Theoretical study of the charge transport through C60-based single-molecule junctions

We present a theoretical study of the conductance and thermopower of single-molecule junctions based on C60 and C60-terminated molecules. We first analyze the transport properties of gold-C60-gold junctions and show that these junctions can be highly conductive (with conductances above 0.1G0, where G0 is the quantum of conductance). Moreover, we find that the thermopower in these junctions is negative due to the fact that the LUMO dominates the charge transport, and its magnitude can reach several tens of micro-V/K, depending on the contact geometry. On the other hand, we study the suitability of C60 as an anchoring group in single-molecule junctions. For this purpose, we analyze the transport through several dumbbell derivatives using C60 as anchors, and we compare the results with those obtained with thiol and amine groups. Our results show that the conductance of C60-terminated molecules is rather sensitive to the binding geometry. Moreover, the conductance of the molecules is typically reduced by the presence of the C60 anchors, which in turn makes the junctions more sensitive to the functionalization of the molecular core with appropriate side groups.Comment: 9 pages, 7 figure

Measuring dopant concentrations in compensated p-type crystalline silicon via iron-acceptor pairing

We present a method for measuring the concentrations of ionized acceptors and donors in compensated p-type silicon at room temperature.Carrier lifetimemeasurements on silicon wafers that contain minute traces of iron allow the iron-acceptor pair formation rate to be determined, which in turn allows the acceptor concentration to be calculated. Coupled with an independent measurement of the resistivity and a mobility model that accounts for majority and minority impurity scatterings of charge carriers, it is then possible to also estimate the total concentration of ionized donors. The method is valid for combinations of different acceptor and donor species.D.M. is supported by an Australian Research Council fellowship. L.J.G. would like to acknowledge SenterNovem for support

Anderson transition in systems with chiral symmetry

Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped semiconductors. We investigate the interplay of these two phenomena in the context of a three-dimensional disordered system. We show that chiral symmetry induces an Anderson transition (AT) in the region close to the band center. Typical properties at the AT such as multifractality and critical statistics are quantitatively affected by this additional symmetry. The origin of the AT has been traced back to the power-law decay of the eigenstates; this feature may also be relevant in systems without chiral symmetry.Comment: RevTex4, 4 two-column pages, 3 .eps figures, updated references, final version as published in Phys. Rev.

On the use of reproducing kernel Hilbert spaces in functional classification

The H\'ajek-Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon-Nikodym density for each measure with respect to the other one) or mutually singular. Unlike the case of finite dimensional Gaussian measures, there are non-trivial examples of both situations when dealing with Gaussian stochastic processes. This paper provides: (a) Explicit expressions for the optimal (Bayes) rule and the minimal classification error probability in several relevant problems of supervised binary classification of mutually absolutely continuous Gaussian processes. The approach relies on some classical results in the theory of Reproducing Kernel Hilbert Spaces (RKHS). (b) An interpretation, in terms of mutual singularity, for the "near perfect classification" phenomenon described by Delaigle and Hall (2012). We show that the asymptotically optimal rule proposed by these authors can be identified with the sequence of optimal rules for an approximating sequence of classification problems in the absolutely continuous case. (c) A new model-based method for variable selection in binary classification problems, which arises in a very natural way from the explicit knowledge of the RN-derivatives and the underlying RKHS structure. Different classifiers might be used from the selected variables. In particular, the classical, linear finite-dimensional Fisher rule turns out to be consistent under some standard conditions on the underlying functional model

Non-ergodic phases in strongly disordered random regular graphs

We combine numerical diagonalization with a semi-analytical calculations to prove the existence of the intermediate non-ergodic but delocalized phase in the Anderson model on disordered hierarchical lattices. We suggest a new generalized population dynamics that is able to detect the violation of ergodicity of the delocalized states within the Abou-Chakra, Anderson and Thouless recursive scheme. This result is supplemented by statistics of random wave functions extracted from exact diagonalization of the Anderson model on ensemble of disordered Random Regular Graphs (RRG) of N sites with the connectivity K=2. By extrapolation of the results of both approaches to N->infinity we obtain the fractal dimensions D_{1}(W) and D_{2}(W) as well as the population dynamic exponent D(W) with the accuracy sufficient to claim that they are non-trivial in the broad interval of disorder strength W_{E}<W<W_{c}. The thorough analysis of the exact diagonalization results for RRG with N>10^{5} reveals a singularity in D_{1,2}(W)-dependencies which provides a clear evidence for the first order transition between the two delocalized phases on RRG at W_{E}\approx 10.0. We discuss the implications of these results for quantum and classical non-integrable and many-body systems.Comment: 4 pages paper with 5 figures + Supplementary Material with 5 figure

Two-dimensional discrete solitons in rotating lattices

We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two species of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance $R$ from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities $$ and 2. At a fixed value of rotation frequency $\Omega$, a stability interval for the FSs is found in terms of the lattice coupling constant $C$, , with monotonically decreasing $C_{\mathrm{cr}}(R)$. VSs with S=1 have a stability interval, \tilde{C}_{\mathrm{cr}%}^{(S=1)}(\Omega), which exists for $$ below a certain critical value, $\Omega_{\mathrm{cr}}^{(S=1)}$. This implies that the VSs with S=1 are \emph{destabilized} in the weak-coupling limit by the rotation. On the contrary, VSs with S=2, that are known to be unstable in the standard DNLS equation, with $\Omega =0$, are \emph{stabilized} by the rotation in region $0<C<C_{\mathrm{cr}}^{(S=2)}$%, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a function of $\Omega$. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by $\Omega \neq 0$.Comment: To be published in Physical Review

Impulse-induced localized nonlinear modes in an electrical lattice

Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the efectiveness of generic periodic excitations of variable waveform at generating discrete breathers in such lattices. We have found that this generation phenomenon is optimally controlled by the impulse transmitted by the external excitation (time integral over two consecutive zerosComment: 5 pages, 8 figure

Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections

Motivated by recent scanning tunneling microscopy experiments on single magnetic impurities on superconducting surfaces, we present here a comprehensive theoretical study of the interplay between Yu-Shiba-Rusinov bound states and (multiple) Andreev reflections. Our theory is based on a combination of an Anderson model with broken spin degeneracy and nonequilibrium Green's function techniques that allows us to describe the electronic transport through a magnetic impurity coupled to superconducting leads for arbitrary junction transparency. Using this combination we are able to elucidate the different tunneling processes that give a significant contribution to the subgap transport. In particular, we predict the occurrence of a large variety of Andreev reflections mediated by Yu-Shiba-Rusinov bound states that clearly differ from the standard Andreev processes in non-magnetic systems. Moreover, we provide concrete guidelines on how to experimentally identify the subgap features originating from these tunneling events. Overall, our work provides new insight into the role of the spin degree of freedom in Andreev transport physics.Comment: 15 pages, 10 figure

Critical generalized inverse participation ratio distributions

The system size dependence of the fluctuations in generalized inverse participation ratios (IPR's) $I_{\alpha}(q)$ at criticality is investigated numerically. The variances of the IPR logarithms are found to be scale-invariant at the macroscopic limit. The finite size corrections to the variances decay algebraically with nontrivial exponents, which depend on the Hamiltonian symmetry and the dimensionality. The large-$q$ dependence of the asymptotic values of the variances behaves as $q^2$ according to theoretical estimates. These results ensure the self-averaging of the corresponding generalized dimensions.Comment: RevTex4, 5 pages, 4 .eps figures, to be published in Phys. Rev.