We report a study of disorder effects on epitaxial graphene in the vicinity of the Dirac point by magneto-transport. Hall effect measurements show that the carrier density increases quadratically with temperature, in good agreement with theoretical p
redictions which take into account intrinsic thermal excitation combined with electron-hole puddles induced by charged impurities. We deduce disorder strengths in the range 10.2 $sim$ 31.2 meV, depending on the sample treatment. We investigate the scattering mechanisms and estimate the impurity density to be $3.0 sim 9.1 times 10^{10}$ cm$^{-2}$ for our samples. An asymmetry in the electron/hole scattering is observed and is consistent with theoretical calculations for graphene on SiC substrates. We also show that the minimum conductivity increases with increasing disorder potential, in good agreement with quantum-mechanical numerical calculations.
We propose a new method, semi-penalized inference with direct false discovery rate control (SPIDR), for variable selection and confidence interval construction in high-dimensional linear regression. SPIDR first uses a semi-penalized approach to const
ructing estimators of the regression coefficients. We show that the SPIDR estimator is ideal in the sense that it equals an ideal least squares estimator with high probability under a sparsity and other suitable conditions. Consequently, the SPIDR estimator is asymptotically normal. Based on this distributional result, SPIDR determines the selection rule by directly controlling false discovery rate. This provides an explicit assessment of the selection error. This also naturally leads to confidence intervals for the selected coefficients with a proper confidence statement. We conduct simulation studies to evaluate its finite sample performance and demonstrate its application on a breast cancer gene expression data set. Our simulation studies and data example suggest that SPIDR is a useful method for high-dimensional statistical inference in practice.
High quality strongly correlated two-dimensional (2D) electron systems at low temperatures $Trightarrow 0$ exhibits an apparent metal-to-insulator transition (MIT) at a large $r_s$ value around 40. We have measured the magnetoresistance of 2D holes i
n weak perpendicular magnetic field in the vicinity of the transition for a series of carrier densities ranging from $0.2-1.5times10^{10}$ $cm^{-2}$. The sign of the magnetoresistance is found to be charge density dependent: in the direction of decreasing density, the sign changes from being positive to negative across a characteristic value that coincides with the critical density of MIT.
Comparing the results of transport measurements of strongly correlated two-dimensional holes in a GaAs heterojunction-insulated-gate field-effect-transistor obtained before and after a brief photo-illumination, the light-induced disorder is found to
cause qualitative changes suggesting altered carrier states. For charge concentrations ranging from $3times10^{10}$ $cm^{-2}$ down to $7times10^{8}$ cm$^{-2}$, the post-illumination hole mobility exhibits a severe suppression for charge densities below $2times10^{10}$ cm$^{-2}$, while almost no change for densities above. The long-ranged nature of the disorder is identified. The temperature dependence of the conductivity is also drastically modified by the disorder reconfiguration from being nonactivated to activated.
We study the absolute penalized maximum partial likelihood estimator in sparse, high-dimensional Cox proportional hazards regression models where the number of time-dependent covariates can be larger than the sample size. We establish oracle inequali
ties based on natural extensions of the compatibility and cone invertibility factors of the Hessian matrix at the true regression coefficients. Similar results based on an extension of the restricted eigenvalue can be also proved by our method. However, the presented oracle inequalities are sharper since the compatibility and cone invertibility factors are always greater than the corresponding restricted eigenvalue. In the Cox regression model, the Hessian matrix is based on time-dependent covariates in censored risk sets, so that the compatibility and cone invertibility factors, and the restricted eigenvalue as well, are random variables even when they are evaluated for the Hessian at the true regression coefficients. Under mild conditions, we prove that these quantities are bounded from below by positive constants for time-dependent covariates, including cases where the number of covariates is of greater order than the sample size. Consequently, the compatibility and cone invertibility factors can be treated as positive constants in our oracle inequalities.
We report the first experimental observation of a characteristic nonlinear threshold behavior from dc dynamical response as an evidence for a Wigner crystallization in high-purity GaAs 2D hole systems in zero magnetic field. The system under increasi
ng current drive exhibits voltage oscillations with negative differential resistance. They confirm the coexistence of a moving crystal along with striped edge states as observed for electrons on helium surfaces. However, the threshold is well below the typical classical levels due to a different pinning and depinning mechanism that is possibly related to a quantum process.
We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is small relative to the sample size.
The statistical problem is to determine which additive components are nonzero. The additive components are approximated by truncated series expansions with B-spline bases. With this approximation, the problem of component selection becomes that of selecting the groups of coefficients in the expansion. We apply the adaptive group Lasso to select nonzero components, using the group Lasso to obtain an initial estimator and reduce the dimension of the problem. We give conditions under which the group Lasso selects a model whose number of components is comparable with the underlying model, and the adaptive group Lasso selects the nonzero components correctly with probability approaching one as the sample size increases and achieves the optimal rate of convergence. The results of Monte Carlo experiments show that the adaptive group Lasso procedure works well with samples of moderate size. A data example is used to illustrate the application of the proposed method.
We explain, in the first quantized path integral formalism, the mechanism behind the Anderson-Higgs effect for a gas of charged bosons in a background magnetic field, and then use the method to prove the absence of the effect for a gas of fermions. T
he exchange statistics are encoded via the inclusion of additional Grassmann coordinates in a manner that leads to a manifest worldline supersymmetry. This extra symmetry is key in demonstrating the absence of the effect for charged fermions.
We study the asymptotic properties of bridge estimators in sparse, high-dimensional, linear regression models when the number of covariates may increase to infinity with the sample size. We are particularly interested in the use of bridge estimators
to distinguish between covariates whose coefficients are zero and covariates whose coefficients are nonzero. We show that under appropriate conditions, bridge estimators correctly select covariates with nonzero coefficients with probability converging to one and that the estimators of nonzero coefficients have the same asymptotic distribution that they would have if the zero coefficients were known in advance. Thus, bridge estimators have an oracle property in the sense of Fan and Li [J. Amer. Statist. Assoc. 96 (2001) 1348--1360] and Fan and Peng [Ann. Statist. 32 (2004) 928--961]. In general, the oracle property holds only if the number of covariates is smaller than the sample size. However, under a partial orthogonality condition in which the covariates of the zero coefficients are uncorrelated or weakly correlated with the covariates of nonzero coefficients, we show that marginal bridge estimators can correctly distinguish between covariates with nonzero and zero coefficients with probability converging to one even when the number of covariates is greater than the sample size.
The zero-field temperature-dependence of the resistivity of two-dimensional holes are observed to exhibit two qualitatively different characteristics for a fixed carrier density for which only the metallic behavior of the so-called metal-insulator tr
ansition is anticipated. As $T$ is lowered from 150 mK to 0.5 mK, the sign of the derivative of the resistivity with respect to $T$ changes from being positive to negative when the temperature is lowered below $sim$30 mK and the resistivity continuously rises with cooling down to 0.5 mK, suggesting a crossover from being metal-like to insulator-like.
