Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times. We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.
In doped semiconductors and metals, the Seebeck coefficient or thermopower decreases monotonically with increasing carrier concentration in agreement with the Pisarenko relation. Here, we establish a fundamental mechanism to modulate and increase the thermopower of silicon (Si)/germanium (Ge) heterostructures beyond this relation, induced by the substrate strain. We illustrate the complex relationship between the lattice strain and the modulated thermopower by investigating the electronic structure and cross-plane transport properties of substrate strained [001] Si/Ge superlattices (SLs) with two independent theoretical modeling approaches: first-principles density functional theory and the analytical Krönig–Penny model in combination with the semi-classical Boltzmann transport equation. Our analysis shows that the SL bands, formed due to the cubic structural symmetry, combined with the potential perturbation and the intervalley mixing effects, are highly tunable with epitaxial substrate strain. The strain tuned energy band shifts lead to modulated thermopowers, with a peak approximately fivefold Seebeck enhancement in strained [001] Si/Ge SLs in the high-doping regime. As a consequence, the power factor of a 2.8% substrate strained SL shows a ≈1.8-fold improvement over bulk Si at high carrier concentrations, ≈12×1020cm−3. It is expected that the fundamental understanding discussed here, regarding the complex effect of lattice strain to control energy bands of heterostructures, will help to exploit strain engineering strategies on a class of future technology-enabling materials, such as novel Si/Ge heterostructures as well as layered materials, including van der Waals heterostructures.
Scanning tunneling microscopy is utilized to investigate the local density of states of a CHNHPbICl perovskite in cross-sectional geometry. Two electronic phases, 10-20 nm in size, with different electronic properties inside the CHNHPbICl perovskite layer are observed by the dI/dV mapping and point spectra. A power law dependence of the dI/dV point spectra is revealed. In addition, the distinct electronic phases are found to have preferential orientations close to the normal direction of the film surface. Density functional theory calculations indicate that the observed electronic phases are associated with local deviation of I/Cl ratio, rather than different orientations of the electric dipole moments in the ferroelectric phases. By comparing the calculated results with experimental data we conclude that phase A (lower contrast in dI/dV mapping at -2.0 V bias) contains a lower I/Cl ratio than that in phase B (higher contrast in dI/dV).
First-principles techniques for electronic transport property prediction have seen rapid progress in recent years. However, it remains a challenge to predict properties of heterostructures incorporating fabrication-dependent variability. Machine-learning (ML) approaches are increasingly being used to accelerate design and discovery of new materials with targeted properties, and extend the applicability of first-principles techniques to larger systems. However, few studies exploited ML techniques to characterize relationships between local atomic structures and global electronic transport coefficients. In this work, we propose an electronic-transport-informatics (ETI) framework that trains on ab initio models of small systems and predicts thermopower of fabricated silicon/germanium heterostructures, matching measured data. We demonstrate application of ML approaches to extract important physics that determines electronic transport in semiconductor heterostructures, and bridge the gap between ab initio accessible models and fabricated systems. We anticipate that ETI framework would have broad applicability to diverse materials classes.
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