Spatially indirect intervalley excitons in bilayer WSe2

Abstract

Spatially indirect excitons with displaced wave functions of electrons and holes play a pivotal role in a large portfolio of fascinating physical phenomena and emerging optoelectronic applications, such as valleytronics, exciton spin Hall effect, excitonic integrated circuit, and high-temperature superfluidity. Here, we uncover three types of spatially indirect excitons (including their phonon replicas) and their quantum-confined Stark effects in hexagonal boron nitride encapsulated bilayer WSe 2 by performing electric field-tunable photoluminescence measurements. Because of different out-of-plane electric dipole moments, the energy order between the three types of spatially indirect excitons can be switched by a vertical electric field. Remarkably, we demonstrate, assisted by first-principles calculations, that the observed spatially indirect excitons in bilayer WSe 2 are also momentum indirect, involving electrons and holes from and K/ valleys in the Brillouin zone, respectively. This is in contrast to the previously reported spatially indirect excitons with electrons and holes localized in the same valley. Furthermore, we find that the spatially indirect intervalley excitons in bilayer WSe 2 can exhibit considerable, doping-sensitive circular polarization. The spatially indirect excitons with momentum-dark nature and highly tunable circular polarization may provide a firm basis for the understanding and engineering of technological applications in photonics and optoelectronics.

Stacking-dependent exciton multiplicity in WSe$_2$ bilayers

“…This insight resolves the recent puzzle of two distinct intralayer KK exciton transitions observed in absorption on nearly aligned WSe 2 BLs [10]. Moreover, our theoretical analysis highlights the multiplicity and degree of layer delocalization FOR interlayer excitons in both 2H in 3R stackings, thus providing an intuitive explanation for different electrostatic dipole moments of QK excitons without the requirement of involving QΓ states [20,21].…”

“…For both stackings we find that the lowestenergy PL is dominated by momentum-indirect QK and Q K excitons with intralayer and interlayer character. The different degrees of layer delocalization give rise to two different electrostatic dipoles, providing an explanation for the recent observations of two distinct slopes in the first-order Stark effect [20,21]. Moreover, our results demonstrate that exciton state multiplicity, transition energies and oscillator strengths sensitively depend on the BL stacking order, and highlight how layerdegenerate excitons in inversion symmetric 2H BLs split into exciton doublets in 3R stacking with broken inversion symmetry and different atomic registries for the top and bottom layers.…”

“…The electrostatic dipole moment depends on the degree of exciton layer delocalization, which in turn is sensitive to the interlayer coupling and thus to the stacking order, as was shown recently by optical absorption for 2H and 3R MoS 2 BLs for transitions involving momentum direct KK excitons [23,24]. In contrast to absorption probing zero-momentum exciton transitions, the photoluminescence (PL) of BLs is dominated by momentum-indirect excitons [25,26] via luminescence phonon sidebands [27][28][29] which exhibit shift linear energy shifts in perpendicular electric fields according to the Stark effect [10,16,20,21]. The most recent observation of two different slopes in the energy dispersion of phonon sideband emission from 2H WSe 2 BL in electric field [20,21] indicates the presence of two degrees of electron-hole layer separation, with respective dipole moments attributed to excitons in distinct QK and QΓ reservoirs [20,21].…”

“…A particularly attractive feature of interlayer excitons in related homobilayer systems is provided by the permanent dipole moment of layer-indirect excitons [13][14][15] which promotes exciton-exciton dipolar interactions, allows employing electric fields to tune the optical properties via the Stark effect [10,[16][17][18][19][20][21] or implementing exciton trapping and routing [22]. The electrostatic dipole moment depends on the degree of exciton layer delocalization, which in turn is sensitive to the interlayer coupling and thus to the stacking order, as was shown recently by optical absorption for 2H and 3R MoS 2 BLs for transitions involving momentum direct KK excitons [23,24].…”

“…In contrast to absorption probing zero-momentum exciton transitions, the photoluminescence (PL) of BLs is dominated by momentum-indirect excitons [25,26] via luminescence phonon sidebands [27][28][29] which exhibit shift linear energy shifts in perpendicular electric fields according to the Stark effect [10,16,20,21]. The most recent observation of two different slopes in the energy dispersion of phonon sideband emission from 2H WSe 2 BL in electric field [20,21] indicates the presence of two degrees of electron-hole layer separation, with respective dipole moments attributed to excitons in distinct QK and QΓ reservoirs [20,21]. Experiments employing strain tuning [30] and magnetic fields [28], on the other hand, suggest that the PL sidebands stem exclusively from QK excitons, indicating shortcomings in the present understanding of the underlying lowest-energy exciton reservoirs with finite center-of-mass momenta.…”