Monolayer transition metal dichalcogenides have strong Coulomb-mediated many-body interactions. Theoretical studies have predicted the existence of numerous multi-particle excitonic states. Two-particle excitons and three-particle trions have been identified by their optical signatures. However, more complex states such as biexcitons have been elusive due to limited spectral quality of the optical emission. Here, we report direct evidence of two biexciton complexes in monolayer tungsten diselenide: the four-particle neutral biexciton and the five-particle negatively charged biexciton. We distinguish these states by power-dependent photoluminescence and demonstrate full electrical switching between them. We determine the band states of the elementary particles comprising the biexcitons through magneto-optical spectroscopy. We also resolve a splitting of 2.5 meV for the neutral biexciton, which we attribute to the fine structure, providing reference for subsequent studies. Our results unveil the nature of multi-exciton complexes in transitionmetal dichalcogenides and offer direct routes towards deterministic control in many-body quantum phenomena.

We report diffusion quantum Monte Carlo calculations of the interlayer binding energy of bilayer graphene. We find the binding energies of the AA-and AB-stacked structures at the equilibrium separation to be 11.5(9) and 17.7(9) meV/atom, respectively. The out-of-plane zone-center optical phonon frequency predicted by our binding-energy curve is consistent with available experimental results. As well as assisting the modeling of interactions between graphene layers, our results will facilitate the development of van der Waals exchange-correlation functionals for density functional theory calculations.PACS numbers: 61.48. Gh, 71.15.Nc, 02.70.Ss van der Waals (vdW) interactions play a crucial role in a wide range of physical and biological phenomena, from the binding of rare-gas solids to the folding of proteins. Significant efforts are therefore being made to develop computational methods that predict vdW contributions to energies of adhesion, particularly for materials such as multilayer graphene. This task has proved to be challenging, however, because vdW interactions are caused by nonlocal electron correlation effects. Standard first-principles approaches such as density functional theory (DFT) with local exchange-correlation functionals do not describe vdW interactions accurately. One technique for including vdW interactions in a first-principles framework is to add energies obtained using pairwise interatomic potentials to DFT total energies; this is the so-called DFT-D scheme [1][2][3][4]. The development of vdW density functionals (vdW-DFs) that can describe vdW interactions in a seamless fashion is another promising approach [5][6][7][8]. DFT-based random-phase approximation (RPA) calculations of the correlation energy [9, 10] provide a more sophisticated method for treating vdW interactions; however, RPA atomization energies are typically overestimated by up to 15% for solids [11,12], and hence the accuracy of this approach is unclear. Symmetry-adapted perturbation theory based on DFT allows one to calculate the vdW interactions between molecules and hence, by extrapolation, between nanostructures [13]. Finally, empirical interatomic potentials with r −6 tails may be used to calculate binding energies [14,15], although such potentials give a qualitatively incorrect description of the interaction of metallic or π-bonded two-dimensional (2D) materials at large separation [16].A key test system for methods purporting to describe vdW interactions between low-dimensional materials is bilayer graphene (BLG). Several theoretical studies have used methods based on DFT to calculate the binding energy (BE) of BLG. Some of the results are summarized in Table I, but there is very little consensus. In this work we provide diffusion quantum Monte Carlo (DMC) data for the BE of BLG and the atomization energy of monolayer graphene (MLG), which we have extrapolated to the thermodynamic limit. We find the DMC BE of BLG to be somewhat less than the BEs predicted by DFT-D, although the latter vary significantly from sche...

Excitonic effects play a particularly important role in the optoelectronic behavior of twodimensional semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide (i) statistically exact diffusion quantum Monte Carlo bindingenergy data for a Mott-Wannier model of (donor/acceptor-bound) excitons, trions, and biexcitons in two-dimensional semiconductors in which charges interact via the Keldysh potential, (ii) contact pair-distribution functions to allow a perturbative description of contact interactions between charge carriers, and (iii) an analysis and classification of the different types of bright trion and biexciton that can be seen in single-layer molybdenum and tungsten dichalcogenides. We investigate the stability of biexcitons in which two charge carriers are indistinguishable, finding that they are only bound when the indistinguishable particles are several times heavier than the distinguishable ones. Donor/acceptor-bound biexcitons have similar binding energies to the experimentally measured biexciton binding energies. We predict the relative positions of all stable free and bound excitonic complexes of distinguishable charge carriers in the photoluminescence spectra of WSe2 and MoSe2.

Excitonic effects play a particularly important role in the optoelectronic behavior of twodimensional (2D) semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide statistically exact diffusion quantum Monte Carlo binding-energy data for Mott-Wannier models of excitons, trions, and biexcitons in 2D semiconductors. We also provide contact pair densities to allow a description of contact (exchange) interactions between charge carriers using first-order perturbation theory. Our data indicate that the binding energy of a trion is generally larger than that of a biexciton in 2D semiconductors. We provide interpolation formulas giving the binding energy and contact density of 2D semiconductors as functions of the electron and hole effective masses and the in-plane polarizability. PACS numbers: 78.20.Bh, 73.20.Hb, The optical properties of two-dimensional (2D) semiconductors such as monolayer MoS 2 , MoSe 2 , WS 2 , WSe 2 , InSe, and phosphorene have recently attracted a great deal of interest [1][2][3][4][5][6][7][8]. Numerous observations have been made of the rich structure of the luminescence spectra of these 2D materials, in which the most pronounced features have been interpreted in terms of neutral excitons [9][10][11][12][13][14], charged excitons (trions) [15][16][17][18][19][20], and biexcitons [21][22][23], while recent experiments on higher-quality monolayer transition-metal dichalcogenide (TMDC) samples have revealed additional structure in their spectra [24][25][26][27].In this work we study a Mott-Wannier model of excitons and excitonic complexes in monolayer 2D semiconductors, taking into account the polarizability of the 2D crystal [28][29][30] and providing data to allow for a perturbative treatment of contact interactions between carriers. We use the diffusion quantum Monte Carlo (DMC) approach [31-33] to find the energies of trions and biexcitons, and we provide approximate formulas for the exciton (U), trion (E T ), and biexciton (E XX ) binding energies as functions of the in-plane polarizability and the electron and hole effective masses, which fit the DMC data to within 5%. We calculate and report contact pair densities, enabling the evaluation of perturbative corrections to the energies of charge-carrier complexes, as well as intervalley scattering, due to contact (exchange) interactions between charge carriers. The strength of the contact interactions could in principle be determined from first-principles calculations for different 2D semiconductors; alternatively, the strengths of the contact interactions can be regarded as parameters to be determined using experimental data in conjunction with the contact pair densities reported here.The energy −U − E T of a trion with one hole (h) and two electrons (e 1 and e 2 ) can be found by solving the Schrödinger equation (in Gaussian units)where m e and m h are the electron and hole effective masses and r ij = r i − r j is the position of particle i relative to particle j. The Keldysh po...