Anomalous Light Cones and Valley Optical Selection Rules of Interlayer Excitons in Twisted Heterobilayers

Yu, Hongyi; Wang, Yong; Tong, Qingjun; Xu, Xiaodong; Yao, Wang

doi:10.1103/physrevlett.115.187002

Cited by 232 publications

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“…They can only recombine if their momentum sum equals the displacement vector between the K MoSe2 and the K WSe2 corners, as recently proposed in [48]. A direct fascinating consequence of this scenario are interlayer excitons with a finite kinematic momentum [48]. In the investigated HS, the displacement vector is expected to be small but finite and only caused by the lattice constant mismatch since the twist angle of 1° is negligible.…”

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confidence: 96%

“…In turn, such bound electron-hole pairs or excitons cannot recombine radiatively in a direct optical transition. They can only recombine if their momentum sum equals the displacement vector between the K MoSe2 and the K WSe2 corners, as recently proposed in [48]. A direct fascinating consequence of this scenario are interlayer excitons with a finite kinematic momentum [48].…”

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confidence: 98%

“…In turn, thermalized IXs are expected with a significantly enhanced IX lifetime and density [21,22,26]. Furthermore, by optical spin-valley pumping in one layer, the spin-and valleydegrees of freedom are preserved by the interlayer transfer of polarized charge carriers [25,27,28,48]. While intralayer excitons in TMD monolayers are perfect in-plane dipoles fostering Förster-type energy transfer between hetero-bilayers [49], interlayer excitons possess a permanent out of plain component altering the coupling to light and enabling to tune the exciton properties by static electric fields perpendicular to the layers.…”

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Long-Lived Direct and Indirect Interlayer Excitons in van der Waals Heterostructures

et al. 2017

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We investigate the photoluminescence of interlayer excitons in heterostructures consisting of monolayer MoSe2 and WSe2 at low temperatures. Surprisingly, we find a doublet structure for such interlayer excitons. Both peaks exhibit long photoluminescence lifetimes of several ten nanoseconds up to 100 ns at low temperatures, which verifies the interlayer nature of both.The peak energy and linewidth of both show unusual temperature and power dependences.In particular, we observe a blue-shift of their emission energy for increasing excitation powers.At a low excitation power and low temperatures, the energetically higher peak shows several spikes. We explain the findings by two sorts of interlayer excitons; one that is indirect in real space but direct in reciprocal space, and the other one being indirect in both spaces. Our results provide fundamental insights into long-lived interlayer states in van der Waals heterostructures with possible bosonic many-body interactions.Keywords: van der Waals heterostructure, indirect excitons, interlayer exciton, photoluminescence, exciton lifetime, transition metal dichalcogenides; 2 Semiconductor heterostructures (HS) are very often the foundation for the observation of novel phenomena in both fundamental science as well as device applications. The electrical and optical properties of such HS can be engineered in a wide range resulting in precisely tailored functionalities. Of particular interest are optically active HS facilitating many device applications such as photo-detectors, solar cells, light-emitting diodes or lasers and fostering the observation of many-body driven quantum phenomena found in systems with reduced dimensionality such as quantum wells or quantum dots. Excitons are electron-hole pairs coupled by attractive Coulomb interaction which results in a ground state with a reduced energy compared to the corresponding single-particle energies. Exciton ensembles exhibit an intriguing interaction driven phase diagram with different classical and quantum phases including quantum liquids and solids [1][2][3]. The bosonic nature of excitons enables these composite particles even to condensate into macroscopic ground state wave functions forming a Bose-Einstein condensate (BEC) [4].Ensembles of indirect a.k.a. interlayer excitons (IXs) are particularly fascinating systems to explore such classical and quantum phases of interacting bosonic ensembles. IXs are composite bosons that feature enlarged lifetimes due to the reduced overlap of the electronhole wave functions resulting in dense IX ensembles that are thermalized to the lattice temperature. Besides IX ensembles in III-V HS [5][6][7][8][9][10][11][12][13][14][15], hetero-bilayers prepared from semiconducting transition metal dichalcogenides (TMDs) exhibit superior potential for studying interacting IX ensembles [3,[16][17][18][19][20][21][22][23][24][25] with intriguing spin-and valley-properties [26][27][28]. At the same time, TMDs are truly two-dimensional (2D) crystals coupled to each other or to substrat...

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Long-Lived Direct and Indirect Interlayer Excitons in van der Waals Heterostructures

et al. 2017

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“…TMD heterostructures have been realized [20][21][22] experimentally and can host interesting effects, for example the observation of valley polarized interlayer excitons with long lifetimes [23], the theoretical prediction of multiple degenerate interlayer excitons [24], and the possibility of achieving spatially indirect exciton condensation [25,26]. Our focus here is instead on the intralayer excitons that are more strongly coupled to light.…”

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Topological Exciton Bands in Moiré Heterojunctions

2017

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Moiré patterns are common in van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moiré potential, and iii) the valley Zeeman field.Stacking two-dimensional (2D) materials into van der Waals heterostructures opens up new strategies for materials property engineering. One increasingly important example is the possibility of using the relative orientation (twist) angle between two 2D crystals to tune electronic properties. For small twist angles and latticeconstant mismatches, heterostructures exhibit long period moiré patterns that can yield dramatic changes. Moiré pattern formed in graphene-based heterostructures has been extensively studied, and many interesting phenomena have been observed, for example gap opening at graphene's Dirac point [1,2], generation of secondary Dirac points [3,4] and Hofstadter-butterfly spectra in a strong magnetic field [1,5,6].In this Letter, we study the influence of moiré patterns on collective excitations, focusing on the important case of excitons in the transition metal dichalcogenide (TMD) 2D semiconductors [7,8] like MoS 2 and WS 2 . Exciton features dominate the optical response of these materials because electron-hole pairs are strongly bound by the Coulomb interaction [9][10][11][12]. An exciton inherits a pseudospin-1/2 valley degree of freedom from its constituent electron and hole, and the exciton valley pseudospin can be optically addressed [13][14][15][16], providing access to the valley Hall effect [17] and the valley selective optical Stark effect [18,19].As in the case of graphene/hexagonal-boron-nitride and graphene/graphene bilayers, a moiré pattern can be established in TMD bilayers by using two different materials with a small lattice mismatch, by applying a small twist, or by combining both effects. TMD heterostructures have been realized [20][21][22] experimentally and can host interesting effects, for example the observation of valley polarized interlayer excitons with long lifetimes [23], the theoretical prediction of multiple degenerate interlayer excitons [24], and the possibility of achieving spatially indirect exciton condensation [25,26]. Our focus here is instead on the intralayer excitons that are more strongly coupled to light. As we explain below, the moiré pattern produces a periodic potential, mixing momentum states separated by moiré reciprocal lattice vectors and producing satellite optical absorption peaks that are revealing. The exciton energy-momentum dispersion can be measured by tracking the dependence of satellite peak energies on twist angle.The valley pseudospin...

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“…Excitation spectroscopy reveals the double-resonance nature of such enhancement, and identifies the two resonant states to be the A exciton transition of monolayer WSe 2 and a new hybrid state present only in WSe 2 /hBN heterostructures. The observation of an interlayer electron-phonon interaction could open up new ways to engineer electrons and phonons for device applications.Van der Waals heterostructures of atomically thin twodimensional (2D) crystals are a new class of material in which novel quantum phenomena can emerge from layer-layer interactions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . For example, electron-electron interactions between adjacent 2D layers can give rise to a variety of fascinating physical behaviours: the interlayer moiré potential between the graphene and hBN layers leads to mini-Dirac cones and the Hofstadter's butterfly pattern in graphene/hBN heterostructures 5-10 ; electronic couplings between MoS 2 and MoS 2 layers lead to a direct-to indirect-bandgap transition in bilayer MoS 2 (refs 11,12); and Coulomb interactions between MoSe 2 and WSe 2 layers lead to interlayer exciton states in MoSe 2 /WSe 2 heterostructures 13,14 .…”

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Interlayer electron–phonon coupling in WSe2/hBN heterostructures

et al. 2016

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Engineering layer-layer interactions provides a powerful way to realize novel and designable quantum phenomena in van der Waals heterostructures 1-16 . Interlayer electron-electron interactions, for example, have enabled fascinating physics that is di cult to achieve in a single material, such as the Hofstadter's butterfly in graphene/boron nitride (hBN) heterostructures [5][6][7][8][9][10] . In addition to electron-electron interactions, interlayer electron-phonon interactions allow for further control of the physical properties of van der Waals heterostructures. Here we report an interlayer electron-phonon interaction in WSe 2 /hBN heterostructures, where optically silent hBN phonons emerge in Raman spectra with strong intensities through resonant coupling to WSe 2 electronic transitions. Excitation spectroscopy reveals the double-resonance nature of such enhancement, and identifies the two resonant states to be the A exciton transition of monolayer WSe 2 and a new hybrid state present only in WSe 2 /hBN heterostructures. The observation of an interlayer electron-phonon interaction could open up new ways to engineer electrons and phonons for device applications.Van der Waals heterostructures of atomically thin twodimensional (2D) crystals are a new class of material in which novel quantum phenomena can emerge from layer-layer interactions [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] . For example, electron-electron interactions between adjacent 2D layers can give rise to a variety of fascinating physical behaviours: the interlayer moiré potential between the graphene and hBN layers leads to mini-Dirac cones and the Hofstadter's butterfly pattern in graphene/hBN heterostructures 5-10 ; electronic couplings between MoS 2 and MoS 2 layers lead to a direct-to indirect-bandgap transition in bilayer MoS 2 (refs 11,12); and Coulomb interactions between MoSe 2 and WSe 2 layers lead to interlayer exciton states in MoSe 2 /WSe 2 heterostructures 13,14 . Similar to electron-electron interactions, electron-phonon interactions also play a key role in a wide range of phenomena in condensed matter physics: the electron-phonon coupling sets the intrinsic limit of electron mobility 17 , dominates the ultrafast carrier dynamics 18 , leads to the Peierls instability 19 , and enables the formation of Cooper pairs 20 . Exploiting interactions between electrons in one layered material and phonons in an adjacent material could enable new ways to control electron-phonon coupling and realize novel quantum behaviour that has not previously been possible. For example, it has been recently shown that electrons in monolayer FeSe can couple strongly with phonons in the adjacent SrTiO 3 substrate, which may play an important role in the anomalously high critical temperature for superconductivity in the system 21,22 . However, the unusual interlayer electron-phonon interactions in the van der Waals heterostructures have been little explored so far, although there have been indications that interlayer interactions between graphene ...

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Anomalous Light Cones and Valley Optical Selection Rules of Interlayer Excitons in Twisted Heterobilayers

Cited by 232 publications

References 50 publications

Long-Lived Direct and Indirect Interlayer Excitons in van der Waals Heterostructures

Long-Lived Direct and Indirect Interlayer Excitons in van der Waals Heterostructures

Topological Exciton Bands in Moiré Heterojunctions

Interlayer electron–phonon coupling in WSe2/hBN heterostructures

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