Author Correction: Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures.

An Amendment to this paper has been published and can be accessed via a link at the top of the paper.

Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures.

Atomically thin layers of two-dimensional materials can be assembled in vertical stacks that are held together by relatively weak van der Waals forces, enabling coupling between monolayer crystals with incommensurate lattices and arbitrary mutual rotation1,2. Consequently, an overarching periodicity emerges in the local atomic registry of the constituent crystal structures, which is known as a moiré superlattice3. In graphene/hexagonal boron nitride structures4, the presence of a moiré superlattice can lead to the observation of electronic minibands5-7, whereas in twisted graphene bilayers its effects are enhanced by interlayer resonant conditions, resulting in a superconductor-insulator transition at magic twist angles8. Here, using semiconducting heterostructures assembled from incommensurate molybdenum diselenide (MoSe2) and tungsten disulfide (WS2) monolayers, we demonstrate that excitonic bands can hybridize, resulting in a resonant enhancement of moiré superlattice effects. MoSe2 and WS2 were chosen for the near-degeneracy of their conduction-band edges, in order to promote the hybridization of intra- and interlayer excitons. Hybridization manifests through a pronounced exciton energy shift as a periodic function of the interlayer rotation angle, which occurs as hybridized excitons are formed by holes that reside in MoSe2 binding to a twist-dependent superposition of electron states in the adjacent monolayers. For heterostructures in which the monolayer pairs are nearly aligned, resonant mixing of the electron states leads to pronounced effects of the geometrical moiré pattern of the heterostructure on the dispersion and optical spectra of the hybridized excitons. Our findings underpin strategies for band-structure engineering in semiconductor devices based on van der Waals heterostructures9.

Nano-imaging of intersubband transitions in van der Waals quantum wells.

The science and applications of electronics and optoelectronics have been driven for decades by progress in the growth of semiconducting heterostructures. Many applications in the infrared and terahertz frequency range exploit transitions between quantized states in semiconductor quantum wells (intersubband transitions). However, current quantum well devices are limited in functionality and versatility by diffusive interfaces and the requirement of lattice-matched growth conditions. Here, we introduce the concept of intersubband transitions in van der Waals quantum wells and report their first experimental observation. Van der Waals quantum wells are naturally formed by two-dimensional materials and hold unexplored potential to overcome the aforementioned limitations-they form atomically sharp interfaces and can easily be combined into heterostructures without lattice-matching restrictions. We employ near-field local probing to spectrally resolve intersubband transitions with a nanometre-scale spatial resolution and electrostatically control the absorption. This work enables the exploitation of intersubband transitions with unmatched design freedom and individual electronic and optical control suitable for photodetectors, light-emitting diodes and lasers.

Dissociation of two-dimensional excitons in monolayer WSe2.

Two-dimensional (2D) semiconducting materials are promising building blocks for optoelectronic applications, many of which require efficient dissociation of excitons into free electrons and holes. However, the strongly bound excitons arising from the enhanced Coulomb interaction in these monolayers suppresses the creation of free carriers. Here, we identify the main exciton dissociation mechanism through time and spectrally resolved photocurrent measurements in a monolayer WSe2 p-n junction. We find that under static in-plane electric field, excitons dissociate at a rate corresponding to the one predicted for tunnel ionization of 2D Wannier-Mott excitons. This study is essential for understanding the photoresponse of 2D semiconductors and offers design rules for the realization of efficient photodetectors, valley dependent optoelectronics, and novel quantum coherent phases.

Dark trions and biexcitons in WS2 and WSe2 made bright by e-e scattering.

The direct band gap character and large spin-orbit splitting of the valence band edges (at the K and K' valleys) in monolayer transition metal dichalcogenides have put these two-dimensional materials under the spot-light of intense experimental and theoretical studies. In particular, for Tungsten dichalcogenides it has been found that the sign of spin splitting of conduction band edges makes ground state excitons radiatively inactive (dark) due to spin and momentum mismatch between the constituent electron and hole. One might similarly assume that the ground states of charged excitons and biexcitons in these monolayers are also dark. Here, we show that the intervalley (K ⇆ K') electron-electron scattering mixes bright and dark states of these complexes, and estimate the radiative lifetimes in the ground states of these "semi-dark" trions and biexcitons to be ~10 ps, and analyse how these complexes appear in the temperature-dependent photoluminescence spectra of WS2 and WSe2 monolayers.

Ferromagnetic bonding: high spin copper clusters (n+1)Cu(n); n = 2-14) devoid of electron pairs but possessing strong bonding.

Density functional theoretic studies are performed for the high-spin copper clusters (n)(+1)Cu(n) (n = 2-14), which are devoid of electron pairs shared between atoms, hence no-pair clusters (J. Phys. Chem. 1988, 92, 1352; Isr. J. Chem. 1993, 33, 455; J. Am. Chem. Soc. 1999, 121, 3165). Despite the lack of electron pairing, it is found that the bond dissociation energy per atom (BDE/n) is significant and converges (to within 1 kcal mol(-1)), around a cluster size (11)Cu(10), to a value of BDE/n = 19 kcal mol(-1). This is a very large bonding energy, much larger than has previously been obtained for no-pair clusters of lithium, BDE/n = 12 kcal mol(-1), or sodium clusters, BDE/n = 3 kcal mol(-1). This bonding, so-called ferromagnetic bonding (FM-bonding) is analyzed using a valence bond (VB) model (J. Phys. Chem. A 2002, 106, 4961; Phys. Chem. Chem. Phys. 2003, 5, 158). As such, FM-bonding in no-pair clusters is described as an ionic fluctuation, of the triplet pair, that spreads over all the close neighbors of a given atom in the clusters. Thus, if we refer to each triplet pair and its ionic fluctuations as a local FM-bond, we can regard the electronic structure of a given (n)(+1)M(n) cluster as a resonance hybrid of all the local FM-bonds between close neighbors. The model shows how a weak interaction in the diatomic triplet molecule can become a remarkably strong binding force that binds together mono-valent atoms without even a single electron pair. This is achieved because the growing number of VB structures exerts a cumulative effect of stabilization that is maximized when the cluster has a compact structure with an optimal coordination number for the atoms.