We study the asymptotic behavior of solution of semi-linear PDEs. Neither periodicity nor ergodicity will be assumed. In return, we assume that the coefficients admit a limit in `{C}esaro sense. In such a case, the averaged coefficients could be disc
ontinuous. We use probabilistic approach based on weak convergence for the associated backward stochastic differential equation in the S-topology to derive the averaged PDE. However, since the averaged coefficients are discontinuous, the classical viscosity solution is not defined for the averaged PDE. We then use the notion of $L^p-$viscosity solution introduced in cite{CCKS}. We use BSDEs techniques to establish the existence of $L^p-$viscosity solution for the averaged PDE. We establish weak continuity for the flow of the limit diffusion process and related the PDE limit to the backward stochastic differential equation via the representation of $L^p$-viscosity solution.
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progre
ss in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler--Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al$_{3}$Mg. The test results show that our implementation can achieve high accuracy, efficiency, and numerical stability for large-scale simulations.
Low-dimensional electronic and glassy phononic transport are two important ingredients of highly-efficient thermoelectric material, from which two branches of the thermoelectric research emerge. One focuses on controlling electronic transport in the
low dimension, while the other on multiscale phonon engineering in the bulk. Recent work has benefited much from combining these two approaches, e.g., phonon engineering in low-dimensional materials. Here, we propose to employ the low-dimensional electronic structure in bulk phonon-glass crystal as an alternative way to increase the thermoelectric efficiency. Through first-principles electronic structure calculation and classical molecular dynamics simulation, we show that the $pi$-$pi$ stacking Bis-Dithienothiophene molecular crystal is a natural candidate for such an approach. This is determined by the nature of its chemical bonding. Without any optimization of the material parameter, we obtain a maximum room-temperature figure of merit, $ZT$, of $1.48$ at optimal doping, thus validating our idea.
We perform detailed magnetotransport studies on two-dimensional electron gases (2DEGs) formed in undoped Si/SiGe heterostructures in order to identify the electron mobility limiting mechanisms in this increasingly important materials system. By analy
zing data from 26 wafers with different heterostructure growth profiles we observe a strong correlation between the background oxygen concentration in the Si quantum well and the maximum mobility. The highest quality wafer supports a 2DEG with a mobility of 160,000 cm^2/Vs at a density 2.17 x 10^11/cm^2 and exhibits a metal-to-insulator transition at a critical density 0.46 x 10^11/cm^2. We extract a valley splitting of approximately 150 microeV at a magnetic field of 1.8 T. These results provide evidence that undoped Si/SiGe heterostructures are suitable for the fabrication of few-electron quantum dots.
We demonstrate a reconfigurable quantum dot gate architecture that incorporates two interchangeable transport channels. One channel is used to form quantum dots and the other is used for charge sensing. The quantum dot transport channel can support e
ither a single or a double quantum dot. We demonstrate few-electron occupation in a single quantum dot and extract charging energies as large as 6.6 meV. Magnetospectroscopy is used to measure valley splittings in the range of 35-70 microeV. By energizing two additional gates we form a few-electron double quantum dot and demonstrate tunable tunnel coupling at the (1,0) to (0,1) interdot charge transition.
We show how the superconducting phase difference in a Josephson junction may be used to split the Kramers degeneracy of its energy levels and to remove all the properties associated with time reversal symmetry. The superconducting phase difference is
known to be ineffective in two-terminal short Josephson junctions, where irrespective of the junction structure the induced Kramers degeneracy splitting is suppressed and the ground state fermion parity must stay even, so that a protected zero-energy Andreev level crossing may never appear. Our main result is that these limitations can be completely avoided by using multi-terminal Josephson junctions. There the Kramers degeneracy breaking becomes comparable to the superconducting gap, and applying phase differences may cause the change of the ground state fermion parity from even to odd. We prove that the necessary condition for the appearance of a fermion parity switch is the presence of a discrete vortex in the junction: the situation when the phases of the superconducting leads wind by $2pi$. Our approach offers new strategies for creation of Majorana bound states as well as spin manipulation. Our proposal can be implemented using any low density, high spin-orbit material such as InAs quantum wells, and can be detected using standard tools.
The quasi-bound states of a superconducting quantum dot that is weakly coupled to a normal metal appear as resonances in the Andreev reflection probability, measured via the differential conductance. We study the evolution of these Andreev resonances
when an external parameter (such as magnetic field or gate voltage) is varied, using a random-matrix model for the $Ntimes N$ scattering matrix. We contrast the two ensembles with broken time-reversal symmetry, in the presence or absence of spin-rotation symmetry (class C or D). The poles of the scattering matrix in the complex plane, encoding the center and width of the resonance, are repelled from the imaginary axis in class C. In class D, in contrast, a number $proptosqrt{N}$ of the poles has zero real part. The corresponding Andreev resonances are pinned to the middle of the gap and produce a zero-bias conductance peak that does not split over a range of parameter values (Y-shaped profile), unlike the usual conductance peaks that merge and then immediately split (X-shaped profile).
Peking University is developing a 1.3 GHz superconducting accelerating section for China Academy of Engineering Physics (CAEP) high power THz free-electron laser. A compact fast/slow tuner has developed by Institute of High Energy Physics (IHEP) for
the accelerating section, to control Lorentz detuning, beam loading effect, compensate for microphonics and liquid Helium pressure fluctuations. The tuner design, warm test and cold test of the first prototype are presented.
We report a Determinant Quantum Monte Carlo investigation which quantifies the behavior of the susceptibility and the entropy in the framework of the periodic Anderson model (PAM), focussing on the evolution with different degree of conduction electr
on (c) -local moment (f) hybridization. These results capture the behavior observed in several experiments, including the universal behavior of the NMR Knight shift anomaly below the crossover temperature, $T^{ast}$. We find that $T^{ast}$ is a measure of the onset of c-f correlations and grows with increasing hybridization. These results suggest that the NMR Knight shift and spin-lattice relaxation rate measurements in non-Fermi liquid materials are strongly influenced by temperature-dependent hybridization processes. Our results provide a microscopic basis for the phenomenological two-fluid model of Kondo lattice behavior, and its evolution with pressure and temperature.
With the best overall electronic and thermal properties, single-crystal diamond (SCD) is the extreme wide bandgap material that is expected to revolutionize power electronics and radio-frequency electronics in the future. However, turning SCD into us
eful semiconductors faces doping challenges, as conventional substitutional doping techniques, such as thermal diffusion and ion-implantation, are not easily applicable to SCD. Here we report a simple and easily accessible doping strategy demonstrating that electrically activated, substitutional boron doping in natural SCD without any phase transitions or lattice damage which can be readily realized with thermal diffusion at relatively low temperature. For the boron doping, we employ a unique dopant carrying medium: heavily doped Si nanomembranes. We further demonstrate selectively doped high-voltage diodes and half-wave rectifier circuits using such doped SCD. Our new doping strategy has established a reachable path toward using SCDs for future high-voltage power conversion systems and for other novel diamond-based electronics.
