Session M56: 2D Semiconductors: Excitonics

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Moiré superlattices formed by van der Waals materials with small lattice mismatch or twist angle open an unprecedented opportunity to tailor interactions between quantum particles and their coupling to electromagnetic field. In this talk, I will describe optical spectroscopy studies on 2D moiré superlattices formed by semiconductor transition metal dichalcogenides (TMDs). I will discuss a recent experimental realization of the two-dimensional triangular lattice Hubbard model. In the presence of strong correlation, we observe an antiferromagnetic Mott insulating state at the doping level of one electron or hole per moiré superlattice cell (i.e. half filling of the first moiré miniband). We also observe layer-hybridized moiré excitons (electron-hole pairs) whose energy and oscillator strength are highly tunable by the quantum-confined Stark effect and are strongly influenced by the formation of the Mott state.   

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Throughout the years, strongly correlated coherent states of excitons have been the subject of intense theoretical and experimental studies. This topic has recently boomed due to new emerging quantum materials such as van der Waals (vdW) bound monolayers of transition metal dichalcogenides (TMDs). Here, we analyze the collective properties of charged interlayer excitons (CIE) observed recently in bilayer TMD heterostructures[1]. We derive the universal binding energy expressions as functions of the electron-hole effective mass ratio and interlayer separation distance to explain the experimental evidence for the negative CIE to have a greater binding energy than that of the positive CIE[1]. By analyzing these binding energy functions, we predict that new strongly correlated phases — crystal and Wigner crystal — can be selectively realized with TMD bilayers of properly chosen electron-hole effective masses by just varying their interlayer separation distance. Our results open up new avenues for nonlinear coherent control, charge transport and spinoptronics applications with quantum vdW heterostructures. – [1]L.A.Jauregui, et al., Science 366, 870 (2019); [2]I.V.Bondarev, et al, arXiv2002.09988   

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Semiconducting transition metal dichalcogenides exhibit extraordinarily strong light matter and Coulomb interactions giving rise to the formation of tightly bound exciton states in the monolayer limit. Of particular interest is the continuously tunable coupling of excitons with free charge carriers that has been broadly explored for the exciton ground state so far. Here, we experimentally demonstrate dressing of the excited exciton states by a Fermi sea of free charge carriers in an electrically contacted hBN-encapsulated monolayer WSe₂ [1]. We identify excited state trions (Fermi polarons) in both n- and p-doped regimes, determining their binding energies in the zero-density limit. At elevated densities we demonstrate a highly efficient redistribution of the oscillator strengths, and provide evidence for autoionization, a process, commonly associated with intrinsically metastable, excited states in atomic systems, which inherently limits the lifetime of excited state trions in monolayer semiconductors.

[1] K. Wagner et al.: arXiv:2007.05396 (2020)   

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Transition metal dichalcogenides constitute a versatile platform for atomically thin opto-electronic devices.
We integrate homobilayer MoS₂ in a dual-gate device structure allowing independent control of the electron density and out-of-plane electric field [1]. On increasing the electric field at close-to-zero electron concentration, we observe two well-separated features in our absorption measurements: the energy degeneracy of the two interlayer exciton configurations is lifted. This result reveals a large in-built electric dipole. It is consistent with an interlayer character of the transition: the electron is localized in the top or the bottom layer, while the hole is delocalized across the bilayer. We tune the energy splitting between these two interlayer excitons by as much as 120 meV such that we are able to bring the interlayer excitons energetically close to resonance with the intralayer states. While the interaction with the intralayer A-exciton is weak, we observe an avoided crossing of the upper interlayer exciton with the intralayer B-exciton.
These highly tunable excitonic transitions with large oscillator strength hold great promise for non-linear optics with polaritons.

[1] N. Leisgang et al., Nature Nanotechnology (2020).   

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Transition metal dichalcogenide (TMD) bilayers provide a promising platform to study interaction-driven physics. In particular, optical spectroscopy of bilayer TMD structures unveils excitonic coupling effects similar to semiconducting coupled quantum wells (CQWs). Excitons in bilayer TMDs can be sorted into two categories: Intralayer and interlayer excitons. For intralayer excitons, the Coulomb-bound electron-hole pair resides in the same layer while for interlayer excitons the electron and hole reside in different layers. The interaction of intralayer and interlayer excitons is studied in a two-dimensional semiconductor, homobilayer MoS₂. The excitonic interaction is well-described by a model of two coupled optical dipoles with different oscillator strength driven by a light field. Applying the model to the excitonic absorption reveals the nature of the excitonic coupling, attractive or repulsive. While the interlayer excitons interact attractively with the A-excitons, they interact repulsively with the B-excitons. Our model also predicts constructive interference in one eigenmode ("bright"), destructive interference in the other eigenmode ("dark"), near the energetic crossing of the bare states. We argue that this is a general feature of coupled excitons.   

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We study direct and indirect magnetoexcitons Rydberg states in monolayers and double-layer heterostructure of Xenes: silicene, germanene, and stanene, encapsulated by h-BN. The monolayers and heterostructures are in external parallel magnetic and electric fields, which are perpendicular to the structure. We calculate binding energies of magnetoexcitons for the Rydberg states 1s, 2s, 3s, and 4s by a solution of the Schrödinger equation using both the Rytova-Keldysh and Coulomb potentials for the description of electron-hole interaction. This allows to understand a role of screening in Xenes. In the external perpendicular electric field, the buckled structure of the Xene monolayers leads to appearance of potential difference between sublattices allowing to tune electron and hole masses and, therefore, the binding energies of magnetoexcitons. We report the energy contribution from magnetic and electric fields to the binding energies and diamagnetic coefficients. The tunability of magnetoexciton properties by parallel magnetic and electric fields is demonstrated. The calculations of the binding energies and diamagnetic coefficients of magnetoexcitons in Xenes monolayers and heterostructure are novel.   

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In the study of correlations in solids, angle-resolved photoemission spectroscopy (ARPES) represents a powerful tool to capture and quantify quasi-particles and interactions throughout momentum space. Coulomb-bound electron-hole pairs (excitons) are typically studied via optical spectroscopies which, however, lack momentum resolution. We will present time-resolved ARPES (trARPES) studies of monolayer MoS₂, evidencing the formation of 2D excitons in transient photoemission signatures. We studied ML MoS₂ on HOPG cooled to 80 K. The sample was optically excited below the gap, followed by femtosecond ARPES probing with 22.3 eV extreme-UV pulses. Transient ARPES maps exhibit a downward dispersing band below the conduction band at K valley, in agreement with theoretically-predicted exciton spectral function. Importantly, we reveal a crossover that occurs in time from an upward to the downward dispersion, evidencing tr-ARPES visualization of exciton formation. We will discuss these dynamics along with co-existing time-dependent band dynamics and theoretical modeling. The results highlight the novel application for tr-ARPES to access excitonic quasi-particles and correlations, forging new paths to exploring many-body interactions in low-dimensional quantum materials.   

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Twisted bilayers of semiconducting transition metal dichalcogenides (TMDs) form moiré patterns when stacked. The twist angle between the layers acts as another degree of freedom, which changes the moiré wavelength and hence the electronic structure. A long-wavelength moiré pattern forms near R-type (0 degree) or H-type (60 degree) stacking in homo- and hetero-bilayer TMD heterostructures leading to moiré flat bands near these angles. The interplay between these moiré flat bands and strong long-range coulomb interactions in the layers can create novel quantum effects. Using scanning tunneling microscopy and spectroscopy (STM/STS) at 4.6 K, we probe twisted bilayer MoSe₂/WSe₂ heterostructures with R-type stacking and report direct measurement of the topographic moiré structure, band alignment, and correlated effects. We have observed a large modulation of the valence band maxima and band gap at the different high symmetry stacking locations in agreement with previous optical spectroscopy measurements.   

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Two-dimensional semiconductors exhibit strongly bound excitons with unconventional dynamics. Here we investigate ultrafast exciton dynamics in monolayer WSe₂ from first principles, using our newly developed formalism to compute exciton-phonon interactions [1] and nonequilibrium exciton dynamics. We present accurate predictions of the temperature-dependent bright exciton photoluminescence (PL) linewidth and the phonon-assisted PL spectrum, including details of the vibronic structure. We further analyze the dominant exciton scattering channels in WSe₂, generating maps of phonon momentum-and mode-dependent exciton relaxation processes. We solve the time-dependent exciton Boltzmann transport equation (BTE) to explicitly simulate nonequilibrium exciton dynamics, and present simulated time-resolved ARPES results to connect our findings with experiments. Real-time tracking of the exciton occupations also reveals details of the bright exciton dephasing on femtosecond time scale. Our work advances the understanding of exciton scattering processes and excited-state dynamics in WSe₂.

[1] H.-Y. Chen, D. Sangalli, and M. Bernardi. Phys. Rev. Lett., 125 107401   

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Exciton dynamics have been investigated extensively in transition metal dichalcogenide (TMDC) monolayers, but comparatively little is known of their behavior in bilayers, due to the presence of multiple low-energy valleys in bilayer TMDC band structures. We find that bright exciton decoherence occurs on a much faster time scale in MoSe2 bilayers than in monolayers, and is limited by pure dephasing processes. Remarkable agreements between the measured and calculated homogeneous linewidths in both the monolayer and bilayer are found by taking into account all relevant exciton-phonon scattering processes. Our microscopic model identies that phonon-emission processes facilitate scattering events from the K valley to lower energy Γ and Λ valleys in the bilayer and induce pure dephasing.   

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Monolayer transition metal dichalcogenides are excellent models for the exploration of semiconductor physics at the 2D limit, with potential applications in electronics, optoelectronics, and quantum devices. The strong Coulomb interactions and distinct structural symmetries in these materials give rise to a rich variety of photoexcited states, including bright and dark excitonic complexes that are tightly bound, and valley-spin polarized. However, directly accessing the momentum-forbidden dark excitons and their dynamics, is not trivial with conventional experimental probes. Here, by performing time- and momentum-resolved photoemission spectroscopy on a micron-scale monolayer flake of WSe₂, we directly observe the momentum-forbidden dark excitons and measure their dynamics under different excitation conditions. Our measurements provide a global view over the entire Brillouin Zone of the ultrafast optical response of 2D semiconductors and demonstrate the impact of dark excitons.   

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We study excitons in suspended membranes of atomically thin WSe₂. We perform reflectance measurements to obtain the peak energies of the 1s, 2s, and 3s states of the A exciton in supported and suspended samples. From the experiments, we calculate the excitonic binding energies by employing the quantum electrostatic heterostructure model and the Rytova-Keldysh potential model. We find that the binding energy of the 1s exciton increases from about 0.3 eV (on the substrate) to above 0.4 eV (suspended) due to the reduced dielectric screening. We also exploit the tunability of the excitons in suspended samples via strain. By applying an air pressure of 40 psi to cause strain, we obtain reversible 0.15 eV redshift in the exciton resonance of a suspended 1L sample on a circular hole of 8 μm diameter. Interestingly, the linewidth of the 1s exciton decreases more than half from about 50 meV to 20 meV under 1.5% biaxial strain, due to the suppression of the intervalley exciton-phonon scattering. By making use of the strain-dependent optical signatures observed, we obtain the 2D elastic moduli of 1L and 2L WSe₂. Our results exemplify the use of suspended 2D materials as novel systems for fundamental studies and, strong and dynamic tuning of their optical properties.   

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We studied the work function, ionization energy, and electron affinity of bulk and few-layer transition-metal dichalcogenides (TMDs) in 2H phase using the density functional theory (DFT) and the GW approximation. We obtained DFT band energies of few-layer TMDs with respect to the vacuum level. For the vacuum level of bulk TMDs, we considered a sufficiently thick slab system which has a similar band gap with bulk. We introduced the GW approximation to obtain the quasiparticle energy shift of valence band maximum and conduction band minimum and estimated the work function, band gap, ionization energy, and electron affinity as functions of the number of layers. We compare our quasiparticle band energies of TMDs with available theoretical and experimental reports, and we discuss types of band alignments in in-plane and out-of-plane junctions of these few-layer and bulk transition-metal dichalcogenides.