Anomalous Hall effect in heavy electron materials

We propose a new empirical formula for the anomalous Hall effect in heavy electron materials based on a phenomenological two-fluid description of the f-electron states. The new formula incorporates two previous theories proposed by Fert and Levy in 1987 and Kontani et al. in the early 1990s and takes into account both incoherent and coherent skew scatterings from local and itinerant f-electrons. We perform experimental analysis in several heavy electron compounds and show that the new formula provides a consistent description of the evolution of the Hall coefficient in the whole temperature range down to only a few Kelvin.Comment: 6 pages, 4 figure

APPLE: Approximate Path for Penalized Likelihood Estimators

In high-dimensional data analysis, penalized likelihood estimators are shown to provide superior results in both variable selection and parameter estimation. A new algorithm, APPLE, is proposed for calculating the Approximate Path for Penalized Likelihood Estimators. Both the convex penalty (such as LASSO) and the nonconvex penalty (such as SCAD and MCP) cases are considered. The APPLE efficiently computes the solution path for the penalized likelihood estimator using a hybrid of the modified predictor-corrector method and the coordinate-descent algorithm. APPLE is compared with several well-known packages via simulation and analysis of two gene expression data sets.Comment: 24 pages, 9 figure

Universal Behavior in Heavy Electron Materials

We present our finding that an especially simple scaling expression describes the formation of a new state of quantum matter, the Kondo Fermi liquid (KL) in heavy electron materials. Emerging at $T^*$ as a result of the collective coherent hybridization of localized f electrons and conduction electrons, the KL possesses a non-Landau density of states varying as $(1-T/T^*)^{3/2}[1+\ln(T^*/T)]$. We show that four independent experimental probes verify this scaling behavior and that for CeIrIn$_5$ the KL state density is in excellent agreement with the recent microscopic calculations of hybridization in this material by Shim, Haule, and Kotliar.Comment: 4 pages, 5 figure