Suppressed Stokes Shifts and Hot Luminescence from Quantum Dots within Plasmonic Nanocavities Junyang Huang1, Shu Hu1,¶, Adam Roach2, Angus Crookes3 , Niclas S. Mueller1,Γ, Junzhi Ye1, Lukas A. Jakob1, Yuling Xiong1, Shijie Zhu1, Akshay Rao1, Angela Demetriadou3, Liangfeng Sun2, Jeremy J. Baumberg1* 1 Cavendish Laboratory, Department of Physics, JJ Thompson Avenue, University of Cambridge, Cambridge, CB3 0HE, UK 2 The Center for Photochemical Sciences and Department of Physics, Bowling Green State University, Bowling Green, Ohio 43403, United States 3 School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK ¶present address: Department of Physics, Xiamen University, Xiamen, 361005, China Γpresent address: Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany *Corresponding author. Email: jjb12@cam.ac.uk (J.J.B.) Abstract Lead sulfide (PbS) quantum dots (QDs) hold great promise for solar energy conversion, yet their efficiency is compromised by a substantial Stokes shift that adversely affects their performance in photonic devices. Here we integrate PbS QDs within single plasmonic nanocavities, significantly mitigating Stokes shifts through Purcell enhancement of their band edge emission. Our approach entails bottom-up assembly of QDs into nanoparticle-on-mirror structures, leading to direct emission from band-edge excitons with radiative lifetimes suppressed below 1 ns, a drastic decrease from the 1600 ns observed in unmodified QDs. This manipulation of the Stokes shift is attributed to the increased photonic density of states within the nanocavity, which accelerates the radiative decay process and modifies exciton relaxation pathways. Our results underscore the critical role of plasmonic nanocavities in modifying QD emission characteristics, offering opportunities for enhancing QD-based device performance across a spectrum of photonic applications. Introduction Colloidal quantum dots (CQDs) based on lead sulfide (PbS) have emerged as a promising material in photovoltaics thanks to their outstanding solar conversion performance1–3. However, one of the key challenges to their application is the particularly large Stokes shift (hundreds of meV) where the emission spectrum is redshifted from the absorption spectrum4,5. This property, critical to the efficiency and application of semiconductor CQDs, plays a dual role depending on the application context. For QD-based light-emitting diodes, a minimal Stokes shift gives a well- populated bright band edge state with short radiative lifetime, enabling high quantum yields through efficient competition with non-radiative processes6. In photovoltaic applications, Stokes shifts restrict device efficiency by reducing the open-circuit voltage due to the mismatch between optical and electronic bandgaps. Conversely, applications such as solar concentrators7–10 and lasers11–13 benefit from a larger Stokes shift, to minimize reabsorption of emission and enhance performance. Mastering control over this Stokes shift is thus crucial for optimizing the performance of CQD-based devices across a spectrum of applications. The origin of the Stokes shift across different QD systems has been widely explored. The Stokes shift in CdSe QDs is ascribed to excitonic fine structure near the band edge, associated with spin- forbidden dark excitons14,15. These dark excitons, undetectable in absorption, play a dominant role in photoluminescence as they form a lower energy reservoir with extended lifetime16–18. This energy splitting between dark and bright excitons leads to the Stokes shift. However, the energy difference between bright and dark excitons in lead chalcogenide QD systems is relatively small (~20 meV), insufficient to account for the observed redshifts exceeding 200 meV4,5,19–22. These observed redshift at room temperature have so far been contributed to kinetically accessing defect states located within the bandgap23. where specific intrinsic defects can cause electron density localization of the band edge states, leading to pronounced Franck-Condon shifts on the order of hundreds of meV24. Coupling QDs to optical cavities can transform their Stokes shift and enhance photonic properties25. In general, QD emission can be manipulated across a wide energy spectrum by amplifying specific vibronic/excitonic transitions via resonance enhancement with coupled plasmonic structures. The pronounced near-field enhancement from resonant plasmons within nanocavities (|𝐸/𝐸0| > 100) facilitates significant Purcell enhancement of their spontaneous emission rates for both solid-state and molecular emitters26–32. Such extreme confinement, in combination with a small optical mode volume (V < 100 nm3), can be utilized to promote polaritonic optical phenomena33,34 and also modify charge relaxation pathways35–38, setting the stage for minimizing the Stokes shift via hot luminescence, where radiative decay occurs from higher energy vibronic states rather than from the lowest excited state. Achieving hot luminescence hinges on creating conditions where the radiative decay from higher energy band edge states competes with the speed of internal relaxation (breaking Kasha’s rule, which states that emission occurs from the lowest excited state). While molecular systems have yielded hot electroluminescence within nanotip-enhanced plasmonic nanocavities at cryogenic temperature, such effects have not been demonstrated at room temperature, nor have similar effects in QDs been demonstrated to our knowledge36. Here, we integrate PbS QDs into single plasmonic nanocavities, achieving a large Purcell enhancement of their spontaneous emission rate by more than 1600-fold while eliminating the Stokes shift in PbS QD emission. This offers a route to manipulate exciton relaxation and alter the dominant radiative state of the QDs. For bare QDs, the Stokes-shifted emission lifetime is 𝜏bare QD = 1600 ns, whereas integrating the QDs into a plasmonic cavity reduces their lifetime to <1 ns and elicits emission directly from the band edge exciton. The elimination of the Stokes shift is directly linked to the gap size of the plasmonic nanocavity, illustrating the critical influence of nanocavity geometry on the emission characteristics. This effect is attributed to the enhanced photonic density of states within the cavity, which significantly accelerates the radiative decay process from the band-edge state, effectively outpacing internal phonon-coupling relaxation mechanisms and thereby altering the exciton relaxation pathways. Our findings highlight the profound impact of nanophotonic engineering on the emission properties of QDs, providing a pathway for optimizing the performance of QD-based photonic devices. Results and discussion Fig. 1. NPoM-modified PbS QD emission. Schematics of (a) bare PbS QDs in solution and (b) a QD monolayer integrated within single NPoM nanocavities. (c, d) Absorption (α) spectra of PbS QDs with two different sizes (QD550 in c, QD690 in d) in solution (blue dashed lines), along with their photoluminescence spectra (red solid lines) showing Stokes shifts. (e) Redshift of emission peak position relative to the first exciton absorption peak for QD solution (cyan) and QD NPoM (yellow). Photoluminescence spectra (red) obtained from (f) QD550 and (g) QD690 embedded in NPoM, using 447 nm and 633 nm CW excitation and the corresponding dark-field (DF) scattering resonances (gray). 500 nm long-pass filters and 633 nm notch filters are used to reject laser in detection. Each spectrum is averaged over > 80 individual NPoMs. We adopt a bottom-up approach for robustly and deterministically integrating QDs into Nanoparticle-on-Mirror (NPoM) nanocavities (Methods). Briefly, a suspension of PbS QDs39 in hexane is deposited onto a diethylene glycol (DEG) surface. Hexane evaporation leads to the formation of a close-packed monolayer of QDs at the DEG-air interface. This QD film is then transferred to a template-stripped Au surface. Subsequently, colloidal Au NPs (D = 80 nm) are drop-cast onto the QD monolayer to form the NPoM construct30. The average core diameter of the PbS QD690 is determined to be 1.6 ± 0.3 nm using transmission electron microscopy (TEM, fig. S1). The thickness of the QD monolayer on the Au substrate, which includes oleic acid capping ligands, is measured to be 5 ± 1 nm using atomic force microscopy (AFM, fig. S2). This thickness will be reduced in the NPoM nanogap due to van der Waals compression from the upper NP. Individual NPoMs are analyzed optically in a custom-built confocal microscope, using fully automated photoluminescence and dark-field scattering spectroscopy. The extinction and emission spectra of bare PbS QDs of two distinct sizes in hexane suspension (Fig. 1c and 1d) clearly show the Stokes shift. The first exciton absorption peaks appear at 550 nm and 690 nm respectively (dashed blue lines). Upon above-band optical excitation of these QD suspensions, photoluminescence (PL) emanating from defect states is observed at 720 nm and 820 nm (red lines) respectively23,24. The Stokes redshift between absorption and emission energy is found to be directly proportional to the first exciton peak energy (Fig. 1e), concurring with previous reports23. In stark contrast, the emission spectra from PbS QDs within NPoM nanocavities do not exhibit a Stokes shift, resulting in emission bands that align spectrally with their first exciton absorption peaks (Fig. 1f and 1g, red). This phenomenon implies that the NPoM nanocavity significantly modifies the exciton relaxation pathway, leading to emission directly from the band- edge exciton. This suppression of Stokes shift is consistently observed across four different QD sizes (Fig. 1e). Notably, for monolayer PbS QDs outside the NPoM nanocavities, the emission is completely quenched by the Au mirror. Consequently, the PL spectra collected here, using a 1.5 μm collection spot diameter are exclusively from the cavity-enhanced emissions. Statistics of cavity dark-field scattering resonances are collected from >100 NPoM nanocavities, yielding an average peak resonance at 810 nm and 770 nm (Fig. 1f and 1g gray lines, fig. S3). The blueshifted cavity resonance in the QD690 NPoM, compared to QD550, is attributed to the increased gap size dictated by the QD diameter40,41. It is important to note that the observed emission bands in NPoMs do not coincide spectrally with the predominant cavity modes in the dark field spectra. Therefore, this characteristic differentiates our findings from previous studies involving nanocube-on-mirror (NCoM) structures with large PbS QD gap sizes, where emission was predominantly influenced by the fundamental modes of the plasmonic cavities26. Fig. 2. Purcell-accelerated emission lifetime. (a) Time-gated PL trace of PbS QD690 multilayer on glass, with 𝜆𝑙=400 nm pulses. (b) Normalized intensity vs time delay from time-gated PL from QD multilayer (red open circles), TCSPC of emission from QD NPoM (blue filled circles), and TCSPC instrument response from Si Raman signal (grey open circles). Laser fluence of 1.2 and 0.07 μJ/cm2/pulse used respectively. (c) Simulation of normalised electric field in the x-z plane of the QD NPoM nanocavity at excitation wavelength of 745 nm. (d) Spontaneous emission rate enhancement as a function of wavelength calculated at the top of the central QD. (e) Bare QDs on glass: photoexcitation of charges followed by relaxation into defect states results in slow redshifted emission (>1 μs). (f) Proposed mechanism for QDs in NPoMs: Purcell enhanced emission from the band-edge exciton surpasses the relaxation pathway to defect states, leading to ultrafast band-edge exciton emission with suppressed Stokes shift. Time-gated PL analysis is employed to quantify the emission lifetime of the PbS QD690. This measurement shows that the ‘bare QD’ (not coupled to any photonic structure) has lifetime 𝜏bare QD = 1600 ns within a solid film matrix (Fig. 2a,b). Initially, the excitons are excited in high- energy band edge states, before they undergo nonradiative Stokes transitions, transferring to lower-energy defect states. Emission from such defect states typically has extended lifetimes on μs timescales (Fig. 2e), due to small electron-hole pair overlap23,42–44. We note that a monolayer of PbS on a glass substrate yields PL signals that are too weak to be detected, impeding direct experimental measurement of the NPoM cavity enhancement factor. By contrast, integrating these QDs into NPoM structures gives a significant reduction in lifetime. Emission centered around 690 nm displays a decay on sub-nanosecond timescales (<1 ns, Fig. 2b, blue). However, this rapid decay rate matches the instrumental response function (IRF) of our time-correlated single photon counting (TCSPC) setup, which has a temporal resolution of 1 ns, indicating that the actual emission lifetime may be much shorter than 1 ns. (Fig. 2b, grey)45. Finite element simulations reveal that QDs positioned within the NPoM nanocavity experience substantial field enhancement (|𝐸/𝐸0| ≈ 340 at the top and bottom of QDs Fig. 2c and fig. S4). In NPoM structures, although the QD emission wavelength is offset from the fundamental cavity mode, which is the most efficient in coupling into the far-field, the nanocavity supports a set of higher-order quasi-normal modes whose energy spans from the single nanoparticle plasmon resonance at ~550 nm to the dominant cavity mode at 770 nm. These higher-order modes, while less pronounced in the scattering spectrum, produce substantial field enhancement within the nanogap, facilitating enhanced spontaneous emission at a broader off-resonance spectral range. Our finite-element simulations presented in Fig. 2d account for the cumulative contributions of these higher-order quasi-normal modes, demonstrating that the spontaneous emission rate enhancement remains significant at the QD emission wavelength of 690 nm, While the calculated Purcell factor can reach 10⁶ under idealized conditions at the point of maximum field enhancement, we acknowledge that the enhancement experienced by a QD dipole distributed throughout its volume is expected to be more moderate in a realistic scenario. Even a more conservative enhancement on the order of 10³ would still be sufficient to accelerate radiative recombination and suppress the Stokes shift. Although we cannot directly measure such a high Purcell factor, both the predicted and measured shortening of emission lifetime readily implies that within NPoM nanocavities the Purcell enhanced emission rate of the band edge excitons can surpass their coupling with surface defect states, which typically occurs on time scales of hundreds of picoseconds,46,47 effectively suppressing the Stokes shift process (Fig. 2f). Fig. 3. Excitation wavelength dependence. Normalized PL spectra from QD690 NPoMs while tuning excitation wavelength 𝜆𝑙 from 530 nm (bottom) to 633 nm (top). Optical excitation is performed with 500 fs pulses of average power <3 μW, except 633 nm with 10 μW CW laser (top). The PL spectra are taken with long path filters >630 nm, and the background of the spectra is attributed to electronic inelastic light scattering. Average dark-field scattering spectrum of NPoM nanocavities shown by red dashed curve. We compare the QD NPoM emission for a range of excitation wavelengths 𝜆l. The PL spectra are recorded while varying the excitation wavelength from 530 nm to 633 nm (Fig. 3). Across all excitation wavelengths, the band-edge emission at 690 nm is consistently observed, and the Stokes-shifted defect emission band at 820 nm, prominent in bare PbS QDs, is absent, indicating the suppression of the Stokes shift persists. In the spectrum with 633 nm excitation, narrower surface-enhanced Raman scattering (SERS) lines from the QD ligands are also observed (FWHM ≈ 5 nm). These inelastic SERS features shift according to the excitation wavelength, while the broader QD excitonic emission (FWHM ≈ 20 nm) remains consistently observed around 690 nm across all excitation wavelengths. For excitation at wavelengths ≤ 600 nm, an additional lower-energy emission band is detected ~760 nm. This emission band coincides with the dark-field scattering resonance of the nanocavity (Fig. 3, red dashed curve). We note that empty NPoM cavities do not yield any photoluminescence signature (fig. S5a-c). The origin of this distinct PL signature in PbS NPoM is attributed to the emission enhanced by the metal nanocavity, where the photo-induced dipole in the QDs couples to the cavity by exciting a plasmon. The subsequent radiative decay of this plasmon outcouples into free space through the dominant (10) optical nanocavity modes26,48–50. Our analysis reveals that the photoluminescence ratio between plasmon and exciton emissions exhibits a pronounced dependence on the laser excitation wavelength, correlating with the (20) cavity mode resonance (fig. S5d)41. This finding shows that aligning the excitation wavelength to the (20) cavity mode matches the spatial excitation profile of the QDs to the (10) cavity mode, which dictates the outcoupling efficiency, and therefore leads to enhanced outcoupling at 760nm. Fig. 4. Gap size dependent emission. (a) Schematics of NPoM gaps defined by monolayer (blue) and bilayer (red) of QD. (b) Dark-field scattering spectra of monolayer (blue) and bilayer (red) QD690 NPoM, with blue- shifted cavity resonance from increased gap size. (c) Normalized PL spectra of monolayer (blue, removing additional ligand SERS peaks in dashed line to give PL) and bilayer (red) QD690 NPoM, for 633 nm CW excitation. Spectral background <670 nm is due to laser leakage. The suppression of the Stokes shift is caused by the Purcell effect, which enhances the spontaneous emission rate of the band edge exciton. This phenomenon is intricately linked to the plasmonic gap size. Specifically, a larger gap reduces the field enhancement within the nanocavity, exponentially lengthening the Purcell-enhanced radiative recombination of the band-edge exciton27. The relationship between the field enhancement in the NPoM nanocavity (𝐸/𝐸0) and its gap size (𝑑) is given by 𝐸𝑚𝑎𝑥 2 𝐸0 2 ∝ Q𝑛𝑔 𝑅2 𝑑2 , where Q is the quality factor of the resonance, 𝑛𝑔the refractive index of the gap, and 𝑅 the radius of the nanoparticle31. If the Purcell effect is insufficient to counteract relaxation into the Stokes shifted transition, it is anticipated that Stokes shifted emission will re-emerge. To validate this hypothesis, we experimentally expand the NPoM gap by incorporating a bilayer of PbS QDs within the nanocavity (dbilayer~10 nm, Fig. 4a). As anticipated, increasing the gap size blueshifts the dark-field resonance relative to the monolayer nanocavity (Fig. 4b)40,41. This blue shift arises because the weaker field confinement within the nanogap leads to a lower effective refractive index for the plasmonic mode, reducing its resonant wavelength.31 With CW above- bandgap excitation at 633 nm, we now observe the re-emergence of Stokes shifted photoluminescence around 810 nm in the bilayer QD NPoMs (Fig. 4c). Despite the presence of a doubled density of QDs in these bilayer NPoMs, the Stokes-shifted emission is observed to be ~4 times weaker compared to the band-edge exciton emission in the monolayer sample (blue line). This disparity is attributed to the reduced Purcell enhancement in the bilayer structure. We also note that using NPoM structures with a QD monolayer of larger thickness (14 nm) formed by scaffolding with CdSe QDs also preserves the Stokes shifted emission (fig. S6), as predicted in this model. These findings address the critical challenge of the substantial Stokes shift in PbS QDs, which has limited their efficiency in photonic devices. By demonstrating significant suppression of the Stokes shift through plasmonic nanocavities, our work provides a new approach to manipulate the exciton relaxation pathway. Such Purcell accelerated emission can lead to better coherence and increased indistinguishability of photons, making it beneficial for applications in quantum information processing. Conclusions In conclusion, our study addresses the critical challenge of the substantial Stokes shift in PbS QDs, which has hindered their efficiency in photonic devices. By integrating PbS QDs with plasmonic nanocavities, we significantly manipulate the relaxation pathways, achieving over 1600-fold Purcell enhancement and complete suppression of the Stokes shift. This suppression minimizes non-radiative recombination and enhances quantum yield, making it particularly beneficial for QD-based LEDs, lasers, and other photonic applications where high brightness and fast radiative decay are advantageous. Our findings demonstrate the power of plasmonic engineering in tailoring QD emissive properties and highlight the importance of nanocavity geometry in emission control. This research lays the foundation for enhancing the performance of QD-based optoelectronic devices, while the Purcell accelerated emission also promises reduced dephasing and higher distinguishability for quantum photonic applications. Materials and Methods PbS ultrasmall QD synthesis Lead oxide (220 mg, 1 mmol), oleic acid (0.64 mL, 2 mmol), and 1-octadecene (9.96 mL) are refluxed and stirred under a sealed nitrogen atmosphere at 150 oC for 1 hour. Then the solution is cooled down to 50 oC and 1 mL of 1,1,2-trichloroethane is added and mixed for 30 minutes. In a separate flask, the sulfur precursor is prepared by adding hexamethyldisilathiane (126 μL, 0.7 mmol) dissolved in 6 mL of 1-octadecene. The solution is stirred under nitrogen protection. 5 mL of sulfur precursor is drawn by a syringe and injected into the lead precursor. They are stirred for 2 minutes and then ice bathed. The product is centrifuged after mixing with toluene and acetone. The precipitated quantum dots are redispersed in toluene and stored in a dark environment39. QD NPoM assembly To assemble QD monolayers, a colloidal PbS QD solution is first diluted to a concentration of approximately 0.1 mg/ml using hexane. Then, 100 μL of this solution is spread over the surface of diethylene glycol (DEG) in a clean petri dish. By covering the petri dish, the hexane evaporates slowly over a period of 5 to 10 minutes, leading to the formation of a dense monolayer film at the DEG-air interface51. For the transfer of the QD film, a template-stripped Au substrate is gently brought into contact with it. As the substrate is lifted, QD monolayers of centimeter scale are dip coated and are subsequently cleaned with 99% ethanol and dried using nitrogen gas. The thickness of the QD monolayer is characterized to be 5±1 nm using atomic force microscopy, as shown in fig. S2. To create the NPoM cavity, AuNPs (BBI solutions, D = 80 nm) are sparsely drop- cast on the QD monolayer and washed with deionized water. Optical measurement Dark-field microscopy and spectroscopy are performed using a customized Olympus BX51 microscope. Dark-field scattering is captured through a confocal fiber-coupled spectrometer (QE65000, Ocean Optics) that has a 1.5 μm collection spot diameter on the sample. The optical excitation of NPoMs is achieved by focusing a continuous wave laser at 447 nm (Coherent CUBE) or 633 nm (Integrated Optics) into a diffraction-limited spot through a ×100 Olympus objective (0.8 NA). PL signals are collected using the same objective, then coupled through a Triax 320 spectrometer, and finally recorded on an Andor Newton EMCCD. For wavelength-tunable excitation, a Spectra-Physics Maitai laser operating at 80 MHz is employed to drive an optical parametric oscillator (Spectra-Physics Inspire), generating 100 fs pulses. These pulses are subsequently filtered by a tunable bandpass filter (PhotonETC LLTF contrast) to 1 nm spectral width, extending the pulse duration to approximately 500 fs. Time-gated PL spectroscopy The gated time-resolved PL is measured with an iCCD camera system (Andor iStarDH740 CCI-010) which it is connected to a grating spectrometer (Andor SR303i). 400 nm laser excitation is obtained from a homebuilt setup with second harmonic generation (SHG) in a BBO crystal from the fundamental output (pulse fundenmetal laser wavelength 800 nm, pulse length 80 fs) of a Ti:Sapphire laser system (Spectra Physics Solstice). A 425 nm long-pass filter is added in the PL collection pass to remove residual 400 nm excitation laser. Temporal resolution of the PL emission was obtained by measuring the PL from the sample and stepping the iCCD gate delay for different delays with respect to the excitation. Measurement laser fluence is 0.064 μJ/cm2/pulse. Purcell Factor Calculations The enhancement of the spontaneous decay rate, 𝑃(𝜔), is obtained by normalising the total energy dissipation within the nanocavity 𝑃𝑐𝑎𝑣 = 𝜔 2 Im(𝐩∗ ⋅ 𝐄(𝐫0)) to the free space dissipation rate 𝑃0 = |𝐩|2𝜔4/12𝜋𝜖0𝑐 3 where 𝐩 is the dipole moment of a dipole with emission frequency 𝜔 at position 𝐫0 . To obtain 𝑃𝑐𝑎𝑣 we perform frequency domain simulations using COMSOL Multiphysics and obtain the partial local density of states 𝜌𝑃𝐿𝐷𝑂𝑆(𝜔) ∝ 𝐩̂ ⋅ 𝐼𝑚(𝐺(𝑟0, 𝑟0, 𝜔)) ⋅ 𝐩̂ as a function of frequency, where 𝐺(𝑟0, 𝑟0, 𝜔) is the Greens function52. 𝑃𝑐𝑎𝑣 is calculated on top of the QDs at 𝒓0 = 0.5𝑑𝑄𝐷 𝒛̂ where the maximum field enhancement occurs (see Supplementary Materials for simulation geometry). Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Acknowledgments Funding: We acknowledge support from European Research Council (ERC) under Horizon 2020 research and innovation programme POSEIDON (Grant Agreement No. 861950), and PICOFORCE (Grant Agreement No. 883703). NSM acknowledges support from the German National Academy of Sciences Leopoldina. L. S. acknowledges the support from the National Science Foundation under Grant No. 1905217. AD gratefully acknowledges support from the Royal Society University Research Fellowship URF\R1\180097 and URF\R\231024, Royal Society Research Fellows Enhancement Award RGF \EA\181038, and funding from EPSRC EP/X012689/1 and EP/Y008774/1. AD and AC acknowledge funding from EPSRC for the CDT in Topological Design EP/S02297X/1. Author contributions: J.H. and J.J.B designed the experiments. J.H. and S.H. performed sample fabrication. A.R. and L.S. synthesised the PbS QDs. A.C. and A.D conducted finite element simulations. A.R. and Y.X carried out TEM and AFM characterization, respectively. 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