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

On the existence of automorphisms with simple Lebesgue spectrum

It is shown that if T is a measure preserving automorphism on a probability space (Ω,B, m) which admits a random variable X0 with mean zero such that the stochastic sequence X0 o Tn,n ε Z is orthonormal and spans L02(Ω,B,m), then for any integer k ≠ 0, the random variables X o Tnk,n ε Z generate B modulom

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

Influence of Trapping on the Exciton Dynamics of Al_xGa_1-xAs Films

We present a systematic study on the exciton relaxation in high purity AlGaAs epilayers. The time for the excitonic photoluminescence to reach its maximum intensity (t_max) shows a non-monotonic dependence on excitation density which is attributed to a competition between exciton localization and carrier-carrier scattering. A phenomenological four level model fully describes the influence of exciton localization on t_max. This localization effect is enhanced by the increase of the Al content in the alloy and disappears when localization is hindered by rising the lattice temperature above the exciton trapping energy.Comment: 4 pages, 3 figures, 16 ref

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

Dynamics of relaxation and trapping of excitons in Al x Ga 1-x As films

PACS 78.47.+p, 78.55.Cr, 78.66.Fd Carrier relaxation in high quality Al x Ga 1-x As (x up to 5%) epilayers has been investigated by means of time resolved photoluminiscence. The time for the excitonic PL to reach the maximum intensity shows a non-monotonic behaviour with increasing excitation density, which is attributed to the competition between exciton localization and carrier-carrier scattering. The increase of the Al content enhances the alloy scattering and increases the number of localization sites, moderately accelerating the dynamics. A fourlevel rate equation model qualitatively describes the influence of trapping in the exciton dynamics at low excitation densities