We present theoretical results for the radiative rates and doping-dependent photoluminescence spectrum of interlayer excitonic complexes localized by donor impurities in MoSe$_2$/WSe$_2$ twisted heterobilayers, supported by quantum Monte Carlo calculations of binding energies and wave-function overlap integrals. For closely aligned layers, radiative decay is made possible by the momentum spread of the localized complexes' wave functions, resulting in few $μ$s$^{-1}$ radiative rates. For strongly misaligned layers, the short-range interaction between the carriers and impurity provides a finite radiative rate with a strong asymptotic twist angle dependence $\propto θ^{-8}$. Finally, phonon-assisted recombination is considered, with emission of optical phonons in both layers resulting in additional weaker emission lines, redshifted by the phonon energy.
We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moiré pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moiré Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the excito…
Transition metal dichalcogenide heterobilayers offer attractive opportunities to realize lattices of interacting bosons with several degrees of freedom. Such heterobilayers can feature moiré patterns that modulate their electronic band structure, leading to spatial confinement of single interlayer excitons (IXs) that act as quantum emitters with $C_3$ symmetry. However, the narrow emission linewidths of the quantum emitters contrast with a broad ensemble IX emission observed in nominally identical heterobilayers, opening a debate regarding the origin of IX emission. Here we report the continuo…
Proximity effects are one of the pillars of exotic phenomena and technological applications of two dimensional materials. However, the interactions nature depends strongly on the materials involved, their crystalline symmetries, and interfacial properties. Here we used large-scale first-principle calculations to demonstrate that strain and twist-angle are efficient knobs to tailor the spin-orbit coupling in graphene transition metal dichalcogenide heterobilayers. We found that by choosing a twist-angle of 30 degrees, the spin relaxation times increase by two orders of magnitude, opening a path…
The emergence of various exciton-related effects in transition metal dichalcogenides (TMDC) and their heterostructures has inspired a significant number of studies and brought forth several possible applications. Often, standard photoluminescence (PL) with microscale lateral resolution is utilized to identify and characterize these excitonic phenomena, including interlayer excitons (IEXs). We studied the local PL signatures of van der Waals heterobilayers composed of exfoliated monolayers of the (Mo,W)(S,Se)$_2$ TMDC family with high spatial resolution (down to 30 nm) using tip-enhanced photol…
Geometrical moiré patterns, generic for almost aligned bilayers of two-dimensional (2D) crystals with similar lattice structure but slightly different lattice constants, lead to zone folding and miniband formation for electronic states. Here, we show that moiré superlattice (mSL) effects in $\mathrm{MoSe}_2/\mathrm{WS}_2$ and $\mathrm{MoTe}_2/\mathrm{MoSe}_2$ heterobilayers that feature alignment of the band edges are enhanced by resonant interlayer hybridization, and anticipate similar features in twisted homobilayers of TMDs, including examples of narrow minibands close to the actual band ed…
Transition-metal dichalcogenide heterostructures exhibit moiré patterns that spatially modulate the electronic structure across the material's plane. For certain material pairs, this modulation acts as a potential landscape with deep, trigonally symmetric wells capable of localizing interlayer excitons, forming periodic arrays of quantum emitters. Here, we study these moiré localized exciton states and their optical properties. By numerically solving the two-body problem for an interacting electron-hole pair confined by a trigonal potential, we compute the localized exciton spectra for differe…
The valence flat bands in transition metal dichalcogenide (TMD) heterobilayers are shown to exhibit strong intralayer spin-orbit coupling. This is reflected in a simple tight-binding model with spin-dependent complex hoppings based on the continuum model. A perpendicular electric field causes interlayer hybridization, such that the effective model is equivalent to the Kane-Mele model of topological insulators. The proposed model can be used as a starting point to understand interactions and the experimentally observed topological phases.
We reveal by first-principles calculations that the interlayer binding in a twisted MoS2/MoTe2 heterobilayer decreases with increasing twist angle, due to the increase of the interlayer overlapping degree, a geometric quantity describing well the interlayer steric effect. The binding energy is found to be a Gaussian-like function of twist angle. The resistance to rotation, an analogue to the interlayer sliding barrier, can also be defined accordingly. In sharp contrast to the case of MoS2 homobilayer, here the energy band gap reduces with increasing twist angle. We find a remarkable interlayer…
Charge separated interlayer excitons in transition metal dichalcogenide (TMDC) heterobilayers are being explored for moiré exciton lattices and exciton condensates. The presence of permanent dipole moments and the poorly screened Coulomb interaction make many body interactions particularly strong for interlayer excitons. Here we reveal two distinct phase transitions for interlayer excitons in the MoSe2/WSe2 heterobilayer using time and spatially resolved photoluminescence imaging: from trapped excitons in the moiré-potential to the modestly mobile exciton gas as exciton density increases to ne…
Due to their unique two-dimensional nature, charge carriers in semiconducting transition metal dichalcogenides (TMDs) exhibit strong unscreened Coulomb interactions and sensitivity to defects and impurities. The versatility of van der Waals layer stacking allows spatially separating electrons and holes between different TMD layers with staggered band structure, yielding interlayer few-body excitonic complexes whose nature is still debated. Here we combine quantum Monte Carlo calculations with spectrally and temporally resolved photoluminescence measurements on a top- and bottom-gated MoSe2/WSe…
We show that, because of the inevitable twist and lattice mismatch in heterobilayers of transition metal dichalcogenides, interlayer excitons have six-fold degenerate light cones anomalously located at finite velocities on the parabolic energy dispersion. The photon emissions at each light cone are elliptically polarized, with major axis locked to the direction of exciton velocity, and helicity specified by the valley indices of the electron and the hole. These finite-velocity light cones allow unprecedented possibilities to optically inject valley polarization and valley current, and the obse…
Recently, the topological flat bands and spin Hall effect have been experimentally observed in the AB-stacked MoTe$_2$/WSe$_2$ heterostructures. In this work, we systematically study the Berry curvature effects in moiré transition metal dichalcogenide (TMD) heterobilayers. We point out that the moiré potential of the remote conduction bands would induce a sizable periodic pseudo-magnetic field (PMF) on the valence band. This periodic PMF creates net Berry curvature flux in each valley of the moiré Brillouin zone. The combination of the effect of the Berry curvature and the spin-valley locking …
The creation of moiré patterns in crystalline solids is a powerful approach to manipulate their electronic properties, which are fundamentally influenced by periodic potential landscapes. In 2D materials, a moiré pattern with a superlattice potential can form by vertically stacking two layered materials with a twist and/or finite lattice constant difference. This unique approach has led to emergent electronic phenomena, including the fractal quantum Hall effect, tunable Mott insulators, and unconventional superconductivity. Furthermore, theory predicts intriguing effects on optical excitations…
We study the dynamical properties of point-like defects, represented by monoatomic chalcogen vacancies, in WS$_2$-graphene and MoS$_2$-graphene heterobilayers. Employing a multidisciplinary approach based on the combination of ab initio, model Hamiltonian and density matrix techniques, we propose a minimal interacting model that allows for the calculation of electronic transition times associated to population and depopulation of the vacancy by an additional electron. We obtain the "coarse-grained" semiclassical dynamics by means of a master equation approach and discuss the potential role of …
Layered two-dimensional materials exhibit rich transport and optical phenomena in twisted or lattice-incommensurate heterostructures with spatial variations of interlayer hybridization arising from moiré interference effects. Here, we report experimental and theoretical studies of excitons in twisted heterobilayers and heterotrilayers of transition metal dichalcogenides. Using MoSe$_2$-WSe$_2$ stacks as representative realizations of twisted van der Waals bilayer and trilayer heterostructures, we observe contrasting optical signatures and interpret them in the theoretical framework of interlay…
We investigate the optical properties of spin-triplet interlayer excitons in heterobilayer transition metal dichalcogenides in comparison with the spin-singlet ones. Surprisingly, the optical transition dipole of the spin-triplet exciton is found to be in the same order of magnitude to that of the spin-singlet exciton, in sharp contrast to the monolayer excitons where the spin triplet species is considered as dark compared to the singlet. Unlike the monolayer excitons whose spin-conserved (spin-flip) transition dipole can only couple to light of in-plane (out-of-plane) polarization, such restr…
The nanoscale periodic potentials introduced by moiré patterns in semiconducting van der Waals (vdW) heterostructures provide a new platform for designing exciton superlattices. To realize these applications, a thorough understanding of the localization and delocalization of interlayer excitons in the moiré potentials is necessary. Here, we investigated interlayer exciton dynamics and transport modulated by the moiré potentials in WS$_2$-WSe$_2$ heterobilayers in time, space, and momentum domains using transient absorption microscopy combined with first-principles calculations. Experimental re…
The optical spectra of vertically stacked MoSe$_2$/WSe$_2$ heterostructures contain additional 'interlayer' excitonic peaks that are absent in the individual monolayer materials and exhibit a significant spatial charge separation in out-of-plane direction. Extending on a previous study, we used a many-body perturbation theory approach to simulate and analyse the excitonic spectra of MoSe$_2$/WSe$_2$ heterobilayers with three stacking orders, considering both momentum-direct and momentum-indirect excitons. We find that the small oscillator strengths and corresponding optical responses of the in…
We use first-principles calculations to investigate the band structure evolution of W$X_2$/Mo$X_2$ ($X$ = S, Se) heterobilayers under a perpendicular electric field. We characterize the extent to which the type-II band alignment in these compounds can be tuned or inverted electrostatically. Our results demonstrate two effects of stacking configuration. First, different stackings produce different net dipole moments, resulting in band offset variations that are larger than 0.1 eV. Second, based on symmetry constraints that depend on stacking, a perpendicular electric field may hybridize W$X_2$ …
The formation of interfacial moiré patterns from angular and/or lattice mismatch has become a powerful approach to engineer a range of quantum phenomena in van der Waals heterostructures. For long-lived and valley-polarized interlayer excitons in transition-metal dichalcogenide (TMDC) heterobilayers, signatures of quantum confinement by the moiré landscape have been reported in recent experimental studies. Such moiré confinement has offered the exciting possibility to tailor new excitonic systems, such as ordered arrays of zero-dimensional (0D) quantum emitters and their coupling into topologi…
A major theoretical challenge of studying twisted transition metal dichalcogenide (TMD) bilayers is that the unit cell of such structures is very large and therefore difficult to address using first-principles methods. However, twisted TMD bilayers form moiré patterns, which consist of regions of commensurate stacking, either smoothly interpolated into one another or separated by sharp domain walls. In this paper, we study twisted TMD bilayers by studying the properties of the constituent commensurate structures. Using density functional theory (DFT), we compute band structures for commensurat…
Moiré superlattices formed in van der Waals bilayers have enabled the creation and manipulation of new quantum states, as is exemplified by the discovery of superconducting and correlated insulating states in twisted bilayer graphene near the magic angle. Twisted bilayer semiconductors may lead to tunable exciton lattices and topological states, yet signatures of moiré excitons have been reported only in closely angularly-aligned bilayers. Here we report tuning of moiré lattice in WS$_{2}$ /MoSe$_{2}$ bilayers over a wide range of twist angles, leading to the continuous tuning of moiré lattice…
We investigate the correction of interlayer exciton binding energy in transition metal dichalcogenides double layers arising from the exciton-optical phonon coupling using the method of Lee-Low-Pines unitary transformation. We find that the binding energy varies in several tens of meV, depending on the polarizability of materials and interlayer distance between double layers. Moreover, the correction of binding energy results in the remarkable increasing of the critical temperature for the condensation of dilute excitonic gas basing on the Berezinskii-Kosterlitz-Thouless model. These results n…
It is assessed in detail both experimentally and theoretically how the interlayer coupling of transition metal dichalcogenides controls the electronic properties of the respective devices. Gated transition metal dichalcogenide structures show electrons and holes to either localize in individual monolayers, or delocalize beyond multiple layers - depending on the balance between spin-orbit inter- action and interlayer hopping. This balance depends on layer thickness, momentum space symmetry points and applied gate fields. A good quantitative agreement of predictions and measurements of the quant…
The availability of accessible fabrication methods based on deterministic transfer of atomically thin crystals has been essential for the rapid expansion of research into van der Waals heterostructures. An inherent issue of these techniques is the deformation of the polymer carrier film during the transfer, which can lead to highly non-uniform strain induced in the transferred two-dimensional material. Here, using a combination of optical spectroscopy, atomic force and Kelvin probe force microscopy, we show that the presence of nanometer scale wrinkles formed due to transfer-induced stress rel…
In heterostructures consisting of different transition-metal dichalcogenide monolayers, a staggered band alignment can occur, leading to rapid charge separation of optically generated electron-hole pairs into opposite monolayers. These spatially separated electron-hole pairs are Coulomb-coupled and form interlayer excitons. Here, we study these interlayer excitons in a heterostructure consisting of MoSe$_2$ and WSe$_2$ monolayers using photoluminescence spectroscopy. We observe a non-trivial temperature dependence of the linewidth and the peak energy of the interlayer exciton, including an unu…
Stacking two-dimensional (2D) van der Waals materials with different interlayer atomic registry in a heterobilayer causes the formation of a long-range periodic superlattice that may bestow the heterostructure with exotic properties such as new quantum fractal states [1-3] or superconductivity [4, 5]. Recent optical measurements of transition metal dichalcogenide (TMD) heterobilayers have revealed the presence of hybridized interlayer electron-hole pair excitations at energies defined by the superlattice potential [6-10]. The corresponding quasiparticle band structure, so-called minibands, hav…
Floquet engineering of topological bands in semiconductor van der Waals heterobilayers
Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Universidad Distrital Francisco José de Caldas（弗朗西斯科·何塞·德卡尔德斯地区大学）；Kennesaw State University（肯尼索州立大学）
Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals heterosructures with a focus on heterobilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those heterobilayers are introduced. Most recent findings focusing on diff…
