder spectrum is related to a strong-localization regime at high field.