Superconductivity in few-layer semiconducting transition-metal dichalcogenides (TMDs) can be induced by field-effect doping through ionic-liquid gating. While several experimental observations have been collected over the years, a fully consistent theoretical picture is still missing. Here we develop a realistic framework that combines the predictive power of first-principles simulations with the versatility and insight of Bardeen-Cooper-Schrieffer gap equations to rationalize such experiments. The multivalley nature of semiconducting TMDs is taken into account, together with the doping- and momentum-dependent electron-phonon and Coulomb interactions. Consistently with experiments, we find that superconductivity occurs when the electron density is large enough that the Q valleys get occupied, as a result of a large enhancement of electron-phonon interactions. Despite being phonon driven, the superconducting state is predicted to be sensitive to Coulomb interactions, which can lead to the appearance of a relative sign difference between valleys and thus to a s + − character. We discuss qualitatively how such scenario may account for many of the observed physical phenomena for which no microscopic explanation has been found so far, including in particular the presence of a large subgap density of states, and the sample-dependent dome-shaped dependence of T c on accumulated electron density. Our results provide a comprehensive analysis of gate-induced superconductivity in semiconducting TMDs, and introduce an approach that will likely be valuable for other multivalley electronic systems, in which superconductivity occurs at relatively low electron density.

Brillouin spectroscopy is a non-invasive method technique for visualizing the mechanical properties of biological samples with sub-micrometer resolution. However, to obtain 2D or even 3D maps, a high-contrast spectrometer is required to effectively reject spurious signals and isolate the signal of interest. In this work, we present an optimized two-stage virtually imaged phased array-based Brillouin spectrometer capable of achieving a contrast of at least 80 dB thanks to a new single diffraction mask, and thus with an unprecedentedly high overall transmission. Numerical simulations of the electric field propagation through the spectrometer and dedicated experiments validate the increase in contrast. We have used the newly developed Brillouin spectrometer coupled to a confocal microscope to obtain 1 h high-resolution 2D images of about 104 spectra of transparent dental pulp stem cells near a MgF2 interface as well as of the much less transparent porcine dentin material, demonstrating its overall stability and reliability.

Mock modular forms, first invented by Ramanujan, provide a beautiful generalization of the usual modular forms. In recent years, it was found that they capture generating functions of the number of microstates of BPS black holes appearing in compactifications of string theory with 8 and 16 supercharges. This review describes these results and their applications which range from the actual computation of these generating functions for both compact and non-compact compactification manifolds (encoding, respectively, Donaldson-Thomas and Vafa-Witten topological invariants) to the construction of new non-commutative structures on moduli spaces of Calabi-Yau threefolds.