Geometry of good sets in n-fold Cartesian product

We propose here a multidimensional generalisation of the notion of link introduced in our previous papers and we discuss some consequences for simplicial measures and sums of function algebras.Comment: 17 pages, no figures, no table

Probing the inter-layer exciton physics in a MoS2_2/MoSe2_2/MoS2_2 van der Waals heterostructure

Stacking atomic monolayers of semiconducting transition metal dichalcogenides (TMDs) has emerged as an effective way to engineer their properties. In principle, the staggered band alignment of TMD heterostructures should result in the formation of inter-layer excitons with long lifetimes and robust valley polarization. However, these features have been observed simultaneously only in MoSe$_2$/WSe$_2$ heterostructures. Here we report on the observation of long lived inter-layer exciton emission in a MoS$_2$/MoSe$_2$/MoS$_2$ trilayer van der Waals heterostructure. The inter-layer nature of the observed transition is confirmed by photoluminescence spectroscopy, as well as by analyzing the temporal, excitation power and temperature dependence of the inter-layer emission peak. The observed complex photoluminescence dynamics suggests the presence of quasi-degenerate momentum-direct and momentum-indirect bandgaps. We show that circularly polarized optical pumping results in long lived valley polarization of inter-layer exciton. Intriguingly, the inter-layer exciton photoluminescence has helicity opposite to the excitation. Our results show that through a careful choice of the TMDs forming the van der Waals heterostructure it is possible to control the circular polarization of the inter-layer exciton emission.Comment: 19 pages, 3 figures. Just accepted for publication in Nano Letters (http://pubs.acs.org/doi/10.1021/acs.nanolett.7b03184

Non equilibrium anisotropic excitons in atomically thin ReS2_2

We present a systematic investigation of the electronic properties of bulk and few layer ReS$_2$ van der Waals crystals using low temperature optical spectroscopy. Weak photoluminescence emission is observed from two non-degenerate band edge excitonic transitions separated by $\sim$ 20 meV. The comparable emission intensity of both excitonic transitions is incompatible with a fully thermalized (Boltzmann) distribution of excitons, indicating the hot nature of the emission. While DFT calculations predict bilayer ReS$_2$ to have a direct fundamental band gap, our optical data suggests that the fundamental gap is indirect in all cases

Non equilibrium anisotropic excitons in atomically thin ReS2

We present a systematic investigation of the electronic properties of bulk and few layer ReS2 van der Waals crystals using low temperature optical spectroscopy. Weak photoluminescence emission is observed from two non-degenerate band edge excitonic transitions separated by similar to 20 meV. The comparable emission intensity of both excitonic transitions is incompatible with a fully thermalized (Boltzmann) distribution of excitons, indicating the hot nature of the emission. While DFT calculations predict bilayer ReS2 to have a direct fundamental band gap, our optical data suggests that the fundamental gap is indirect in all cases

Intervalley Scattering of Interlayer Excitons in a MoS2_2/MoSe2_2/MoS2_2 Heterostructure in High Magnetic Field

Degenerate extrema in the energy dispersion of charge carriers in solids, also referred to as valleys, can be regarded as a binary quantum degree of freedom, which can potentially be used to implement valleytronic concepts in van der Waals heterostructures based on transition metal dichalcogenides. Using magneto-photoluminescence spectroscopy, we achieve a deeper insight into the valley polarization and depolarization mechanisms of interlayer excitons formed across a MoS$_2$/MoSe$_2$/MoS$_2$ heterostructure. We account for the non-trivial behavior of the valley polarization as a function of the magnetic field by considering the interplay between exchange interaction and phonon mediated intervalley scattering in a system consisting of Zeeman-split energy levels. Our results represent a crucial step towards the understanding of the properties of interlayer excitons, with strong implications for the implementation of atomically thin valleytronic devices.Comment: just accepted in Nano Letters, DOI: 10.1021/acs.nanolett.8b0148