Tunable bandgaps and excitons in doped semiconducting carbon nanotubes made possible by acoustic plasmons

Doping of semiconductors is essential in modern electronic and photonic devices. While doping is well understood in bulk semiconductors, the advent of carbon nanotubes and nanowires for nanoelectronic and nanophotonic applications raises some key questions about the role and impact of doping at low dimensionality. Here we show that for semiconducting carbon nanotubes, bandgaps and exciton binding energies can be dramatically reduced upon experimentally relevant doping, and can be tuned gradually over a broad range of energies in contrast to higher dimensional systems. The later feature is made possible by a novel mechanism involving strong dynamical screening effects mediated by acoustic plasmons.Comment: 5 pages, 4 figures, published in Phys. Rev. Lett

Primitive geodesic lengths and (almost) arithmetic progressions

In this article, we investigate when the set of primitive geodesic lengths on a Riemannian manifold have arbitrarily long arithmetic progressions. We prove that in the space of negatively curved metrics, a metric having such arithmetic progressions is quite rare. We introduce almost arithmetic progressions, a coarsification of arithmetic progressions, and prove that every negatively curved, closed Riemannian manifold has arbitrarily long almost arithmetic progressions in its primitive length spectrum. Concerning genuine arithmetic progressions, we prove that every non-compact, locally symmetric, arithmetic manifold has arbitrarily long arithmetic progressions in its primitive length spectrum. We end with a conjectural characterization of arithmeticity in terms of arithmetic progressions in the primitive length spectrum. We also suggest an approach to a well known spectral rigidity problem based on the scarcity of manifolds with arithmetic progressions.Comment: v3: 23 pages. To appear in Publ. Ma

Advances in Feature Selection with Mutual Information

The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the performances of prediction or classification methods, and interpreting the application. In a nonlinear context, the mutual information is widely used as relevance criterion for features and sets of features. Nevertheless, it suffers from at least three major limitations: mutual information estimators depend on smoothing parameters, there is no theoretically justified stopping criterion in the feature selection greedy procedure, and the estimation itself suffers from the curse of dimensionality. This chapter shows how to deal with these problems. The two first ones are addressed by using resampling techniques that provide a statistical basis to select the estimator parameters and to stop the search procedure. The third one is addressed by modifying the mutual information criterion into a measure of how features are complementary (and not only informative) for the problem at hand

Atomistic study of an ideal metal/thermoelectric contact: the full-Heusler/half-Heusler interface

Half-Heusler alloys such as the (Zr,Hf)NiSn intermetallic compounds are important thermoelectric materials for converting waste heat into electricity. Reduced electrical resistivity at the hot interface between the half-Heusler material and a metal contact is critical for device performance, however this has yet to be achieved in practice. Recent experimental work suggests that a coherent interface between half-Heusler and full-Heusler compounds can form due to diffusion of transition metal atoms into the vacant sublattice of the half-Heusler lattice. We study theoretically the structural and electronic properties of such an interface using a first-principles based approach that combines {\it ab initio} calculations with macroscopic modeling. We find that the prototypical interface HfNi$_2$Sn/HfNiSn provides very low contact resistivity and almost ohmic behavior over a wide range of temperatures and doping levels. Given the potential of these interfaces to remain stable over a wide range of temperatures, our study suggests that full-Heuslers might provide nearly ideal electrical contacts to half-Heuslers that can be harnessed for efficient thermoelectric generator devices.Comment: 8 pages, 8 figure