Long-Range Energy-Level Interaction in Small Metallic Particles

We consider the energy level statistics of non-interacting electrons which diffuse in a $d$-dimensional disordered metallic conductor of characteristic Thouless energy $E_c.$ We assume that the level distribution can be written as the Gibbs distribution of a classical one-dimensional gas of fictitious particles with a pairwise additive interaction potential $f(\varepsilon ).$ We show that the interaction which is consistent with the known correlation function of pairs of energy levels is a logarithmic repulsion for level separations $\varepsilon <E_c,$ in agreement with Random Matrix Theory. When $\varepsilon >E_c,$ $f(\varepsilon )$ vanishes as a power law in $\varepsilon /E_c$ with exponents $-{1 \over 2},-2,$ and $-{3 \over 2}$ for $d=1,2,$ and 3, respectively. While for $d=1,2$ the energy-level interaction is always repulsive, in three dimensions there is long-range level attraction after the short-range logarithmic repulsion.Comment: Saclay-s93/014 Email: [email protected] [2017: missing figure included

Theory of scanning gate microscopy

A systematic theory of the conductance measurements of non-invasive (weak probe) scanning gate microscopy is presented that provides an interpretation of what precisely is being measured. A scattering approach is used to derive explicit expressions for the first and second order conductance changes due to the perturbation by the tip potential in terms of the scattering states of the unperturbed structure. In the case of a quantum point contact, the first order correction dominates at the conductance steps and vanishes on the plateaus where the second order term dominates. Both corrections are non-local for a generic structure. Only in special cases, such as that of a centrally symmetric quantum point contact in the conductance quantization regime, can the second order correction be unambiguously related with the local current density. In the case of an abrupt quantum point contact we are able to obtain analytic expressions for the scattering eigenfunctions and thus evaluate the resulting conductance corrections.Comment: 19 pages, 7 figure

Universal Quantum Signatures of Chaos in Ballistic Transport

The conductance of a ballistic quantum dot (having chaotic classical dynamics and being coupled by ballistic point contacts to two electron reservoirs) is computed on the single assumption that its scattering matrix is a member of Dyson's circular ensemble. General formulas are obtained for the mean and variance of transport properties in the orthogonal (beta=1), unitary (beta=2), and symplectic (beta=4) symmetry class. Applications include universal conductance fluctuations, weak localization, sub-Poissonian shot noise, and normal-metal-superconductor junctions. The complete distribution P(g) of the conductance g is computed for the case that the coupling to the reservoirs occurs via two quantum point contacts with a single transmitted channel. The result P(g)=g^(-1+beta/2) is qualitatively different in the three symmetry classes. ***Submitted to Europhysics Letters.****Comment: 4 pages, REVTeX-3.0, INLO-PUB-94032

Semiclassical Theory of Time-Reversal Focusing

Time reversal mirrors have been successfully implemented for various kinds of waves propagating in complex media. In particular, acoustic waves in chaotic cavities exhibit a refocalization that is extremely robust against external perturbations or the partial use of the available information. We develop a semiclassical approach in order to quantitatively describe the refocusing signal resulting from an initially localized wave-packet. The time-dependent reconstructed signal grows linearly with the temporal window of injection, in agreement with the acoustic experiments, and reaches the same spatial extension of the original wave-packet. We explain the crucial role played by the chaotic dynamics for the reconstruction of the signal and its stability against external perturbations.Comment: 4 pages, 1 figur

Shot noise in the chaotic-to-regular crossover regime

We investigate the shot noise for phase-coherent quantum transport in the chaotic-to-regular crossover regime. Employing the Modular Recursive Green's Function Method for both ballistic and disordered two-dimensional cavities we find the Fano factor and the transmission eigenvalue distribution for regular systems to be surprisingly similar to those for chaotic systems. We argue that in the case of regular dynamics in the cavity, diffraction at the lead openings is the dominant source of shot noise. We also explore the onset of the crossover from quantum to classical transport and develop a quasi-classical transport model for shot noise suppression which agrees with the numerical quantum data.Comment: 4 pages, 3 figures, submitted to Phys.Rev.Let

Lifetime of the first and second collective excitations in metallic nanoparticles

We determine the lifetime of the surface plasmon in metallic nanoparticles under various conditions, concentrating on the Landau damping, which is the dominant mechanism for intermediate-size particles. Besides the main contribution to the lifetime, which smoothly increases with the size of the particle, our semiclassical evaluation yields an additional oscillating component. For the case of noble metal particles embedded in a dielectric medium, it is crucial to consider the details of the electronic confinement; we show that in this case the lifetime is determined by the shape of the self-consistent potential near the surface. Strong enough perturbations may lead to the second collective excitation of the electronic system. We study its lifetime, which is limited by two decay channels: Landau damping and ionization. We determine the size dependence of both contributions and show that the second collective excitation remains as a well defined resonance.Comment: 18 pages, 5 figures; few minor change

Growth and optical properties of GaN/AlN quantum wells

We demonstrate the growth of GaN/AlN quantum well structures by plasma-assisted molecular-beam epitaxy by taking advantage of the surfactant effect of Ga. The GaN/AlN quantum wells show photoluminescence emission with photon energies in the range between 4.2 and 2.3 eV for well widths between 0.7 and 2.6 nm, respectively. An internal electric field strength of $9.2\pm 1.0$ MV/cm is deduced from the dependence of the emission energy on the well width.Comment: Submitted to AP

Contribution of polycyclic aromatic hydrocarbon ionization to neutral gas heating in galaxies: model versus observations

[Abridged] The ionization of polycyclic aromatic hydrocarbons (PAHs), by ultraviolet (UV) photons from massive stars is expected to account for a large fraction of the heating of neutral gas in galaxies. Evaluation of this proposal, however, has been limited by our ability to directly compare observational diagnostics to the results of a molecular model describing PAH ionization. The objective of this article is to take advantage of the most recent values of molecular parameters derived from laboratory experiments and quantum chemical calculations on PAHs and provide a detailed comparison between modeled values and observational diagnostics for the PAH charge state and the heating efficiency for PAHs. Despite the use of a simple analytical model, we obtain a good agreement between model results and observational diagnostics over a wide range of radiation fields and physical conditions, in environments such as star-forming regions, galaxies, and protoplanetary disks. In addition, we found that the modeled photoelectric heating rates by PAHs are close to the observed cooling rates given by the gas emission. These results show that PAH ionization is the main source of neutral gas heating in these environments. The results of our photoelectric heating model by PAHs can thus be used to assess the contribution of UV radiative heating in galaxies (vs shocks, for instance). We provide the empirical formulas fitted to the model results, and the full python code itself, to calculate the heating rates and heating efficiencies for PAHs.Comment: Accepted for publication in Astronomy and Astrophysic

Scanning gate experiments: from strongly to weakly invasive probes

An open resonator fabricated in a two-dimensional electron gas is used to explore the transition from strongly invasive scanning gate microscopy to the perturbative regime of weak tip-induced potentials. With the help of numerical simulations that faithfully reproduce the main experimental findings, we quantify the extent of the perturbative regime in which the tip-induced conductance change is unambiguously determined by properties of the unperturbed system. The correspondence between the experimental and numerical results is established by analyzing the characteristic length scale and the amplitude modulation of the conductance change. In the perturbative regime, the former is shown to assume a disorder-dependent maximum value, while the latter linearly increases with the strength of a weak tip potential.Comment: 11 pages, 7 figure

Embedding method for the scattering phase in strongly correlated quantum dots

The embedding method for the calculation of the conductance through interacting systems connected to single channel leads is generalized to obtain the full complex transmission amplitude that completely characterizes the effective scattering matrix of the system at the Fermi energy. We calculate the transmission amplitude as a function of the gate potential for simple diamond-shaped lattice models of quantum dots with nearest neighbor interactions. In our simple models we do not generally observe an interaction dependent change in the number of zeroes or phase lapses that depend only on the symmetry properties of the underlying lattice. Strong correlations separate and reduce the widths of the resonant peaks while preserving the qualitative properites of the scattering phase.Comment: 11 pages, 3 figures. Proceedings of the Workshop on Advanced Many-Body and Statistical Methods in Mesoscopic Systems, Constanta, Romania, June 27th - July 2nd 2011. To appear in Journal of Physics: Conference Serie