Interlayer Affected Diamond Electrochemistry.

Diamond electrochemistry is primarily influenced by quantities of sp3-carbon, surface terminations, and crystalline structure. In this work, a new dimension is introduced by investigating the effect of using substrate-interlayers for diamond growth. Boron and nitrogen co-doped nanocrystalline diamond (BNDD) films are grown on Si substrate without and with Ti and Ta as interlayers, named BNDD/Si, BNDD/Ti/Si, and BNDD/Ta/Ti/Si, respectively. After detailed characterization using microscopies, spectroscopies, electrochemical techniques, and density functional theory simulations, the relationship of composition, interfacial structure, charge transport, and electrochemical properties of the interface between diamond and metal is investigated. The BNDD/Ta/Ti/Si electrodes exhibit faster electron transfer processes than the other two diamond electrodes. The interlayer thus determines the intrinsic activity and reaction kinetics. The reduction in their barrier widths can be attributed to the formation of TaC, which facilitates carrier tunneling, and simultaneously increases the concentration of electrically active defects. As a case study, the BNDD/Ta/Ti/Si electrode is further employed to assemble a redox-electrolyte-based supercapacitor device with enhanced performance. In summary, the study not only sheds light on the intricate relationship between interlayer composition, charge transfer, and electrochemical performance but also demonstrates the potential of tailored interlayer design to unlock new capabilities in diamond-based electrochemical devices.

Graphene-Based Optoelectronic Mixer Device for Time-of-Flight Distance Measurements for Enhanced 3D Imaging Applications.

A large and growing number of applications benefit from innovative and powerful 3D image sensors. Graphene photodetectors can achieve 3D sensing functionalities by intrinsic optoelectronic frequency mixing due to the nonlinear output characteristics of the sensor. In first proof of principle distance measurement demonstrations, we achieve modulation frequencies of 3.1 MHz, signal-to-noise ratios of ∼40 dB, distance detection up to at least 1 m, and a mean accuracy of 25.6 mm. The scalable More than Moore detector approach enables geometrical fill factors close to 100% and can easily complement powerful functionalities by simple back-end integration on top of CMOS electronics.

Kinetic Analysis of the Cation Exchange in Nanorods from Cu2-xS to CuInS2: Influence of Djurleite's Phase Transition Temperature on the Mechanism.

In the syntheses of ternary I-III-VI2 compounds, such as CuInS2, it is often difficult to balance three precursor reactivities to achieve the desired size, shape, and atomic composition of nanocrystals. Cation exchange reactions offer an attractive two-step alternative, by producing a binary compound with the desired morphology and incorporating another atomic species postsynthetically. However, the kinetics of such cation exchange reactions, especially for anisotropic nanocrystals, are still not fully understood. Here, we present the cation exchange reaction from Cu-deficient djurleite Cu2-xS nanorods to wurtzite CuInS2, with size and shape retention. With reaction parameters in a broad temperature range between 40 °C and 160 °C, we were able to obtain various intermediates. Djurleite has a bulk phase transition temperature at 93 °C, which influences the cation exchange considerably. Below the phase transition temperature, indium is only incorporated into the surface of the nanorods, while, at temperatures above the phase transition temperature, we observe a Janus-type exchange mechanism and the formation of CuInS2 bands in the djurleite nanorods. The findings suggest that the diffusion above the phase transition temperature is strongly favored along the copper planes of the copper sulfide nanorods over the diffusion through the sulfur planes. This results in a difference of 37 kJ mol-1 in the activation energy of the cation exchange below and above the phase transition temperature.

Uncertainty Relation between Detection Probability and Energy Fluctuations.

A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.

An in situ and real time study of the formation of CdSe NCs.

Magic Size Clusters (MSCs) have been identified in the last few years as intermediates in the synthesis of nanocrystals (NCs), and ever since there has been increased interest in understanding their exact role in the NC synthesis. Many studies have been focused on understanding the influence of precursors or ligands on the stability of MSCs and on whether the presence of MSCs influences the reaction pathway. However, their kinetic nature calls for an in situ temporal evolution study of the reaction, from the first seconds until the formation of regular nanocrystals, in order to unravel the role of MSCs in the formation of NCs. We have studied the synthesis of CdSe nanocrystals (NCs) in a continuous-flow reactor with in situ optical and small angle X-ray scattering characterization (SAXS). Our results show that MSCs are always formed, regardless the temperature, as necessary intermediates in the formation of CdSe NCs, and that their accumulation in solution depends only on the reaction time. These results explain why MSCs were, in some cases, not observed in some previous studies.

First Detected Arrival of a Quantum Walker on an Infinite Line.

The first detection of a quantum particle on a graph is shown to depend sensitively on the distance ξ between the detector and initial location of the particle, and on the sampling time τ. Here, we use the recently introduced quantum renewal equation to investigate the statistics of first detection on an infinite line, using a tight-binding lattice Hamiltonian with nearest-neighbor hops. Universal features of the first detection probability are uncovered and simple limiting cases are analyzed. These include the large ξ limit, the small τ limit, and the power law decay with the attempt number of the detection probability over which quantum oscillations are superimposed. For large ξ the first detection probability assumes a scaling form and when the sampling time is equal to the inverse of the energy band width nonanalytical behaviors arise, accompanied by a transition in the statistics. The maximum total detection probability is found to occur for τ close to this transition point. When the initial location of the particle is far from the detection node we find that the total detection probability attains a finite value that is distance independent.

Using Hilbert transform and classical chains to simulate quantum walks.

We propose a simulation strategy which uses a classical device of linearly coupled chain of springs to simulate quantum dynamics, in particular quantum walks. Through this strategy, we obtain the quantum wave function from the classical evolution. Specially, this goal is achieved with the classical momenta of the particles on the chain and their Hilbert transform, from which we construct the many-body momentum and Hilbert transformed momentum pair correlation functions yielding the real and imaginary parts of the wave function, respectively. With such a wave function, we show that the classical chain's energy and heat spreading densities can be related to the wave function's modulus square. This relation provides a new perspective to understand ballistic heat transport. The results here may give a definite answer to Feynman's idea of using a classical device to simulate quantum physics.

Time averages in continuous-time random walks.

We investigate the time-averaged square displacement (TASD) of continuous-time random walks with respect to the number of steps N which the random walker performed during the data acquisition time T. We prove that in each realization the TASD grows asymptotically linear in the lag time τ and in N, provided the steps cannot accumulate in small intervals. Consequently, the fluctuations of the latter are dominated by the fluctuations of N, and fluctuations of the walker's thermal history are irrelevant. Furthermore, we show that the relative scatter decays as 1/sqrt[N], which suppresses all nonlinear features in a plot of the TASD against the lag time. Parts of our arguments also hold for continuous-time random walks with correlated steps or with correlated waiting times.

Effective-medium approximation for lattice random walks with long-range jumps.

We consider the random walk on a lattice with random transition rates and arbitrarily long-range jumps. We employ Bruggeman's effective-medium approximation (EMA) to find the disorder-averaged (coarse-grained) dynamics. The EMA procedure replaces the disordered system with a cleverly guessed reference system in a self-consistent manner. We give necessary conditions on the reference system and discuss possible physical mechanisms of anomalous diffusion. In the case of a power-law scaling between transition rates and distance, lattice variants of Lévy-flights emerge as the effective medium, and the problem is solved analytically, bearing the effective anomalous diffusivity. Finally, we discuss several example distributions and demonstrate very good agreement with numerical simulations.

Scaled Brownian motion as a mean-field model for continuous-time random walks.

We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient D(t)=αD0tα-1 (Batchelor's equation) which, for α<1, is often used for fitting experimental data for subdiffusion of unclear genesis. We show that this process is a close relative of subdiffusive continuous-time random walks and describes the motion of the rescaled mean position of a cloud of independent walkers. It shares with subdiffusive continuous-time random walks its nonstationary and nonergodic properties. The nonergodicity of sBm does not however go hand in hand with strong difference between its different realizations: its heterogeneity ("ergodicity breaking") parameter tends to zero for long trajectories.

Weak ergodicity breaking in an anomalous diffusion process of mixed origins.

The ergodicity breaking parameter is a measure for the heterogeneity among different trajectories of one ensemble. In this report, this parameter is calculated for fractional Brownian motion with a random change of time scale, often called "subordination." We show that this quantity is the same as the known continuous time random walks case.

Disentangling sources of anomalous diffusion.

We show that some important properties of subdiffusion of unknown origin (including ones of mixed origins) can be easily assessed when finding the "fundamental moment" of the corresponding random process, i.e., the one which is additive in time. In subordinated processes, the index of the fundamental moment is inherited from the parent process and its time dependence from the leading one. In models of a particle's motion in disordered potentials, the index is governed by the structural part of the disorder while the time dependence is given by its energetic part.

Anomalous diffusion in run-and-tumble motion.

A random walk scheme, consisting of alternating phases of regular Brownian motion and Lévy walks, is proposed as a model for run-and-tumble bacterial motion. Within the continuous-time random walk approach we obtain the long-time and short-time behavior of the mean squared displacement of the walker as depending on the properties of the dwelling time distribution in each phase. Depending on these distributions, normal diffusion, superdiffusion, and ballistic spreading may arise.