Fragmentation of percolation clusters at the percolation threshold

A scaling theory and simulation results are presented for fragmentation of percolation clusters by random bond dilution. At the percolation threshold, scaling forms describe the average number of fragmenting bonds and the distribution of cluster masses produced by fragmentation. A relationship between the scaling exponents and standard percolation exponents is verified in one dimension, on the Bethe lattice, and for Monte Carlo simulations on a square lattice. These results further describe the structure of percolation clusters and provide kernels relevant to rate equations for fragmentation

Microwave-frequency scanning gate microscopy of a Si/SiGe double quantum dot

Conventional quantum transport methods can provide quantitative information on spin, orbital, and valley states in quantum dots, but often lack spatial resolution. Scanning tunneling microscopy, on the other hand, provides exquisite spatial resolution of the local electronic density of states, but often at the expense of speed. Working to combine the spatial resolution and energy sensitivity of scanning probe microscopy with the speed of microwave measurements, we couple a metallic probe tip to a Si/SiGe double quantum dot that is integrated with a local charge detector. We first demonstrate that a dc-biased tip can be used to change the charge occupancy of the double dot. We then apply microwave excitation through the scanning tip to drive photon-assisted tunneling transitions in the double dot. We infer the double dot energy level diagram from the frequency and detuning dependence of the photon-assisted tunneling resonance condition. These measurements allow us to resolve $\sim$65 $\mu$eV excited states, an energy scale consistent with typical valley splittings in Si/SiGe. Future extensions of this approach may allow spatial mapping of the valley splitting in Si devices, which is of fundamental importance for spin-based quantum processors

Scaling in Late Stage Spinodal Decomposition with Quenched Disorder

We study the late stages of spinodal decomposition in a Ginzburg-Landau mean field model with quenched disorder. Random spatial dependence in the coupling constants is introduced to model the quenched disorder. The effect of the disorder on the scaling of the structure factor and on the domain growth is investigated in both the zero temperature limit and at finite temperature. In particular, we find that at zero temperature the domain size, $R(t)$, scales with the amplitude, $A$, of the quenched disorder as $R(t) = A^{-\beta} f(t/A^{-\gamma})$ with $\beta \simeq 1.0$ and $\gamma \simeq 3.0$ in two dimensions. We show that $\beta/\gamma = \alpha$, where $\alpha$ is the Lifshitz-Slyosov exponent. At finite temperature, this simple scaling is not observed and we suggest that the scaling also depends on temperature and $A$. We discuss these results in the context of Monte Carlo and cell dynamical models for phase separation in systems with quenched disorder, and propose that in a Monte Carlo simulation the concentration of impurities, $c$, is related to $A$ by $A \sim c^{1/d}$.Comment: RevTex manuscript 5 pages and 5 figures (obtained upon request via email [email protected]

Modeling, Design, and Optimization of a Solid State Electron Spin Qubit

This paper describes a solid state system in which a qubit is realized as the spin of a single trapped electron in a quantum dot and read functionality is via an adjacent quantum wire with a single or a small number of conductive states. Because of the limited design window for this system, simulation is an important guide to an experimental search for successful designs. We use a semianalytic approximation that is accurate enough to provide meaningful results and computationally simple enough to allow high throughput, as needed for design and optimization. In particular, we find designs that achieve double pinchoff (i.e., a single trapped electron in the dot and a single conductive state in the wire). After relaxing the design requirements to allow for a small number of conductive states in the wire, we find successful designs that are optimally robust, in the sense that their success is unlikely to be affected by fabrication errors

Kinetics of Phase Separation in the Presence of Two Disparate Energy Scales

We develop a dynamical model for phase separation in a system with two disparate energy scales. Monte Carlo computer simulations of this model reveal a "pinning" of the structure factor during spinodal decomposition that obeys new scaling relations. We propose a mechanism for the pinning which allows us to predict The model contains monomers and solvent molecules on a lattice, with the key feature that nearest-neighbor monomers can interact with two different energies One probe in phase separation experiments is the dynamic structure factor, S(k, t), which contains information on the time evolution of the various length scales k . In ordinary spinodal decomposition, the characteristic wave vector moves to smaller values of k following a quench to the unstable region. One measure of this characteristic wave vector is the first moment of S(k), ki = Q"kS(k)/Q"S(k

Pinning in phase-separating systems.

We study a dynamical model of a system with two disparate energy scales, and focus on the kinetics of phase separation. In this model, nearest-neighbor monomers can interact with one of two quite distinct energies, thereby describing a system with, e. g., van der Waals and hydrogen bond interactions. While the model has been described by an efFective Ising model in equilibrium, the nonequilibrium dynamics of phase separation have never been explored. Here we use Monte Carlo computer simulations of spinodal decomposition to show that the model exhibits "pinning" of the structure factor, a behavior also seen in phase-separating polymer gels and binary alloys with impurities. The rate of strong bond formation depends on an entropic parameter 0, and we fInd both the pinned domain size and the crossover time between "normal" spinodal decomposition and the pinning scale with 0 as power laws with exponents that relate simply to the usual growth exponent. We propose a speci6c mechanism for pinning that permits the prediction of exact values for the pinning exponents. Finally, we discuss applications of the model to binary alloys with quenched disorder and polymer gels