# Fileset

[shan-et-al-2023-overbias-photon-emission-from-light-emitting-devices-based-on-monolayer-transition-metal-dichalcogenides.pdf](https://mdr.nims.go.jp/filesets/10c9d8cd-4f25-44ff-b60a-601251b7898b/download)

## Creator

Shengyu Shan, Jing Huang, Sotirios Papadopoulos, Ronja Khelifa, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Lujun Wang, Lukas Novotny

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Overbias Photon Emission from Light-Emitting Devices Based on Monolayer Transition Metal Dichalcogenides](https://mdr.nims.go.jp/datasets/75b992c0-ee1d-4b5d-9498-9077c58fbd53)

## Fulltext

Overbias Photon Emission from Light-Emitting Devices Based on Monolayer Transition Metal DichalcogenidesOverbias Photon Emission from Light-Emitting Devices Based onMonolayer Transition Metal DichalcogenidesShengyu Shan,# Jing Huang,# Sotirios Papadopoulos, Ronja Khelifa, Takashi Taniguchi, Kenji Watanabe,Lujun Wang, and Lukas Novotny*Cite This: Nano Lett. 2023, 23, 10908−10913 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Tunneling light-emitting devices (LEDs) based on transitionmetal dichalcogenides (TMDs) and other two-dimensional (2D) materials area new platform for on-chip optoelectronic integration. Some of the physicalprocesses underlying this LED architecture are not fully understood, especiallythe emission at photon energies higher than the applied electrostatic potential,so-called overbias emission. Here we report overbias emission for potentialsthat are near half of the optical bandgap energy in TMD-based tunnelingLEDs. We show that this emission is not thermal in nature but consistent withexciton generation via a two-electron coherent tunneling process.KEYWORDS: transition metal dichalcogenides, van der Waals LED, overbias photon emission, exciton generation, multielectron tunneling,energy transferIn 2015, the first two-dimensional (2D) material-basedtunneling light-emitting device (LED) was realized.1,2 Itemployed graphene (Gr) as a conductor for electrical contacts,transition metal dichalcogenides (TMDs) as semiconductors,and hexagonal boron nitride (hBN) as an insulator. This LEDarchitecture has inspired investigations on cavity integration,3,4single defect LEDs,5 and exciton modulation.6 It also openedup a new perspective for integrated on-chip optoelectronicdevices.7A typical device architecture is shown in Figure 1a. Itconsists of a Gr-hBN-WSe2-hBN-Gr heterostructure with twomonolayer Gr flakes acting as transparent electrodes and twohBN multilayers defining the tunnel barriers. A monolayer ofWSe2 is sandwiched in the middle and serves as the activematerial. Such double-tunnel barrier LEDs provide large-areaexciton light emission with an external quantum efficiency(EQE) on the order of 10−2 at room temperature.1,2 Here,excitons are formed by the charge injection of both electronsand holes into the active layer. This requires the applied biaspotential (eVb, where e is the elementary charge and Vb is thebias voltage) to be larger than the optical bandgap energy sothat electrons and holes can tunnel from the Gr electrodes toWSe2, thereby forming excitons.8However, there are also alternative ways to generate excitonsfor light emission such as by energy transfer. This processinvolves inelastic electron tunneling (IET), in which theelectron couples its energy to TMD excitons during thetunneling process.9−11 Such energy transfer can occurefficiently in van der Waals (vdW) heterostructures and isdue to strong near-field coupling between the tunnelingReceived: August 21, 2023Revised: November 24, 2023Accepted: November 28, 2023Published: December 4, 2023Figure 1. (a) Illustration of a double-barrier tunneling LED. Thejunction is encapsulated in hBN on both sides (not shown). (b, c) ELspectra of the double-barrier LED for Vb = 1.65 V and Vb = 1.04 V,respectively. The measured spectra (green areas) are fitted with thesum of two pseudo-Voigt functions (black lines) representing the A-exciton and trion. (d) EQE (in the spectral range from 1.4 to 1.8 eV)as a function of applied bias. The green dots represent data points,and the black curve is a guide to the eye.Letterpubs.acs.org/NanoLett© 2023 The Authors. Published byAmerican Chemical Society10908https://doi.org/10.1021/acs.nanolett.3c03155Nano Lett. 2023, 23, 10908−10913This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on December 17, 2023 at 04:29:00 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Shengyu+Shan"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jing+Huang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sotirios+Papadopoulos"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ronja+Khelifa"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Lujun+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Lujun+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Lukas+Novotny"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.3c03155&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=tgr1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig1&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03155?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://acsopenscience.org/open-access/licensing-options/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/electrons and the active material. Thus, excitons in TMDs canbe generated either by charge injection or by energy transfer.In both processes energy conservation requires that the biaspotential eVb is larger than the optical bandgap energy ℏωBG(ℏωBG ≃ 1.64 eV for monolayer WSe2 at room temperature,12where ℏ is the reduced Planck constant and ωBG is the angulartransition frequency); no excitonic photon emission isexpected for eVb < ℏωBG.8,9In this paper, we report on exciton light emission from amonolayer TMD tunneling LED driven by bias potentials (eVb≃ 1.00 eV) much smaller than the optical bandgap energy(ℏωBG ≃ 1.64 eV). To identify the physical origins of thisoverbias emission, we perform electroluminescence (EL)measurements on various LED designs and at differenttemperatures.In addition to double-barrier LEDs we also investigatesingle-barrier Gr-TMD-hBN-gold heterostructures withTMD = {WSe2, MoSe2}. Compared with double-barrierLEDs, single-barrier LEDs can reach higher currents underthe same bias voltage, thus allowing us to observe excitonemission at very low bias voltages. With this architecture, westart to detect light emission from the A-exciton in WSe2 at0.81 V and at 0.74 V in MoSe2. The measured thresholdvoltages correspond to approximately half the optical bandgapenergies. This observation hints at a second-order energytransfer process based on multielectron tunneling.13−15We note that overbias emission has been observed before inlight-emitting junctions, apart from vdW heterostructures.Depending on experimental conditions, this emission can begenerated by thermal upconversion,16,17 non-thermal equili-brium carrier generation,18−21 and coherent multielectronprocesses.13−15,22,23 Also, upconversion in 2D materials hasbeen accomplished optically via two-photon excitation24 orfacilitated by an intermediate state, for example, by Augerscattering of interlayer excitons.25 Nevertheless, electricallydriven overbias emission has never been reported in monolayerTMD-based LEDs.We first describe our results for the double-barrier LEDshown in Figure 1a. The core structure is a vertical assembly ofGr-hBN-WSe2-hBN-Gr, in which two Gr flakes serve aselectrodes. The hBN thickness corresponds to 4 ± 1 atomiclayers. This tunnel junction is encapsulated in two thick hBNflakes. The full encapsulation creates a homogeneous dielectricenvironment, enhancing uniformity of both the electricalproperties of graphene26 and the optical properties of TMDs.27We fabricate our devices by using the dry pick-up and transfermethod,28 where we transfer the entire device onto a glasscoverslip. After transfer we fabricate edge contacts to the twographene electrodes.29,30 EL is collected with an oil-immersionobjective from the glass side and detected by a spectrometer(see the Supporting Information, Sections I and II).Monolayer WSe2 has an electronic bandgap of ∼1.82 eV31and an optical bandgap of ∼1.64 eV at room temperature.12Based on energy conservation, we expect that electricalgeneration of excitons requires bias potentials eVb that arelarger than the optical bandgap energy.8 In order to generateexcitons at a bias below this threshold, higher-order processesor phonon-assisted interactions are required. Figure 1b shows arepresentative EL spectrum for Vb = 1.65 V. The peak of thespectrum centers at ∼1.64 eV, which corresponds to the A-exciton of WSe2.8 The asymmetric broadening at lowerenergies can be associated with trions.8 However, we alsoobserve exciton light emission for eVb significantly smaller thanthe optical bandgap. As an example, Figure 1c shows the ELspectrum for Vb = 1.04 V. Compared to Figure 1b, thisspectrum has the same main peak position and similar linewidth, indicating that the spectrum is also dominated by thecontribution from A-excitons. The spectral shape remainssimilar, but the intensity and hence the EQE decrease. Wedefine EQE asI eEQE /X= , where ΓX is the photon count ratein the spectral range from 1.4 to 1.8 eV and I is the electricalcurrent (for more details, see the Supporting Information,Section III). As shown in Figure 1d, the EQE dropsexponentially with decreasing Vb and disappears in the noisefloor at ∼0.93 V. To extend the measurement range to evenlower bias voltages, we require a higher emission intensity andhence a higher tunnel current. Therefore, in a next step, weeliminate one of the tunnel barriers and repeat the measure-ments for a single-barrier device.The architecture of a single-barrier LED is shown in Figure2a. The device is composed of a Gr-WSe2-hBN-goldheterostructure, where the monolayer Gr is in contact with asecond gold electrode. As shown in Figure 2c, by using asingle-barrier device (hBN with 3 ± 1 atomic layers), we areable to increase the current density by ∼4 orders of magnitudeover the previous double-barrier device.A typical EL spectrum of the single-barrier device obtainedat 1.62 V is shown in Figure 2d. The spectrum has a peak atFigure 2. (a) Illustration of a single-barrier LED. The stack isencapsulated by a top hBN flake (not shown). (b) EL spectra for Vbranging from 0.7 to 0.95 V. The horizontal dotted line indicates theneutral exciton energy (1.62 eV), and the vertical dotted line denotesthe threshold for exciton emission. There is a factor of 10 differencebetween the two dashed contour lines (see Section V of theSupporting Information for more spectra). (c) Current density−voltage (J−V) curve of a single- and double-barrier LED. (d)Normalized EL spectra for Vb = 0.81 and 1.62 V.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03155Nano Lett. 2023, 23, 10908−1091310909https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03155?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as∼1.62 eV, which is slightly red-shifted compared to that of thedouble-barrier LED. Consequentially, we assign this peak tothe neutral A-exciton, which is shifted to lower energies due tothe stronger dielectric screening of the directly contactingGr.32,33 The overall EL intensity is moderately quenchedcompared to the double-barrier device, and the spectrumbecomes trion-free due to both charge and energy transfer.34,35Figure 2b shows the EL spectra as a function of Vb in theoverbias emission regime. The horizontal axis represents thebias voltage with each vertical cross section denoting an ELspectrum corresponding to the applied bias. As we graduallylower Vb, the exciton peak remains visible in the spectrum,even for eVb = 0.81 eV (vertical dotted line), corresponding tohalf of the WSe2 optical bandgap energy (ℏωBG = 1.62 eV).The EL spectrum for Vb = 0.81 V is shown in Figure 2d (lightorange area). Its shape is almost identical with that of thespectrum recorded for 1.62 V (solid orange curve). Thisobservation hints at a second-order process involving twoelectrons.In order to further strengthen our interpretation, we replaceWSe2 by MoSe2, which has a lower bandgap and shouldtherefore lead to EL at even lower bias voltages. Furthermore,it is known that the exciton emission from MoSe2 is lessaffected by Gr quenching,34 thus yielding stronger EL emissionand providing a better signal-to-noise ratio. Figure 3a showsvoltage-dependent EL spectra of a MoSe2-based device. Whenthe bias voltage Vb is 0.70 V, the spectrum is primarilycharacterized by background noise. As the bias is increased, thefirst feature, near 1.56 eV (horizontal dotted line), appears at0.74 V (vertical dotted line). This feature is associated with thered-shifted A-exciton (1s state) of monolayer MoSe2.34 Thethreshold bias potential of 0.74 eV is again much lower thanthe photon energy of 1.56 eV. At higher biases, two side peaksappear near 1.66 and 1.74 eV. According to their energy offsetsrelative to the A-exciton, we assign the first to the 2s and 3sstates of A-exciton and the second to the B-exciton.36,37 Weestimate the binding energy of the A-exciton in our device tobe ∼133 meV by the energy difference between the groundstate and excited states. This value is smaller than thosereported in refs 34 and 36, and we attribute this to thedielectric screening from both Gr and gold electrodes.To analyze the voltage dependence of these three features,we fit the spectra with three pseudo-Voigt functions. Thecorresponding fitting amplitudes are plotted in Figure 3b as afunction of the bias voltage (see the Supporting Information,Section IV). We observe that the three peaks emerge atdifferent bias voltages: the lowest state of A-exciton with a peakposition near 1.56 eV appears for Vb > 0.74 V, the 2s and 3sexcited states near 1.66 eV have an onset voltage of 0.82 V, andthe B-exciton with the highest energy (∼1.74 eV) emerges nearVb = 0.86 V. Altogether, each of the three features in MoSe2emerges near bias potentials of half the photon energy (eVb ≃ℏω/2), similar to the WSe2 device.Besides a second-order process involving two electrons,other processes can also give rise to overbias emission. Theseinclude (1) blackbody radiation of hot carriers, in which theeffective temperature is related to the bias voltage or the inputpower;18−20,38,39 (2) recombination of out-of-equilibriumcarriers,21 in which electrons and holes in the high-energytail of the Fermi−Dirac distribution tunnel into the TMD toform excitons; (3) second-order nonlinear optical processes, inwhich photons generated by IET40,41 excite excitons in theTMD; and (4) second-order energy transfer, in which theenergy from pairs of coherently tunneling electrons13−15 isforming excitons in the TMD.To exclude the first two processes, we fabricate yet anothersingle-barrier MoSe2 LED and measure its EL at cryogenictemperature (∼10 K) (see the Supporting Information, SectionVI). To rule out the thermal origin for the observed overbiasemission, we use the following blackbody radiation model forthe radiated power:18−20Pc k Texp( / ) 1( ) dther022 3B=(1)where c is the speed of light, ω the photon angular frequency,kB the Boltzmann constant, T′ the effective hot carriertemperature, and ϵ″ the emissivity of the TMD exciton,which can be derived from the refractive index.42 For resistiveheating we obtain the linear dependence19,20T TekV0Bb= +(2)where T0 is the lattice temperature and κ is a temperature-independent dimensionless constant that can be derived fromexperimental data at room temperature. With this κ, eq 1predicts that the radiated power in the spectral region of theexciton should decrease by roughly 9 orders of magnitudewhen T0 is reduced from 300 to 10 K. However, ourmeasurements show only a decrease of less than 2 orders ofmagnitude. This huge discrepancy between model andmeasurement indicates that blackbody radiation is not thesource of the observed overbias emission. The same is true forthe second scenario, the recombination of out-of-equilibriumcarriers, because our measurements reveal that the dependenceof the radiated power on bias voltage is unaffected by thelattice temperature (see the Supporting Information, SectionVI, for analysis details).Figure 3. (a) EL spectra of a single-barrier LED based on MoSe2. Thehorizontal dotted line indicates the neutral exciton energy (1.56 eV),and the vertical dotted line denotes the threshold for excitonemission. There is a factor of 10 between adjacent dashed contourlines. (b) Dependence of the integrated EL intensity of A1s, A2s + A3s,and B1s excitons on bias voltage.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03155Nano Lett. 2023, 23, 10908−1091310910https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig3&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03155?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asThe third scenario involves two steps, namely photonemission by IET40,41 and a subsequent nonlinear opticalprocess. Comparing the photon emission efficiencies of theIET and the observed overbias emission, we require anonlinear optical process with unit efficiency to explain ourmeasurements. Therefore, it is safe to discard the thirdscenario as an explanation for our observation.We are left with the fourth scenario, illustrated in Figure 4a.In this scenario, excitons are generated by the action of twoelectrons. This process is supported by two recent observa-tions. First, it has been demonstrated that excitons can beefficiently excited by tunneling electrons via nonradiativeenergy transfer.9 Second, it has been reported that multi-electron coherent tunneling can generate overbias emission inplasmonic tunnel junctions.13−15,22,23 Therefore, we identifythe multielectron IET as the most likely mechanismresponsible for the observed overbias emission.In plasmonic tunnel junctions, overbias light emission basedon two-electron IET depends on the interplay between higher-order quantum noise and the local density of optical states(LDOS).13,14 Here we adopt this theory to form a TMD-coupled tunnel junction. The nonsymmetrized power spectraldensity of the fluctuating tunnel current reads as43,44S V e n eV I V en eV I V e( , ) 1 ( ) ( / )( ) ( / )ii b B b bB b b= {[ + ]+ + + } (3)where I(Vb) is the bias-dependent tunnel current andn x x k T( ) (exp( / ) 1)B B1= is the Bose−Einstein distributionat temperature T. We are concerned with the absorption ofelectromagnetic energy generated by the fluctuating tunnelingcurrent, which is described by the positive frequency part ofSii.45The absorption depends on the local environment of thetunnel junction and is mathematically described by theLDOS (ρ) and the system’s Green’s function.46 Forfrequencies that correspond to the TMD exciton energy, theabsorption is dominated by the LDOS of the TMD (ρTMD). Ina two-electron process, the locally absorbed energy is no longerlinearly dependent on Sii. In analogy to previous studies,15,22,23the two-electron energy absorption rate γ2e can be representedasV S VS V( , ) ( ) ( ) ( , )( , ) diiii2e b TMD 00TMD bb× (4)where ρTMD is calculated by following ref 41. Equation 4describes a two-electron tunneling process in which the energyof two electrons is absorbed by the TMD to generate anexciton (Figure 4a). Because excitons can only be generated byenergies larger than the exciton energy (ℏω > EX), we canrepresent the exciton light emission intensity ΓX asV V( ) ( , ) dEXb/ 2e bX (5)As can be seen in Figure 4b, the exciton EL intensity increasesexponentially with increasing Vb, and the calculated ΓX(Vb)according to eq 5 agrees well with the experimental results (seethe Supporting Information, Section VIII). This agreementsupports our interpretation that the overbias emission in ourTMD-based LEDs results from two-electron tunneling,followed by energy transfer.In summary, we investigated exciton light emission forpotentials lower than the optical bandgap energy in TMD-based tunneling LEDs. We are able to measure excitonemission for bias potentials of only half the optical bandgapenergy. We explain this overbiased emission by a second-orderenergy transfer process. Our work contributes to theunderstanding of light emission from vdW tunnel junctionsand to the development of energy-efficient LEDs based on 2Dmaterials.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155.Descriptions of sample fabrication, measurementsmethods, efficiency calculations of the LED, spectraprocessing and fitting methods, EL spectra acquiredunder the negative bias conditions of the device depictedin Figure 2, measurements and analysis of overbiasemission at cryogenic environments, and the model ofenergy transfer based on the multielectron tunnelingprocess (PDF)■ AUTHOR INFORMATIONCorresponding AuthorLukas Novotny − Photonics Laboratory, ETH Zürich, 8093Zürich, Switzerland; orcid.org/0000-0002-9970-8345;Email: lnovotny@ethz.chAuthorsShengyu Shan − Photonics Laboratory, ETH Zürich, 8093Zürich, Switzerland; orcid.org/0000-0001-5865-3694Jing Huang − Photonics Laboratory, ETH Zürich, 8093Zürich, Switzerland; orcid.org/0009-0000-8323-2197Sotirios Papadopoulos − Photonics Laboratory, ETH Zürich,8093 Zürich, Switzerland; orcid.org/0000-0002-3225-8239Ronja Khelifa − Photonics Laboratory, ETH Zürich, 8093Zürich, Switzerland; orcid.org/0000-0003-0285-6913Figure 4. (a) Energy transfer based on two-electron coherenttunneling. A pair of electrons tunnel inelastically, and their combinedenergy generates excitons in the TMD. (b) Exciton EL intensity (ΓX)of a single-barrier WSe2 LED as a function of bias voltage Vb. Theinset shows the data on a semilogarithmic scale. The data pointscorrespond to the integrated EL photon count rate in the spectralrange from 1.4 to 1.8 eV. The dashed curve is the fitting result of eq 5.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03155Nano Lett. 2023, 23, 10908−1091310911https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c03155/suppl_file/nl3c03155_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Lukas+Novotny"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-9970-8345mailto:lnovotny@ethz.chhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Shengyu+Shan"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0001-5865-3694https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jing+Huang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0009-0000-8323-2197https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sotirios+Papadopoulos"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-3225-8239https://orcid.org/0000-0002-3225-8239https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ronja+Khelifa"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-0285-6913https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?fig=fig4&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03155?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asTakashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Kenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Lujun Wang − Photonics Laboratory, ETH Zürich, 8093Zürich, SwitzerlandComplete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.3c03155Author Contributions#S.S. and J.H. contributed equally to this work. L.N., L.W., andS.P. conceived the project. J.H., S.S., and R.K. fabricated thedevices and performed the experiments. L.N., L.W., and S.P.supervised the project. T.T. and K.W. synthesized the h-BNcrystals. S.S., J.H., and L.N. analyzed the data and cowrote themanuscript.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis work has been supported by the Swiss National ScienceFoundation (Grant 200020_192362/1). The authors aregrateful to Olivier Huber, Deepankur Thureja, Atac Imamoglu,and Jian Zhang for kindly helping us perform the cryogenicmeasurements. We acknowledge Hsiang-Lin Liu for providingus with the original data of TMD optical constants from ref 42.We also thank Antti Moilanen, Anna Kuzmina, Achint Jain,Yesim Koyaz, Yang Xu, Nicola Carlon Zambon, MoritzCavigelli, Martin Frimmer, Jonas David Ziegler, and GiacomoScalari for fruitful discussions and support. The use of thefacilities of the FIRST center for micro- and nanoscience atETH Zürich is gratefully acknowledged. K.W. and T.T.acknowledge support from JSPS KAKENHI (Grants19H05790, 20H00354, and 21H05233).■ REFERENCES(1) Withers, F.; Del Pozo-Zamudio, O.; Mishchenko, A.; Rooney, A.P.; Gholinia, A.; Watanabe, K.; Taniguchi, T.; Haigh, S. J.; Geim, A.K.; Tartakovskii, A. I.; Novoselov, K. S. Light-emitting diodes byband-structure engineering in van der Waals heterostructures. Nat.Mater. 2015, 14, 301.(2) Withers, F.; Del Pozo-Zamudio, O.; Schwarz, S.; Dufferwiel, S.;Walker, P. M.; Godde, T.; Rooney, A. P.; Gholinia, A.; Woods, C. R.;Blake, P.; Haigh, S. J.; Watanabe, K.; Taniguchi, T.; Aleiner, I. L.;Geim, A. K.; Fal’Ko, V. I.; Tartakovskii, A. I.; Novoselov, K. S. WSe2Light-Emitting Tunneling Transistors with Enhanced Brightness at RoomTemperature. Nano Lett. 2015, 15, 8223.(3) Liu, C. H.; Clark, G.; Fryett, T.; Wu, S.; Zheng, J.; Hatami, F.;Xu, X.; Majumdar, A. Nanocavity integrated van der Waalsheterostructure light-emitting tunneling diode. Nano Lett. 2017, 17,200.(4) Del Pozo-Zamudio, O.; Genco, A.; Schwarz, S.; Withers, F.;Walker, P. M; Godde, T.; Schofield, R. C.; Rooney, A. P.; Prestat, E.;Watanabe, K.; Taniguchi, T.; Clark, C.; Haigh, S. J.; Krizhanovskii, D.N.; Novoselov, K. S.; Tartakovskii, A. I. Electrically pumped WSe2-based light-emitting van der Waals heterostructures embedded inmonolithic dielectric microcavities. 2D Mater. 2020, 7, 031006.(5) Clark, G.; Schaibley, J. R.; Ross, J.; Taniguchi, T.; Watanabe, K.;Hendrickson, J. R.; Mou, S.; Yao, W.; Xu, X. Single defect light-emitting diode in a van der Waals heterostructure. Nano Lett. 2016,16, 3944.(6) Ryu, H.; Kwon, J.; Yang, S.; Watanabe, K.; Taniguchi, T.; Kim,Y. D.; Hone, J.; Lee, C. H.; Lee, G. H. Electrical Modulation ofExciton Complexes in Light-Emitting Tunnel Transistors of a van derWaals Heterostructure. ACS Photonics 2021, 8, 3455.(7) Mak, K. F.; Shan, J. Photonics and optoelectronics of 2Dsemiconductor transition metal dichalcogenides. Nat. Photonics 2016,10, 216.(8) Binder, J.; Withers, F.; Molas, M. R.; Faugeras, C.; Nogajewski,K.; Watanabe, K.; Taniguchi, T.; Kozikov, A.; Geim, A. K.; Novoselov,K. S.; Potemski, M. Sub-bandgap Voltage Electroluminescence andMagneto-oscillations in a WSe2 Light-Emitting van der WaalsHeterostructure. Nano Lett. 2017, 17, 1425.(9) Papadopoulos, S.; Wang, L.; Taniguchi, T.; Watanabe, K.;Novotny, L. Energy transfer from tunneling electrons to excitons, 2022;arXiv:2209.11641, https://arxiv.org/abs/2209.11641 (accessed 2023-11-15).(10) Pommier, D.; Bretel, R.; López, L. E. P.; Fabre, F.; Mayne, A.;Boer-Duchemin, E.; Dujardin, G.; Schull, G.; Berciaud, S.; Le Moal, E.Scanning Tunneling Microscope-Induced Excitonic Luminescence ofa Two-Dimensional Semiconductor. Phys. Rev. Lett. 2019, 123,027402.(11) Peña Román, R. J.; Pommier, D.; Bretel, R.; Parra López, L. E.;Lorchat, E.; Chaste, J.; Ouerghi, A.; Le Moal, S.; Boer-Duchemin, E.;Dujardin, G.; Borisov, A. G.; Zagonel, L. F.; Schull, G.; Berciaud, S.;Le Moal, E. Electroluminescence of monolayer WS2 in a scanningtunneling microscope: Effect of bias polarity on spectral and angulardistribution of emitted light. Phys. Rev. B 2022, 106, 085419.(12) Kozawa, D.; Kumar, R.; Carvalho, A.; Kumar Amara, K.; Zhao,W.; Wang, S.; Toh, M.; Ribeiro, R. M.; Castro Neto, A. H.; Matsuda,K.; Eda, G. Photocarrier relaxation pathway in two-dimensionalsemiconducting transition metal dichalcogenides. Nat. Commun.2014, 5, 4543.(13) Xu, F.; Holmqvist, C.; Belzig, W. Overbias light emission due tohigher-order quantum noise in a tunnel junction. Phys. Rev. Lett. 2014,113, 66801.(14) Xu, F.; Holmqvist, C.; Rastelli, G.; Belzig, W. DynamicalCoulomb blockade theory of plasmon-mediated light emission from atunnel junction. Phys. Rev. B 2016, 94, 245111.(15) Peters, P.-J.; Xu, F.; Kaasbjerg, K.; Rastelli, G.; Belzig, W.;Berndt, R. Quantum Coherent Multielectron Processes in an AtomicScale Contact. Phys. Rev. Lett. 2017, 119, 066803.(16) Pechou, R.; Coratger, R.; Ajustron, F.; Beauvillain, J. Cutoffanomalies in light emitted from the tunneling junction of a scanningtunneling microscope in air. Appl. Phys. Lett. 1998, 72, 671.(17) Su, Q.; Chen, S. Thermal assisted up-conversion electro-luminescence in quantum dot light emitting diodes. Nat. Commun.2022, 13, 369.(18) Buret, M.; Uskov, A. V.; Dellinger, J.; Cazier, N.;Mennemanteuil, M. M.; Berthelot, J.; Smetanin, I. V.; Protsenko, I.E.; Colas-Des-Francs, G.; Bouhelier, A. Spontaneous Hot-ElectronLight Emission from Electron-Fed Optical Antennas. Nano Lett. 2015,15, 5811.(19) Zhu, Y.; Cui, L.; Natelson, D. Hot-carrier enhanced lightemission: The origin of above-threshold photons from electricallydriven plasmonic tunnel junctions. J. Appl. Phys. 2020, 128, 233105.(20) Cui, L.; Zhu, Y.; Abbasi, M.; Ahmadivand, A.; Gerislioglu, B.;Nordlander, P.; Natelson, D. Electrically Driven Hot-CarrierGeneration and Above-Threshold Light Emission in PlasmonicTunnel Junctions. Nano Lett. 2020, 20, 6067.(21) Lian, Y.; Lan, D.; Xing, S.; Guo, B.; Ren, Z.; Lai, R.; Zou, C.;Zhao, B.; Friend, R. H.; Di, D. Ultralow-voltage operation of light-emitting diodes. Nat. Commun. 2022, 13, 3845.(22) Fung, E. D.; Venkataraman, L. Too Cool for BlackbodyRadiation: Overbias Photon Emission in Ambient STM Due toMultielectron Processes. Nano Lett. 2020, 20, 8912.(23) Zhu, Y.; Cui, L.; Abbasi, M.; Natelson, D. Tuning LightEmission Crossovers in Atomic-Scale Aluminum Plasmonic TunnelJunctions. Nano Lett. 2022, 22, 8068.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03155Nano Lett. 2023, 23, 10908−1091310912https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-1467-3105https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-3701-8119https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Lujun+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c03155?ref=pdfhttps://doi.org/10.1038/nmat4205https://doi.org/10.1038/nmat4205https://doi.org/10.1021/acs.nanolett.5b03740?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b03740?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b03740?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.6b03801?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.6b03801?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1088/2053-1583/ab8542https://doi.org/10.1088/2053-1583/ab8542https://doi.org/10.1088/2053-1583/ab8542https://doi.org/10.1021/acs.nanolett.6b01580?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.6b01580?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsphotonics.1c01286?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsphotonics.1c01286?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acsphotonics.1c01286?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1038/nphoton.2015.282https://doi.org/10.1038/nphoton.2015.282https://doi.org/10.1021/acs.nanolett.6b04374?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.6b04374?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.6b04374?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://arxiv.org/abs/2209.11641https://doi.org/10.1103/PhysRevLett.123.027402https://doi.org/10.1103/PhysRevLett.123.027402https://doi.org/10.1103/PhysRevB.106.085419https://doi.org/10.1103/PhysRevB.106.085419https://doi.org/10.1103/PhysRevB.106.085419https://doi.org/10.1038/ncomms5543https://doi.org/10.1038/ncomms5543https://doi.org/10.1103/PhysRevLett.113.066801https://doi.org/10.1103/PhysRevLett.113.066801https://doi.org/10.1103/PhysRevB.94.245111https://doi.org/10.1103/PhysRevB.94.245111https://doi.org/10.1103/PhysRevB.94.245111https://doi.org/10.1103/PhysRevLett.119.066803https://doi.org/10.1103/PhysRevLett.119.066803https://doi.org/10.1063/1.120841https://doi.org/10.1063/1.120841https://doi.org/10.1063/1.120841https://doi.org/10.1038/s41467-022-28037-whttps://doi.org/10.1038/s41467-022-28037-whttps://doi.org/10.1021/acs.nanolett.5b01861?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.5b01861?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1063/5.0024392https://doi.org/10.1063/5.0024392https://doi.org/10.1063/5.0024392https://doi.org/10.1021/acs.nanolett.0c02121?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.0c02121?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.0c02121?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1038/s41467-022-31478-yhttps://doi.org/10.1038/s41467-022-31478-yhttps://doi.org/10.1021/acs.nanolett.0c03994?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.0c03994?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.0c03994?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.2c02013?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.2c02013?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.2c02013?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aspubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03155?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as(24) He, K.; Kumar, N.; Zhao, L.; Wang, Z.; Mak, K. F.; Zhao, H.;Shan, J. Tightly bound excitons in monolayer WSe2. Phys. Rev. Lett.2014, 113, 026803.(25) Binder, J.; Howarth, J.; Withers, F.; Molas, M. R.; Taniguchi,T.; Watanabe, K.; Faugeras, C.; Wysmolek, A.; Danovich, M.; Fal’ko,V. I.; Geim, A. K.; Novoselov, K. S.; Potemski, M.; Kozikov, A.Upconverted electroluminescence via Auger scattering of interlayerexcitons in van der Waals heterostructures. Nat. Commun. 2019, 10,2335.(26) Decker, R.; Wang, Y.; Brar, V. W.; Regan, W.; Tsai, H.-Z.; Wu,Q.; Gannett, W.; Zettl, A.; Crommie, M. F. Local electronic propertiesof graphene on a BN substrate via scanning tunneling microscopy.Nano Lett. 2011, 11, 2291.(27) Cadiz, F.; Courtade, E.; Robert, C.; Wang, G.; Shen, Y.; Cai,H.; Taniguchi, T.; Watanabe, K.; Carrere, H.; Lagarde, D.; et al.Excitonic linewidth approaching the homogeneous limit in MoS2-based van der Waals heterostructures. Phys. Rev. X 2017, 7, 021026DOI: 10.1103/PhysRevX.7.021026.(28) Zomer, P. J.; Guimaraẽs, M. H.; Brant, J. C.; Tombros, N.; VanWees, B. J. Fast pick up technique for high quality heterostructures ofbilayer graphene and hexagonal boron nitride. Appl. Phys. Lett. 2014,105, 013101.(29) Wang, L.; Meric, I.; Huang, P. Y.; Gao, Q.; Gao, Y.; Tran, H.;Taniguchi, T.; Watanabe, K.; Campos, L. M.; Muller, D. A.; Guo, J.;Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R. One-DimensionalElectrical Contact to a Two-Dimensional Material. Science 2013, 342,614.(30) Overweg, H.; Eggimann, H.; Chen, X.; Slizovskiy, S.; Eich, M.;Pisoni, R.; Lee, Y.; Rickhaus, P.; Watanabe, K.; Taniguchi, T.; Fal’Ko,V.; Ihn, T.; Ensslin, K. Electrostatically Induced Quantum PointContacts in Bilayer Graphene. Nano Lett. 2018, 18, 553.(31) Gutiérrez-Lezama, I.; Ubrig, N.; Ponomarev, E.; Morpurgo, A.F. Ionic gate spectroscopy of 2D semiconductors. Nat. Rev. Phys.2021, 3, 508.(32) Ugeda, M. M.; Bradley, A. J.; Shi, S. F.; Da Jornada, F. H.;Zhang, Y.; Qiu, D. Y.; Ruan, W.; Mo, S. K.; Hussain, Z.; Shen, Z. X.;Wang, F.; Louie, S. G.; Crommie, M. F. Giant bandgaprenormalization and excitonic effects in a monolayer transitionmetal dichalcogenide semiconductor. Nat. Mater. 2014, 13, 1091.(33) Raja, A.; Chaves, A.; Yu, J.; Arefe, G.; Hill, H. M.; Rigosi, A. F.;Berkelbach, T. C.; Nagler, P.; Schüller, C.; Korn, T.; et al. Coulombengineering of the bandgap and excitons in two-dimensionalmaterials. Nat. Commun. 2017, 8, 15251.(34) Lorchat, E.; López, L. E.; Robert, C.; Lagarde, D.; Froehlicher,G.; Taniguchi, T.; Watanabe, K.; Marie, X.; Berciaud, S. Filtering thephotoluminescence spectra of atomically thin semiconductors withgraphene. Nat. Nanotechnol. 2020, 15, 283.(35) Froehlicher, G.; Lorchat, E.; Berciaud, S. Charge Versus EnergyTransfer in Atomically Thin Graphene-Transition Metal Dichalcoge-nide van der Waals Heterostructures. Phys. Rev. X. 2018, 8, 11007.(36) Goryca, M.; Li, J.; Stier, A. V.; Taniguchi, T.; Watanabe, K.;Courtade, E.; Shree, S.; Robert, C.; Urbaszek, B.; Marie, X.; Crooker,S. A. Revealing exciton masses and dielectric properties of monolayersemiconductors with high magnetic fields. Nat. Commun. 2019, 10,4172.(37) Han, B.; Robert, C.; Courtade, E.; Manca, M.; Shree, S.;Amand, T.; Renucci, P.; Taniguchi, T.; Watanabe, K.; Marie, X.;Golub, L. E.; Glazov, M. M.; Urbaszek, B. Exciton States inMonolayer MoSe2 and MoTe2 Probed by Upconversion Spectrosco-py. Phys. Rev. X 2018, 8, 031073.(38) Joulain, K.; Carminati, R.; Mulet, J.-P.; Greffet, J.-J. Definitionand measurement of the local density of electromagnetic states closeto an interface. Phys. Rev. B 2003, 68, 245405.(39) Greffet, J. J.; Bouchon, P.; Brucoli, G.; Marquier, F. LightEmission by Nonequilibrium Bodies: Local Kirchhoff Law. Phys. Rev.X 2018, 8, 21008.(40) Kuzmina, A.; Parzefall, M.; Back, P.; Taniguchi, T.; Watanabe,K.; Jain, A.; Novotny, L. Resonant Light Emission from Graphene/Hexagonal Boron Nitride/Graphene Tunnel Junctions. Nano Lett.2021, 21, 8332.(41) Parzefall, M.; Szabó, Á.; Taniguchi, T.; Watanabe, K.; Luisier,M.; Novotny, L. Light from van der Waals quantum tunneling devices.Nat. Commun. 2019, 10, 292.(42) Liu, H. L.; Yang, T.; Chen, J. H.; Chen, H. W.; Guo, H.; Saito,R.; Li, M. Y.; Li, L. J. Temperature-dependent optical constants ofmonolayer MoS2, MoSe2, WS2, and WSe2: spectroscopic ellipsometryand first-principles calculations. Sci. Rep. 2020, 10, 15282.(43) Roussel, B.; Degiovanni, P.; Safi, I. Perturbative fluctuationdissipation relation for nonequilibrium finite-frequency noise inquantum circuits. Phys. Rev. B 2016, 93, 045102.(44) Février, P.; Gabelli, J. Tunneling time probed by quantum shotnoise. Nat. Commun. 2018, 9, 4940.(45) Blanter, Y.; Büttiker, M. Shot noise in mesoscopic conductors.Phys. Rep. 2000, 336, 1.(46) Novotny, L.; Hecht, B. Principles of Nano-optics; CambridgeUniversity Press: 2012.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c03155Nano Lett. 2023, 23, 10908−1091310913https://doi.org/10.1103/PhysRevLett.113.026803https://doi.org/10.1038/s41467-019-10323-9https://doi.org/10.1038/s41467-019-10323-9https://doi.org/10.1021/nl2005115?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/nl2005115?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1103/PhysRevX.7.021026https://doi.org/10.1103/PhysRevX.7.021026https://doi.org/10.1103/PhysRevX.7.021026?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1063/1.4886096https://doi.org/10.1063/1.4886096https://doi.org/10.1126/science.1244358https://doi.org/10.1126/science.1244358https://doi.org/10.1021/acs.nanolett.7b04666?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.7b04666?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1038/s42254-021-00317-2https://doi.org/10.1038/nmat4061https://doi.org/10.1038/nmat4061https://doi.org/10.1038/nmat4061https://doi.org/10.1038/ncomms15251https://doi.org/10.1038/ncomms15251https://doi.org/10.1038/ncomms15251https://doi.org/10.1038/s41565-020-0644-2https://doi.org/10.1038/s41565-020-0644-2https://doi.org/10.1038/s41565-020-0644-2https://doi.org/10.1103/PhysRevX.8.011007https://doi.org/10.1103/PhysRevX.8.011007https://doi.org/10.1103/PhysRevX.8.011007https://doi.org/10.1038/s41467-019-12180-yhttps://doi.org/10.1038/s41467-019-12180-yhttps://doi.org/10.1103/PhysRevX.8.031073https://doi.org/10.1103/PhysRevX.8.031073https://doi.org/10.1103/PhysRevX.8.031073https://doi.org/10.1103/PhysRevB.68.245405https://doi.org/10.1103/PhysRevB.68.245405https://doi.org/10.1103/PhysRevB.68.245405https://doi.org/10.1103/PhysRevX.8.021008https://doi.org/10.1103/PhysRevX.8.021008https://doi.org/10.1021/acs.nanolett.1c02913?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.nanolett.1c02913?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1038/s41467-018-08266-8https://doi.org/10.1038/s41598-020-71808-yhttps://doi.org/10.1038/s41598-020-71808-yhttps://doi.org/10.1038/s41598-020-71808-yhttps://doi.org/10.1103/PhysRevB.93.045102https://doi.org/10.1103/PhysRevB.93.045102https://doi.org/10.1103/PhysRevB.93.045102https://doi.org/10.1038/s41467-018-07369-6https://doi.org/10.1038/s41467-018-07369-6https://doi.org/10.1016/S0370-1573(99)00123-4pubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c03155?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as