Abstract
Interlayer excitons in van der Waals heterostructures are fascinating for applications like exciton condensation, excitonic devices and moiré-induced quantum emitters. The study of these charge-transfer states has almost exclusively focused on band edges, limiting the spectral region to the near-infrared regime. Here we explore the above-gap analogues of interlayer excitons in bilayer WSe2 and identify both neutral and charged species emitting in the ultraviolet. Even though the transitions occur far above the band edge, the states remain metastable, exhibiting linewidths as narrow as 1.8 meV. These interlayer high-lying excitations have switchable dipole orientations and hence show prominent Stark splitting. The positive and negative interlayer high-lying trions exhibit significant binding energies of 20–30 meV, allowing for a broad tunability of transitions via electric fields and electrostatic doping. The Stark splitting of these trions serves as a highly accurate, built-in sensor for measuring interlayer electric field strengths, which are exceedingly difficult to quantify otherwise. Such excitonic complexes are further sensitive to the interlayer twist angle and offer opportunities to explore emergent moiré physics under electrical control. Our findings more than double the accessible energy range for applications based on interlayer excitons.
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Data availability
The raw data that support the plots within this paper and the other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.
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Acknowledgements
We thank S. Krug and I. Gronwald for technical assistance. Financial support is gratefully acknowledged from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) SPP 2244 Project-ID 443378379 (K.-Q.L. and S.B.), 443405595 (A.S. and A.C.), and 443405595 (J.F.), SFB 1277 Project-ID 314695032 projects B03 (S.B. and J.M.L.), B05 (A.C.) and B11 (K.-Q.L. and J.F.) and DFG Instrumentation Grant Project-ID 403134862 (J.M.L.). A.C. acknowledges the DFG Emmy-Noether Grant (Project-ID CH 1672/1-1, 287022282) and the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project-ID 390858490). M.F. acknowledges support from the Alexander von Humboldt Foundation. The growth of the hBN crystals was supported by JSPS KAKENHI (grant nos. 19H05790, 20H00354 and 21H05233).
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K.-Q.L. conceived the project and carried out the experiments with input from S.B., F.H., J.M.B. and F.B. J.D.Z. and A.C. contributed to the samples. K.W. and T.T. provided the hBN crystals. P.E.F.J. and J.F. contributed to the density functional theory calculations of the electronic band structures under an electric field. R.H., M.F. and A.S. contributed to the theoretical description of HXs and high-lying trions. K.-Q.L., S.B., A.C. and J.M.L. analysed the data and wrote the paper, with input from all authors.
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Extended data
Extended Data Fig. 1 Charging model to compute Fz along with a microscopic image of the bilayer WSe2 dual gate transistor device.
a, Electrostatic model for dual-gated bilayer devices. The semiconducting WSe2 bilayer with interlayer spacing \({t}_{{\rm{WS}}{{\rm{e}}}_{2}}\) is sandwiched between hBN gate insulators and contacted by graphite electrodes. The graphite bottom and top gates at voltages Vbg and Vtg control the accumulation of charges in the WSe2 bottom and top layers with charge densities of \({n}_{{\rm{bl}}}\) and ntl, as well as the interlayer electric field Fz. ttg and tbg label the thickness of the top and bottom hBN insulator layers. b, Microscope image of the bilayer WSe2 dual-gate transistor device on a silicon substrate with 285 nm SiO2. Graphite thin films (few-layer graphene) are used as top and bottom gate electrodes and as contacts between pre-patterned gold finger electrodes and the WSe2. The thickness of top and bottom hBN layers is characterized by atomic force microscopy to be 30 nm and 44.5 nm. To reach an undoped regime in Fig. 1 in the main text, the top and bottom gate voltages (Vtg and Vbg) are set to keep the total charge density \(n={{\rm{c}}}_{{\rm{tg}}}{V}_{{\rm{tg}}}+{{\rm{c}}}_{{\rm{bg}}}{V}_{{\rm{bg}}}=0\), where \({{\rm{c}}}_{{\rm{tg}}}\) and \({{\rm{c}}}_{{\rm{bg}}}\) are the top and bottom gate geometric capacitances per unit area. For an electric-field-dependent measurement in Fig. 1, top and bottom gate voltages are swept while keeping \({V}_{{\rm{tg}}}/{{\rm{t}}}_{{\rm{tg}}}=-{V}_{{\rm{bg}}}/{{\rm{t}}}_{{\rm{bg}}}\).
Extended Data Fig. 2 Comparison of monolayer and bilayer WSe2 on the band-edge excitons and the high-lying excitons.
PL spectrum of the band-edge exciton (a) and upconverted luminescence of the high-lying exciton (b) in monolayer and bilayer WSe2. The band-edge exciton in bilayer WSe2 is about 100 times weaker than that in monolayer WSe2. The high-lying exciton in bilayer WSe2 is more than 10 times brighter than that in monolayer WSe2, which could be due to a weaker coupling to the phonon and a resultingly lower non-radiative decay rate for interlayer HX in bilayer WSe2. Panel b indicates a Huang-Rhys factor smaller than 1 for the interlayer HX in the bilayer and of approx. 4 for the intralayer HX in the monolayer. The SHG is suppressed in the bilayer due to its inversion symmetry.
Extended Data Fig. 3 Temperature dependence of HX UPL.
The HX shifts to lower energies and its linewidth broadens with increasing temperature.
Extended Data Fig. 4 Dependence of HX UPL on the laser power.
Power-dependent UPL (a) without and (b) with an out-of-plane electric field. The laser spot area is approximately 2.8 μm2.
Extended Data Fig. 5 HX Stark shift for different sweep directions of the out-of-plane electric field.
Dependence of the HX UPL on electric field strength Fz, (a) when sweeping from low Fz to high Fz, and (b) when sweeping from high Fz to low Fz. No difference is observed. No other PL feature is detected over a wide range of photon energy.
Extended Data Fig. 6 Dependence of the band-edge excitons on the out-of-plane electric field in a dual-gate monolayer WSe2 transistor device.
Stark shift is not observable for band-edge excitons in monolayer WSe2.
Extended Data Fig. 7 HX UPL from a 30° twisted bilayer WSe2 dual-gate transistor device.
a, Dependence of the HX UPL on out-of-plane electric-field strength Fz, showing Stark splitting of both the zero-phonon line and the trion. The neutral HX UPL in this case is 128 meV higher in energy than that of natural bilayer WSe2 (equivalent to a 60° twisted bilayer). b, Energy of the zero-phonon line as a function of the electric field, revealing a large permanent dipole moment of 0.56 e·nm and a small polarizability of 0.28 eV·nm2·V−2.
Extended Data Fig. 8 Effect of an electric field on the electronic band structure of natural bilayer (2H-stacking) WSe2.
Band structure calculated for different vertical electric-field strengths with layer decomposition indicated by color (top) and resolved by spin state (bottom).
Extended Data Fig. 9 Binding energy of four different high-lying trion species as a function of density n of the doping electrons for temperatures of 50 K, 100 K and 200 K.
a, The binding energies relative to the high-lying interlayer exciton. b, The energy difference between both Q-trions (tbbQ- and tbtQ-trion) and both K-trions (tbbK- and tbtK-trion). The short terms ‘tbt’ and ‘tbb’ specify the dominant localization of all three charge carriers of the trion in the order ‘hole, electron 1 (high-lying), electron 2 (band-edge)’, with ‘b’ standing for ‘bottom’ and ‘t’ for ‘top’, and labels Q and K marking the Q- and K-valleys.
Extended Data Fig. 10 Carrier-density dependence of interlayer high-lying trions at different out-of-plane electric-field strengths.
UPL of the high-lying exciton and trions as a function of the total charge density at different values of the difference between top and bottom gate potential, \(\Delta V={V}_{{\rm{bg}}}-{V}_{{\rm{tg}}}\).
Supplementary information
Supplementary Information
Supplementary Notes 1–4, Figs. 1–3, Tables 1 and 2 and Video 1.
Supplementary Video 1
Carrier-density dependence of interlayer high-lying trions at different out-of-plane electric-field strengths.
Source data
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Source Data Extended Data Fig./Table 2
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Source Data Extended Data Fig./Table 10
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Lin, KQ., Faria Junior, P.E., Hübner, R. et al. Ultraviolet interlayer excitons in bilayer WSe2. Nat. Nanotechnol. 19, 196–201 (2024). https://doi.org/10.1038/s41565-023-01544-7
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DOI: https://doi.org/10.1038/s41565-023-01544-7
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