Unveiling the radiative local density of optical states of a plasmonic nanocavity by STM

Atomically-sharp tips in close proximity of metal surfaces create plasmonic nanocavities supporting both radiative (bright) and non-radiative (dark) localized surface plasmon modes. Disentangling their respective contributions to the total density of optical states remains a challenge. Electroluminescence due to tunnelling through the tip-substrate gap could allow the identification of the radiative component, but this information is inherently convoluted with that of the electronic structure of the system. In this work, we present a fully experimental procedure to eliminate the electronic-structure factors from the scanning tunnelling microscope luminescence spectra by confronting them with spectroscopic information extracted from elastic current measurements. Comparison against electromagnetic calculations demonstrates that this procedure allows the characterization of the meV shifts experienced by the nanocavity plasmonic modes under atomic-scale gap size changes. Therefore, the method gives access to the frequency-dependent radiative Purcell enhancement that a microscopic light emitter would undergo when placed at such nanocavity.

7. How robust is the fitting of the peaks in the STML spectra, especially regarding the peak position of the 2.6 eV peak? The low-energy wing of the spectra below 2.5 eV, as for example that at 3.3 V in Fig. 1 c), seems very structured (with potentially more than two peaks underneath), and it is questionable if this can be fitted unambiguously by two gaussians. How sensitive is the factor 2.2 to the fitting? As the relevant shifts are in the few 10 meV range, robustness of the fit needs to be carefully discussed.
8. The authors model the tip-sample nanocavity by a sphere on a flat substrate. The STM tip, however, is not a closed nanoparticle but a half-terminated structure, which might support very different plasmonic modes. Moreover, STM tips often exhibit small nanoprotrusions on a larger tip apex due to tip conditioning, which deviates strongly from the employed sphere model. How much are the results dependent on the geometrical shape of the nanoparticle? Would e.g. a nanorod or conical nano-cylinder yield similar results? How much do the gap modes depend on the semiinfinite tip shaft? The authors should justify the use of a sphere model and provide evidence that this yields comparable and correct plasmonic modes.
9. Related to 7: The simulations yield a proportionality factor of 1.15 between the spectral shift of the dipolar and quadrupolar modes. How does this factor depend on the geometry (e.g. sphere vs. nanorod)? Does this provide a valid (universal) reference for the tip geometry? As the main conclusion of the manuscript relies on the comparison of the experimentally observed shifts to that number, this needs to be clarified.
10. (How) do the number of peaks and their spectral distribution vary for different tips? Given that the manuscript intends to provide a universal 'recipe' how to use STML to probe radiative plasmon modes in nanocavities, its sensitivity on the exact geometry and tip condition should be discussed, and reproducibility of the procedure for at least a second tip needs to be shown.
11. The title suggests experimental probing of the radiative phDOS, but it is poorly discussed in the manuscript how the STML spectra are connected to the phDOS. The authors should explain more clear how STML accesses the (radiative) phDOS.
12. The authors introduce plasmonic pseudomodes to explain the peaks in the simulated phDOS (starting line 153). Whereas the comparison of STML spectra to the simulated far-field spectra is obvious and clear, the connection to the phDOS and the role of the pseudomodes for SMTL remains vague. A clear connection of the pseudomodes and phDOS to the STML/far-field spectra and a detailed discussion of its relevance for the experimental data should be given.
13. An explanation of the gray errors in Fig. 2 should be given in the figure caption.
14. The phDOS (far-field spectra) in Fig. 2b) are scaled by delta^9 (delta^8). Is there a physical meaning of these exponents? Or is this used based on empirical findings? Such numbers should be explained properly.
15. The authors claim that the dependence of the inelastic transmission function on the photon energy can be neglected. However, one could expect that the probability to excite a plasmon via a tunneling electron depends on the available photonic density of states of the nanocavity, which is a function of the photon energy. In that sense, the authors need to justify this assumption, and it needs to be explained why this dependence is (significantly) weaker than the overlap of initial and final states.
16. At the end of the results section it has been explained that the STML spectra after normalization are governed solely by the radiative plasmonic modes in the nanocavity. Again, it however remains unclear to the reader how this connects to and unveils the radiative phDOS, as suggested in the title. In that regard the title is not chosen adequate enough.
17. The discussion part would benefit from a more detailed discussion on the wide-ranging implications of the results for the understanding of the photonic and plasmonic properties of nanocavities (also compared to other methods), beyond the technical achievement to use STML as a probe for the radiative properties of such nanocavities.
Reviewer #3: Remarks to the Author: In this manuscript, the authors report an experimental procedure to evaluate optical response of a plasmonic nanocavity formed between an STM tip and metal substrate. They showed bias voltage dependency of STML spectrum and explained the main spectral features with the aid of theoretical EM simulations. Then they discussed the influence of electronic structures of the STM tip and metal substrate on STML spectra to derive a simple expression for rate of inelastic tunneling (4). Finally, they demonstrated that STML spectra can be very easily normalized to show only optical properties of the plasmonic nanocavity which is independent of the electronic structures of the STM junction. The major novelty of the present manuscript lies in establishment of an easy method to disentangle the optical and electronic properties of a nanocavity, which can be utilized widely in this kind of experiment. The demonstration is remarkable to my perspective since the extremely small size of the electromagnetic field at the nanocavity usually makes it very difficult to understand the nature of the field itself, and, at the same time, the small EM field is the source of many intriguing application of plasmonics. For deeper understanding of nanocavity plasmons STM combined with an optical system is a promising platform. With the achievement in this manuscript I expect we start to understand the nature of the important EM field. I recommend publication of this article in Nature Communications after my criticism listed below has been taken into account.
1. I believe the most important part of this study is the normalization procedure, so I recommend to put Figures S1 and S2 into the main text.
2. To generalize the findings, several different data sets (different tip conditions) should be added. This also contributes to making the effectiveness of the method clearer.
3. In line with the previous comment, raw experimental data and normalized data measured at both negative and positive voltages should be added and discussed.
4. The authors suggested 5 nm tip radius based on the EM calculations. However, 5 nm sound too small for a radius of an STM tip and I believe the real STM tip radius is much larger than 5 nm. If it is possible, addition of an SEM image showing the tip radius is desirable, or adds some comments on discrepancy between the experiment and theoretical simulation. 5. It is a well-known fact that Ag(111) surface has a surface electronic state located around 50 meV below the Fermi level, and it can be expected that the surface state play a role in the inelastic tunneling process based on the conclusions of this work. I believe that the quality of this work would be considerably improved if the authors can show the signature of the surface state in STML spectrum.
Minor comments; 1. The first sentence in the abstract is not easy to understand, especially to general people.
Probably because too much jargons are used. 2. I recommend to include a schematic diagram to Fig.1 which illustrate the experiment in a simple way. 3. The optical system consists of three plano-convex lenses to lead the emitted light from a point underneath the STM tip to the detector. This is not a normal setup, because even number of plano-convex lenses should be used. It is helpful to includes a schematic diagram of the experimental setup. 4. I don't understand why two plano-convex lenses outside of the camber have very long focal lengths, 300 and 200 mm. 5. In the expression (S2), z should be δ. 6. In figure S3 (b) the vertical axis should be angstrom.

Subject: Reply to referees -"Unveiling the Radiative Local Density of Optical States of a Plasmonic
Nanocavity by STM Luminescence and Spectroscopy" Dear Referees, We would like to thank you for your effort in refereeing our manuscript. Indeed, your referee reports have been extremely helpful to identify a few unclear points in the original version of the manuscript, and your constructive criticisms have sparkled new experiments, analysis and calculations that have also helped us to build a more robust case for our conclusions. Including all this new work, we have generated a new version of the manuscript which we believe meets every demand you made in your reports. In the following, we discuss all the points you raised, and describe the changes performed on the manuscript to address them: We thank Referee 1 for his/her enthusiastic report. We have addressed both suggestions as follows: 1) The meaning of R as the tip radius variable is now explicitly mentioned in line 160 of the main text. 2) We have now clarified the electric nature of the dipole sources and the axialsymmetric character of the simulation domains in lines 149-150 in the main text and lines 351-352 in the Methods section.

Reviewer #2 (Remarks to the Author):
The present work reports an experimental normalization procedure to eliminate the influence of the electronic structure of a given tip-sample system in STM to the electroluminescence spectra. According to comparison with electromagnetic simulations, the corrected STML spectra provide 'clean' access to the radiative plasmonic modes of the junction/nanocavity. This is novel and an interesting aspect for the STML community. We thank Referee 2 for his/her positive opinion about the quality of the work and the relevance of our research for the STML community. We understand that, in the previous version of the manuscript, the broader implications of our work were not sufficiently stressed and/or clarified. We have now completely rewritten the introduction to underline the main aspect of our work: our experimental technique allows gaining access to the radiative electromagnetic modes of the plasmonic nanocavity between a metallic tip and a metallic surface. This type of nanocavities are relevant for many different applications, now mentioned in the introduction, but the study of their optical properties has been somewhat hampered by their characteristic geometry. Thus, different optical methods have been successfully exploited to study the total Photonic DOS (PhDOS), but they do not allow disentangling the contribution from radiative modes, the ones that would govern the far-field signatures of the polaritonic states that could potentially be formed when placing a quantum emitter at the nanocavity. On the other hand, cathodoluminiscence (CL) microscopy allows, in principle, characterizing the radiative modes of plasmonic nanocavities. However, for this particular geometry, in which the dipoles oscillate along the direction perpendicular to the surface (along the axis of the tip), the excitation of these plasmonic modes would require a normal incidence of the electron beam, which is precluded due to the shadowing effect of the tip. In a sense, thus, we can regard our method as a way to launch electrons in the perpendicular direction of the surface, by making them flow through the metallic tip onto the surface via tunneling. As mentioned earlier, the introduction has been completely rewritten to clarify all these points. In particular, the nature of bright and dark plasmonic modes is now described in detail in lines 39-41 and the so-called Purcell enhancement is described in lines 43-47 in connection to the plasmonic modes introduced above. We have also tried to clarify our statements somewhat further. For example, we do not claim that STML gives access to the total PhDOS, which on the other hand would not be so novel, since, as discussed above, optical techniques have been previously used to that effect. Our claim, instead, is that STML gives access to the radiative contribution to the PhDOS, which is characterized by the radiated power of the nanocavity. This is now further stressed in the two paragraphs from line 249 to 262, where we discuss the relation between the tunnel current and the far-field intensity emerging from our analysis. In this respect, the characterization of the radiative modes sustained in this kind of tip-on-surface plasmonic nanocavities by STML is, to our knowledge unique, since, as previously discussed, CL microscopy is hampered by the shadowing effect of the tip. Our new introduction contains new citations (references 11, 14 and 17) to cover the different aspects that Referee 2 considered were missing in the previous version of the manuscript.

The authors claim that EELS is problematic for purely metallic samples because of large scattering of the electron beam. But in Ref. 13 and other work, metallic samples are investigated, partially also combined with CL (e.g. Losquin et al. 2015). Could the authors provide some evidence/reference for the stated problem of strong scattering, and what this implies?
The referee is right in pointing to this statement from our previous version of the manuscript as our sentence was too broad in scope. EELS can be and has been used in combination with CL to discriminate between bright and dark plasmonic modes in metallic nanostructures. What we actually intended to convey was that EELS cannot be used for these particular metallic nanocavities with a tip-on-surface geometry because the large scattering suffered by the electron beam precludes a normal incidence, and thus prevents the characterization of the plasmonic modes to which vertically oriented dipole light sources (quantum emitters) would couple. We thank Referee 2 for noticing this overstatement, which has now been rewritten in the new version of the introduction as: "the large scattering experienced by the probing electron beam when penetrating thick metallic regions, which precludes the incidence of the electron beam from the direction normal to the gap and, thereby, the excitation of gap modes, whose dipole moments are oriented perpendicular to the gap.." (lines 67-70).
Figure 1 now includes such a scheme as described by Referee 2. The caption and the main text (lines 81-84) have been modified to include its description.
7. How robust is the fitting of the peaks in the STML spectra, especially regarding the peak position of the 2.6 eV peak? The low-energy wing of the spectra below 2.5 eV, as for example that at 3.3 V in Fig. 1 c), seems very structured (with potentially more than two peaks underneath), and it is questionable if this can be fitted unambiguously by two gaussians. How sensitive is the factor 2.2 to the fitting? As the relevant shifts are in the few 10 meV range, robustness of the fit needs to be carefully discussed.
As the referee points out, our experimental spectra show noticeable structure at energies below 2.5 eV. In order to address the robustness of our fitting, we have tried to include one more peak in this energy region. The analysis is now shown in Figure S1, and discussed in the first section of the Supplementary Information. Including the extra peak indeed improves the quality of the fitting, but the effect on the main peak positions is small (completely negligible for the high-energy 3 eV peak, and of only 3-5 meV in the 2.5 peak). More importantly for the present work, the shifts with stabilization voltage remain unchanged both for the normalized and raw spectra. We thus conclude that the fitting procedure is quite robust towards reasonable choices of our fitting functions. In order to address this sensitive issue of our model, we have performed further theoretical calculations, now included in the third section of the Supplementary Information, and presented through Figures S4 and S5. In brief, the exact shape of the nanoparticle does not seem to play an important role, as can be evidenced by comparing the modes supported by the nanocavities formed by ellipsoidal nanoparticles with different aspect ratios ( Figure S4). Moving from finite nanoparticles to semi-infinite tip geometries, however, can lead to substantial changes depending on the apex geometry. This can be seen in Figure S5, where we have modelled the tip as a cone with a spherical protrusion. It can be observed that when the distance between the center of the sphere and the apex of the cone is small (simulating a rounded conical tip), the far-field spectra becomes dominated by leaky propagating modes (not confined to the cavity). However, for sufficiently large sphere-apex distances (i.e., when our tip can be thought of as having a well-defined protrusion), scattering at the kinked areas prevents the coupling of the localized plasmonic modes at the gap cavity to these leaky modes propagating along the cone surface. Thus, the far-field spectra becomes once again very similar to that of our spherical model ( Figure S5a). This effect is even enhanced with increasing tip angles ( Figure S5b). From these results, we can safely conclude that relatively broad tips with small but well-defined protrusions should behave largely as finite nanoparticles, thereby supporting our initial model. Of course, a broad tip can have more than one single protrusion, overlapping with each other in different ways, which explains the large variability of the observed experimental spectra depending on tip conditions. 9. Related to 7: The simulations yield a proportionality factor of 1.15 between the spectral shift of the dipolar and quadrupolar modes. How does this factor depend on the geometry (e.g. sphere vs. nanorod)? Does this provide a valid (universal) reference for the tip geometry? As the main conclusion of the manuscript relies on the comparison of the experimentally observed shifts to that number, this needs to be clarified.
As described in our comments to the previous point, more realistic geometries consisting on a broad tip with a small protrusion display essentially the same spectra as geometries in which the whole tip is replaced only by the protrusion, so the peak shifts with distance should be the same.

(How) do the number of peaks and their spectral distribution vary for different tips?
Given that the manuscript intends to provide a universal 'recipe' how to use STML to probe radiative plasmon modes in nanocavities, its sensitivity on the exact geometry and tip condition should be discussed, and reproducibility of the procedure for at least a second tip needs to be shown.
The variability of the experimental spectra with different tip conditions is rather large. As mentioned in the main text, most of the experimental spectra display one or two peaks in the range of energy between 1.5 and 3 eV, but some examples can be found with more than two peaks. Moreover, very often a finer structure can be observed in the shape of shoulders in the spectra that might reflect other plasmonic modes. The normalization procedure, however, removes quite efficiently the dependence of the spectra on the tunneling conditions in all studied cases. This is clearly shown in the new Figure S6 in the Supplementary Information. For this tip, we observe two relatively narrow peaks at 2.0 and 2.1 eV on top of a relatively broad intensity in the range of 1.6-2.2 eV. While the raw spectra show a rather marked dependence on the stabilization voltage, the normalization procedure makes the spectra indistinguishable.
11. The title suggests experimental probing of the radiative phDOS, but it is poorly discussed in the manuscript how the STML spectra are connected to the phDOS. The authors should explain more clear how STML accesses the (radiative) phDOS.
As discussed above, the radiative PhDOS can be characterized through the electromagnetic power radiated by the nanocavity into the far-field. According to Equation (5), it can be experimentally obtained for each photon energy by means of our normalization procedure. We have modified the discussion of the Equation (5)  As previously discussed, STML is not sensitive to the dark modes and, therefore, this technique is not sensitive to the plasmonic pseudomodes that govern the total PhDOS. Such plasmonic pseudomodes, however, control the Purcell enhancement and associated fluorescence lifetime reduction, which can be accessed by optical means. By showing the total PhDOS in the insets of Figure 2a and 2b we aim at making clear that with STML we only observe the radiative modes, and such information is complementary to, but different from, the information that can be retrieved by a purely optical characterization.
13. An explanation of the gray errors in Fig. 2 should be given in the figure caption.
The gray arrows correspond to the energy positions for which the electric field intensity and charge density maps in Figure 2c are plotted. This is now described in the last sentence of the caption of Figure 2.
14. The phDOS (far-field spectra) in Fig. 2b)  There is not any physical meaning to those exponents. These factors are simply chosen to allow the direct comparison among different spectra.
15. The authors claim that the dependence of the inelastic transmission function on the photon energy can be neglected. However, one could expect that the probability to excite a plasmon via a tunneling electron depends on the available photonic density of states of the nanocavity, which is a function of the photon energy. In that sense, the authors need to justify this assumption, and it needs to be explained why this dependence is (significantly) weaker than the overlap of initial and final states.
Referee 2 is right when stating that the probability for inelastic tunneling should be larger for energy losses corresponding to plasmon energies with a high PhDOS, but this effect simply adds the PhDOS as a new factor to the rate without changing the transmission. This can be simply obtained from Fermi's Golden Rule as follows: we consider our base states to include the occupation numbers for the electron states at the tip, the electron states at the sample and the plasmon states. An inelastic tunneling event is one in which one electron is annihilated, say, from an electronic state at the tip with a given energy, created at an electronic state at the surface with a lower energy and a plasmon with energy equal to the difference in electronic energies is created. According to Fermi's Golden Rule, the rate of such inelastic events for a given plasmon energy is simply proportional to the sum of the squared matrix elements of the Hamiltonian to all such initial and final many-body states. By replacing the sum over states to an integral over energies, one obtains Equation (5), allowing for the identification of the transmission factors with the squared matrix elements of the Hamiltonian between initial and final states. Because these matrix elements are referred to well-defined many body states, they can be calculated without consideration of how many states are there at one particular energy and, therefore, they are independent of the electronic and plasmonic DOS, as we stated above. We have included this discussion in a somewhat more pedagogical way in our new version of the manuscript. The rate of inelastic transitions is now defined for a hypothetical case of a plasmonic mode with perfectly defined energy, i.e., the photonic density of states is a delta function (lines 202-213). The rest of the argument remains the same, and we arrive to the conclusion that the rate of inelastic transitions in this hypothetical case should just be the tunnel current at a different voltage. Notice that for this situation there can be no dependence of the transmission functions on the PhDOS. Now, for the more realistic situation in which the PhDOS is a relatively broad and structured function, we just apply Fermi's Golden Rule and conclude that the real inelastic current would just be the product of the previously obtained rate of inelastic transitions times the PhDOS. The light intensity thus results from considering that not all the plasmonic states radiate with equal efficiency, and thus we should substitute the total PhDOS for the radiative power of the cavity that characterizes the radiative density of optical states (lines 249-262).
16. At the end of the results section it has been explained that the STML spectra after normalization are governed solely by the radiative plasmonic modes in the nanocavity. Again, it however remains unclear to the reader how this connects to and unveils the radiative phDOS, as suggested in the title. In that regard the title is not chosen adequate enough.
As it has been discussed in previous points, the radiative PhDOS is characterized by the radiative power of the nanocavity and, according to Equation (5), this is precisely what is obtained from our normalization process.
17. The discussion part would benefit from a more detailed discussion on the wide-ranging implications of the results for the understanding of the photonic and plasmonic properties of nanocavities (also compared to other methods), beyond the technical achievement to use STML as a probe for the radiative properties of such nanocavities.
Our findings do not only show that STML is a valid characterization tool for plasmonic nanostructures. In addition, they reveal that STML provides experimental insights into the key, and up to our knowledge unexplored, question of the role of radiative optical modes in archetypal gap nanocavity geometries. We believe that this point is clearly made in the new version of the manuscript.

Reviewer #3 (Remarks to the Author):
In this manuscript, the authors report an experimental procedure to evaluate optical response of a plasmonic nanocavity formed between an STM tip and metal substrate. They showed bias voltage dependency of STML spectrum and explained the main spectral features with the aid of theoretical EM simulations. Then they discussed the influence of electronic structures of the STM tip and metal substrate on STML spectra to derive a simple expression for rate of inelastic tunneling (4). Finally, they demonstrated that STML spectra can be very easily normalized to show only optical properties of the plasmonic nanocavity which is independent of the electronic structures of the STM junction. The major novelty of the present manuscript lies in establishment of an easy method to disentangle the optical and electronic properties of a nanocavity, which can be utilized widely in this kind of experiment. The demonstration is remarkable to my perspective since the extremely small size of the electromagnetic field at the nanocavity usually makes it very difficult to understand the nature of the field itself, and, at the same time, the small EM field is the source of many intriguing application of plasmonics. For deeper understanding of nanocavity plasmons STM combined with an optical system is a promising platform. With the achievement in this manuscript I expect we start to understand the nature of the important EM field. I recommend publication of this article in Nature Communications after my criticism listed below has been taken into account.