Abstract
Plasmonics has attracted tremendous interests for its ability to confine light into subwavelength dimensions, creating novel devices with unprecedented functionalities. New plasmonic materials are actively being searched, especially those with tunable plasmons and low loss in the visible–ultraviolet range. Such plasmons commonly occur in metals, but many metals have high plasmonic loss in the optical range, a main issue in current plasmonic research. Here, we discover an anomalous form of tunable correlated plasmons in a Mottlike insulating oxide from the Sr_{1−x}Nb_{1−y}O_{3+δ} family. These correlated plasmons have multiple plasmon frequencies and low loss in the visible–ultraviolet range. Supported by theoretical calculations, these plasmons arise from the nanometrespaced confinement of extra oxygen planes that enhances the unscreened Coulomb interactions among charges. The correlated plasmons are tunable: they diminish as extra oxygen plane density or film thickness decreases. Our results open a path for plasmonics research in previously untapped insulating and stronglycorrelated materials.
Introduction
Plasmonics offers a crossroad between photonics and nanoelectronics by combining the former’s highbandwidth capability with the latter’s nanoscale integrability^{1,2,3,4,5}. Plasmonics utilizes plasmon, a collective excitation of charges that arises from interactions between electromagnetic fields (such as photons) and free charges^{3}. Conventionally, the plasmon frequency depends on the freecharge density^{3}; thus, highfrequency plasmons are usually found in metals^{3,4,5} due to their abundance of free charges, but are rarely observed in conventional wide bandgap insulators.
In stronglycorrelated materials, conventional forms of plasmons have been observed in the metallic or superconducting phases of these materials, and there have been studies to explore their potential for plasmonics in vanadium oxides^{6,7,8} and cuprates^{9,10}. In particular, localized conventional surface plasmons have been observed in the metallic phase of VO_{2}, and its temperaturedependent metal–insulator transition has been utilized for plasmonic switching and sensing^{6,7,8}. However, in stronglycorrelated, insulating phases of these materials (such as in Mott insulators^{11}), correlated forms of plasmons under longrange Coulomb interactions have only been theoretically investigated^{12} but not experimentally observed.
Meanwhile, the Sr_{1−x}Nb_{1−y}O_{3+δ} family of oxides are known to have rich structures and electronic properties that vary with oxygen content. For example, perovskite SrNbO_{3} is conducting with an Nb4d^{1} electronic structure^{13,14,15,16}, and Sr_{1−x}NbO_{3} (ref. 14) has been found to potentially be a good photocatalyst in water splitting applications^{15}. On the other hand, oxygenrich SrNbO_{3.4} and SrNbO_{3.5}, derived by interspersing the perovskite lattice of SrNbO_{3} with extra oxygen planes along the [101] direction at certain periodic intervals^{16,17} (see Supplementary Note 1 for details), is a quasionedimensional conductor^{16,17,18,19,20,21} and a ferroelectric insulator^{22,23}, respectively. Previously, there are no reported studies on plasmons in this family of oxides.
In this study, several Sr_{1−x}NbO_{3+δ} films with varying oxygen content, electrical conductivity (from metallic to insulatorlike) and film thicknesses are studied using spectroscopic ellipsometry (SE), atomicresolution transmission electron microscopy (TEM), transport measurements and supported by theoretical calculations based on coupled harmonic oscillators model and density functional theory. The results show a surprising observation of a new form of correlated plasmons in the insulatorlike film, itself also revealed to be a stronglycorrelated Mottlike insulator. The correlated plasmons unusually have multiple plasmon frequencies (∼1.7, ∼3.0 and ∼4.0 eV) and low loss (several times lower than gold) in the visible–ultraviolet range. Supported by theoretical calculations, these correlated plasmons arise from collective excitations of correlated electrons in the film, where the nanometrespaced confinement of extra oxygen planes causes increased Coulomb repulsions among the electrons. The correlated plasmons are reproducible and tunable: they diminish and ultimately vanish as extra oxygen plane density or film thickness decreases. In particular, the decrease of extra oxygen plane density increases the electrical conductivity, and, as correlated plasmons are vanishing in the metallic films, the increased freecharge density causes conventional plasmon to arise at ∼1.9 eV.
Results
Transport measurements results
The main batch of pressuredependent Sr_{1−x}NbO_{3+δ} films is deposited on (001)LaAlO_{3} substrates using pulsedlaser deposition under three oxygen pressure conditions: 5 × 10^{−6}, 3 × 10^{−5} and 1 × 10^{−4} Torr, labelled as lpSNO, mpSNO and hpSNO, respectively. Transport measurements reveal that lpSNO and mpSNO are metallic with roomtemperature resistivity of 1 × 10^{−4} and 6 × 10^{−3} Ωcm, respectively, while hpSNO is insulatorlike with roomtemperature resistivity of 6 Ωcm. The conducting lpSNO have an unusually large roomtemperature freecharge density of ∼1 × 10^{22} cm^{−3}, while for mpSNO it is ∼4 × 10^{21} cm^{−3}. The roomtemperature mobility of the conducting films is ∼2.5 cm^{2} V^{−1} s^{−1} for lpSNO and ∼0.3 cm^{2} V^{−1} s^{−1} for mpSNO. The thickness of the three main films is ∼196, ∼218 and ∼168 nm for lpSNO, mpSNO and hpSNO, respectively. For thicknessdependent study, thinner hpSNO films with varying thicknesses of ∼81, ∼52 and ∼20 nm are also deposited. For reproducibility, a second batch of pressuredependent films is deposited as well under six oxygen pressure conditions: 5 × 10^{−6} Torr (lpSNO2), 1 × 10^{−5} Torr (mlpSNO2), 3 × 10^{−5} Torr (mpSNO2), 7 × 10^{−5} Torr (mhpSNO2), 1 × 10^{−4} Torr (hpSNO2) and 5 × 10^{−4} (hrpSNO2). The lpSNO2, mlpSNO2, mpSNO2, and mhpSNO2 films are conducting, while the hpSNO2 and hrpSNO2 films are insulating, and their thicknesses are kept to be within a narrow range of ∼159–182 nm (see Supplementary Table 1 for details). The crystal structures of the representative main batch films are studied using Xray diffractions (XRDs) shown in Supplementary Fig. 1.
Complex dielectric function and loss function
Figure 1 shows the complex dielectric function, ɛ(ω)=ɛ_{1}(ω)+iɛ_{2}(ω), and loss function (LF), , of the pressuredependent Sr_{1−x}NbO_{3+δ} films extracted from SE, where ω is the photon angular frequency (see Supplementary Figs 2–5 for details). Each peak in the transverse ɛ(ω) spectra indicates an optical excitation, while each peak in the longitudinal LF spectra indicates a plasmonic excitation. For subXray photons, the photon momentum transfer, q, is finite but approaches zero because it is much less than the crystal momentum. In this limit, the distinction between longitudinal (l) and transverse (t) ɛ(ω) vanishes, that is, , which allows subXray optical spectroscopy to probe both optical and plasmonic properties of materials in the lowq limit^{24}. All of the optical and plasmonic peaks are listed in Table 1. It should be noted that longitudinal LF spectrum is also the quantity probed by electron energy loss spectroscopy, which is another common technique used in the study of plasmonic properties of materials. However, as hpSNO is insulatorlike, such photoemissionbased spectroscopy measurements might be challenging for hpSNO due to significant charging effects.
The ɛ_{2}(ω) of lpSNO (Fig. 1b) shows an intraband Drude peak (A_{1}) and the first interband transition peak (A_{2} and A_{3}, >4.6 eV), which has been attributed as O2p→Nb4d transition^{15,16}. (Note that in the cited studies, the theoretical bandgap between O2p and Nb4d calculated using density functional theory was underestimated^{25}. Nevertheless, the A_{2} peak from ∼4.6 eV should still be regarded as originated from O2p→Nb4d transition because it is the lowestenergy interband transition in lpSNO.) The LF of lpSNO (Fig. 1b) shows a large peak (A′_{1}, ∼1.9 eV), which coincides with the zerocrossing of ɛ_{1}(ω) at ∼1.84 eV (Fig. 1a) and is very close to the reflectivity minimum at ∼2.1 eV (Supplementary Fig. 6), indicating that the peak comes from a conventional plasmon excitation^{3}. There is a slight blueshift between the A′_{1} peak and the ɛ_{1}(ω) zerocrossing due to the freeelectron scattering. Consequently, from this blueshift along with the fullwidth halfmaximum (FWHM) of the A′_{1} peak (see equations 5 and 6), we can estimate the freeelectron scattering, 1/τ, in lpSNO to be ∼0.47 eV and its conventional plasmon dephasing time^{3}, T_{2}, to be ∼2.8 fs.
Meanwhile, in the lessconducting mpSNO, the conventional plasmon peak (B′_{1} in Fig. 1c) redshifts to ∼1.7 eV due to the decrease in freecharge density. From the FWHM of the B′_{1} peak and its blueshift with respect to the ɛ_{1}(ω) zerocrossing at ∼1.62 eV, the 1/τ and T_{2} in mpSNO can be estimated to be ∼0.52 eV and ∼2.5 fs, respectively. The reflectivity minimum also redshifts to ∼1.9 eV (Supplementary Fig. 6). Besides the Drude (B_{1}) and the first interband transition peaks (B_{4} and B_{5}), the ɛ_{2}(ω) of mpSNO also shows two additional peaks at ∼3.5 (B_{2}) and ∼4.5 eV (B_{3}). Particularly for B_{2}, it shares the same shape and energy position with the B′_{2} of the corresponding LF spectrum. As discussed below, B′_{2} is a new form of correlated plasmon, with a different origin from the B′_{1} conventional plasmon.
An important observation is shown in the ɛ_{2}(ω) and LF spectra of hpSNO (Fig. 1d). The ɛ_{2}(ω) shows that hpSNO has no apparent Drude peak, consistent with transport measurement, with a wide bandgap of ∼4.6 eV (C_{5} and C_{6}). Interestingly, below this bandgap there exist several midgap peaks at ∼1.7 (C_{1}), ∼3.0 (C_{2}), ∼4.0 (C_{3}) and ∼4.5 eV (C_{4}) with low overall ɛ_{2}(ω) (<1 for C_{1} and C_{2}). Particularly, C_{1}, C_{2} and C_{3} peaks share very similar shapes and energy positions with another group of three peaks in the LF spectrum: C′_{1}, C′_{2} and C′_{3}, respectively (just like the similarities between B_{2} and B′_{2} peaks of mpSNO). The energy positions of both group of peaks are also very close to the reflectivity minima of hpSNO (Supplementary Fig. 6) at ∼1.9, ∼3.2 and ∼4.2 eV. These indicate that the two groups of peaks come from a similar origin. The appearance of these midgap peaks in the LF spectrum indicates that they arise from plasmonic excitations^{3} and not from other effects such as spin–orbit coupling, phononic, excitonic or anisotropic effects (see Supplementary Note 2). Meanwhile, their concurrent existence in ɛ_{2}(ω) spectrum indicates that there is a coupling between optical and plasmonic excitations in hpSNO (and to a lesser extent, in mpSNO). As discussed later, these midgap plasmonic excitations are born from collective excitations of correlated electrons, and are thus called correlated plasmons.
As a first approximation, the dephasing time of these correlated plasmons may be estimated from FWHM of each peak. The FWHM of C_{1}′, C_{2}′, and C_{3}′ peaks is ∼0.7, ∼0.68 and ∼0.38 eV, respectively. This leads to the dephasing time of ∼1.9, ∼1.9 and ∼3.5 fs, respectively. We note that the scattering and dephasing mechanisms in correlated systems might be different from those in weakly correlated metals due to longrange correlation effects, as discussed later.
Meanwhile, the C_{4} peak may be excitonic in origin due to its relative sharpness, asymmetric shape and energy position that is just below the bandgap. This peak diminishes as freecharge density increases in conducting mpSNO (see the similar B_{3} peak in mpSNO), and ultimately vanishes in lpSNO. If this peak is indeed excitonic, its presence in hpSNO indicates that electron–hole interactions are unscreened in the insulating hpSNO film, while its diminishing behaviour in mpSNO and lpSNO indicates that electron–hole interactions are heavily screened in the conducting films.
Differences between correlated and conventional plasmons
The correlated plasmons of hpSNO are fundamentally different from conventional (bulk) plasmon in lpSNO, conventional metals such as gold^{3,5,26} and the metallic phases of strongly correlated materials such as metallic VO_{2} (refs 6, 7, 8) for the following reasons. First, since hpSNO is insulatorlike, the correlated plasmons do not originate from collective excitations of free charges. In fact, as freecharge density increases in mpSNO, the correlated plasmons instead become weaker and ultimately vanish in lpSNO. Second, in lpSNO and gold the ɛ_{1}(ω) is negative below the conventional plasmon energy and conventional plasmons occur at the zerocrossing of ɛ_{1}(ω) (albeit with slight blueshifts due to the freeelectron scattering), while the ɛ_{1}(ω) of hpSNO stays positive below the correlated plasmon energies. Third, conventional plasmons as in lpSNO and gold usually only have one (bulk) plasmon energy, while hpSNO has at least three observable correlated plasmon energies with a seemingly ordered energy ratio. This is somewhat similar to a previous theoretical result^{12} where the presence of longrange Coulomb interaction in correlated systems could induce multiple correlated plasmon energies to appear. These theoretical plasmon energies also had an ordered ratio of U* and U*/2, where U* was the effective local Coulomb interaction, although the energy ratio of the observed correlated plasmons of hpSNO is not as straightforward to deduce (see Supplementary Note 3 for details). Fourth, the correlated plasmons appear in both ɛ_{2}(ω) and LF spectra of hpSNO, which means that the correlated plasmons can readily be excited by, decay radiatively into and thus couple with freespace photons without any external mechanisms. This is unlike conventional surface plasmon resonance in metals, which needs external phasematching mechanisms such as grating, Otto and Kretschmann configurations^{3,27,28} to couple the plasmons with freespace photons. Intriguingly, the ɛ_{2}(ω) of hpSNO below its bandgap is several times (for example, ∼6 times at 3.0 eV) lower than that of gold^{3,5,26}, which means the correlated plasmons have low loss in the optical visible–ultraviolet range. To explain these differences, we further study the optical conductivity (σ_{1}(ω)=ɛ_{0}ɛ_{2}(ω)ω, where ɛ_{0} is the vacuum permittivity), spectral weight transfer and atomic structure of the films.
Optical conductivity and spectral weight analysis
The σ_{1}(ω) analysis (Fig. 2a) is important because it obeys the fsum (charge conservation) rule^{24,29,30}, where n, e and m_{e} is the total electron density, elementary charge and electron mass, respectively. From this rule, a partial spectral weight integral of an energy region (for example, from E_{1} to E_{2}) can be defined as . The W is proportional to the effective number of electrons participating in the optical excitations, which means by analysing the evolution of W we can study the various charge transfers that occur in the films and gauge their electronic correlations^{11,24,30,31,32,33,34,35}. For this purpose, the σ_{1}(ω) spectra are divided into three energy regions: W_{1} for the Drude peak (0.6–2.0 eV), W_{2} for the midgap plasmonic peaks (2.0–4.3 eV) and W_{3} for the first interband transition of O2p→Nb4d (4.3–6.5 eV). The evolution of each W across the three films is shown in Fig. 2b (see also Supplementary Fig. 7 for more details).
As freecharge density decreases from lpSNO to mpSNO, the decrease of W_{1} (Drude region) is accompanied by an increase of W_{3}. This can be understood because the decreased number of electrons in the conduction band (Nb4d) increases the available unoccupied states necessary for the first interband transition of O2p→Nb4d. Thus, as freecharge density further decreases and ultimately vanishes during a transition from metal to insulator, the diminishing of Drude peak is expected to be accompanied by a further increase of W_{3}. Surprisingly, Fig. 2 shows this is not the case for the metal–insulator transition (MIT) between mpSNO and hpSNO, because instead W_{1} and W_{3} both anomalously decrease as MIT occurs, leading to an overall decrease of W below 6.5 eV (W_{tot}). According to the fsum rule^{24,29,30} and because hpSNO is insulatorlike with no apparent Drude peak, this decrease has to be compensated by an equivalent increase of W above 6.5 eV, implying spectral weight transfers over wide energy ranges on the onset of the MIT. Such widerange anomalous spectral weight transfers are a direct evidence of strong electronic correlation^{11,24,30,31,32,33,34,35} and has also been observed in other stronglycorrelated materials such as cuprates^{11,30,33}, vanadium oxides^{34} and manganites^{11,30,35}. This anomalous spectral weight transfer behaviour signifies that hpSNO is most likely a Mottlike insulator and the MIT occurs as the Coulomb repulsion between electrons becomes stronger (that is, unscreened) and electronic correlation increases. This also means that the plasmons in hpSNO are a new type of correlated plasmons born from collective excitations of correlated electrons.
Transmission electron microscopy
The three films are also studied using TEM to determine their microstructures. Atomic resolution zcontrast scanning TEM images of lpSNO, mpSNO and hpSNO are shown in Fig. 3a–c. The global arrangement of the atomic structure of lpSNO (Fig. 3a) exhibits a longrange perovskite structure^{13}, whereas those of mpSNO and lpSNO (Fig. 3b,c) exhibit a shortrange perovskite structure interspersed with high densities of ordered {101} and {−101} extra oxygen planes that occur every few unit cells (shown in high magnification in Fig. 3d). Their positionaveraged atomic structure (Fig. 3e) matches with the known extra oxygen plane structure of bulk SrNbO_{3.4} (ref. 17) shown overlaid onto the image (see Supplementary Note 1 for details). The density of these planes qualitatively appears to increase with oxygen deposition pressure (Fig. 3a–c), and quantitatively (see Supplementary Figs 8 and 9 for details), there is a fourfold increase from mpSNO to hpSNO. This is consistent with an increased incorporation of extra oxygen with higher oxygen deposition pressure.
Thicknessdependent study of correlated plasmons
To examine sizedependent effects on the properties of the correlated plasmons, hpSNO films with thinner thicknesses of ∼81, ∼52 and ∼20 nm are also deposited and studied using SE, and the results are shown in Fig. 4 (see also Supplementary Figs 10 and 11 for more details). Interestingly, both the energy and number of excited correlated plasmons in hpSNO change when the film thickness changes. In particular, the number of correlated plasmon peaks decreases as the film thickness decreases. When the film thickness decreases further to ∼20 nm, the correlated plasmon disappears (Fig. 4d). This means that besides using the oxygen deposition pressure, the correlated plasmons can also be tuned by varying the thickness of the hpSNO film. This is again fundamentally different from conventional plasmons where only the plasmon energy is changing when the metallic nanoparticle size is changed^{3}.
The disappearance of correlated plasmons in the ∼20 nm hpSNO film is particularly interesting. To investigate this further, we study the σ_{1}(ω) and W of the thicknessdependent hpSNO films shown in Fig. 5. It can be seen that as the film thickness decreases, the spectral weight of the first interband region (>4.3 eV), W_{3}, increases. This means that these thinner hpSNO films have less widerange spectral weight transfer that signifies their correlation strength^{11,24,30,31,32,33,34,35}. In particular, the W_{3} of the ∼20 nm hpSNO film is almost as high as that of the metallic mpSNO (Figs 2b and 5b), which means that the ∼20 nm hpSNO is most likely a weaklycorrelated system. This further emphasizes the connection between the correlated plasmons, electronic correlation and the film dimensionality: as the film becomes thinner, the electronic correlation and thus the correlated plasmons also become weaker and ultimately vanish.
One possible reason for this thicknessdependent behaviour of the correlated plasmons might be due to the role of lattice mismatch. From Supplementary Fig. 1, it can be seen that the inplane lattice constant of the Sr_{1−x}NbO_{3+δ} films is 4.04 Å, while the lattice constant of the LaAlO_{3} substrate is 3.791 Å (ref. 36), which means that there is a relatively large lattice mismatch of ∼6.6% between the films and the substrate. In thinner films, this large lattice mismatch should play a more significant role in influencing the electronic band structure of the whole film due to their relative thinness. The large lattice mismatch may reduce the unscreened Coulomb interactions between the electrons, resulting in less correlations and correlated plasmon excitations in thinner films. On the other hand, the role of lattice mismatch should be more minimized in thicker films, because their relative thickness should allow them to have more complete relaxations, leading to stronger correlations and more correlated plasmon excitations compared to thinner films.
Reproducibility of correlated plasmons
To test the reproducibility of the correlated plasmons, a second batch of pressuredependent Sr_{1−x}NbO_{3+δ} films are deposited and measured using SE, and the analyses and results are shown in Supplementary Figs 12–17. The thickness of each film in this batch is kept within a narrow range of ∼159–182 nm to minimize thicknessdependent effects (see Supplementary Table 1). From Supplementary Fig. 14, it can be seen that, in general, the behaviours of the correlated and conventional plasmons as well as excitonic peaks in this batch are very similar to what was observed in the mainbatch films shown in Fig. 1 (see Supplementary Note 4 for details). Furthermore, Supplementary Fig. 16 also shows that the pressuredependent MIT is reproducible as well, and that the films deposited under higher oxygen pressures consistently have the signature of strong electronic correlations. This indicates that the correlated plasmons are indeed reproducible, and its pressuredependent behaviour can be reproduced consistently within similar thicknesses.
Discussion
The presence of extra oxygen planes in hpSNO and their absence in lpSNO accompanied by remarkable changes in ɛ(ω) and σ_{1}(ω) spectra indicate that the interplay between extra oxygen planes and electronic correlations plays important roles in the plasmonics excitations and MIT between the films. For lpSNO, its negative ɛ_{1}(ω) value below ∼1.9 eV, strong Drude response and no excitonic peak indicate that the Coulomb interactions between its Nb4d electrons as well as between its electrons and holes are screened, making it a weaklycorrelated metal similar to Sr_{1−x}NbO_{3} (refs 14, 15, 16). Meanwhile, nonnegative ɛ_{1}(ω) value, widerange spectral weight transfer and presence of excitonic signature in thick (∼168 nm) hpSNO indicate the Coulomb interactions among its Nb4d electrons as well as between its electrons and holes are unscreened, which leads to strong electronic correlation. In this regard, the extra oxygen planes in the thick hpSNO act as highpotential walls that prevent the Nb4d electrons from hopping across the planes, confining them and making them feel stronger Coulomb repulsions. This changes their behaviour from itinerant to localized and transforms the system into a stronglycorrelated Mottlike insulator^{11}.
Furthermore, since the extra oxygen planes are embedded throughout the volume of the hpSNO film, the correlated plasmons disappear in the very thin hpSNO film, and as hpSNO itself is a Mottlike insulator with little to no free electrons at its surface, the observed correlated plasmons are most likely bulk plasmons instead of surface plasmons. The occurrence of the extra oxygen planes every few unit cells (every 5 unit cells for SrNbO_{3.4}) also means that the correlated plasmons have nanometrespaced (∼2 nm for SrNbO_{3.4}) confinement in the film (see Supplementary Fig. 1 for the films lattice constants).
The electronic confinement is further supported by density functional theory (DFT) calculations shown in Fig. 6a,b. The calculations show that the presence of oxygen planes in SrNbO_{3.4}, which shares similar extra oxygen plane structure with hpSNO, can indeed induce the electronic confinement on Nb4d electrons (Fig. 6b), consistent with previous report^{16} (see also Supplementary Fig. 18 for details). This confinement is not observed in SrNbO_{3} (Fig. 8a), which has no extra oxygen planes similar to lpSNO. In the following discussion, we model and explain the conventional and correlated plasmons of the thick films based on this electronic confinement induced by the extra oxygen planes.
Conventional plasmon can be classically described using the Drude model^{3} as a collective oscillation of free charges against a positively charged ionic background (Fig. 6c). The theoretically calculated ɛ(ω) and LF spectra of lpSNO using Drude model (Fig. 6e,f) agree very well with the experimental data below the bandgap. The theoretical LF of SrNbO_{3} calculated using DFT with random phase approximation (RPA) method is also able to resemble qualitatively the experimental LF of lpSNO (see Supplementary Fig. 19a and Supplementary Note 5 for details). This is not surprising because lpSNO is a metal with little to no correlations and thus can be modelled using DFTbased calculations.
On the other hand, the theoretical LF of SrNbO_{3.4} calculated using DFT and RPA is not able to resemble the experimental LF of thick hpSNO, particularly the three correlated plasmons peak that we observe in thick hpSNO (Supplementary Fig. 19b). This is because hpSNO is a correlated system, which cannot be properly treated using DFT. Thus, to model the correlated plasmons of thick hpSNO, we instead use a phenomenological model in which the effective Coulomb interactions between neighbouring correlated electrons is modelled as that of an elastic spring, at least in the low wave vector (or momentum transfer, q→0) limit. In this model (Fig. 6d and Supplementary Fig. 20), we qualitatively treat plasmonic oscillations of the correlated electrons as those of a chain of coupled harmonic oscillators bounded by two oxygen walls (where the walls are the extra oxygen planes that confine the Nb4d electrons). Because the correlated electrons might have different effective masses and charges from bare electrons due to correlation effects^{12}, in the calculations we vary these along with the number of oscillators in one chain to find the set of parameters that can best describe the experimental data (see Supplementary Fig. 21 and Supplementary Note 3 for details).
From the calculation results (Fig. 6e,g), we find that the coupled oscillator model is able to resemble qualitatively the experimental ɛ(ω), LF and correlated plasmons of thick hpSNO below the bandgap when the chain between the oxygen walls contains seven oscillators. To get the correct magnitude of ɛ(ω), the effective masses of the quasielectrons are set to ∼25m_{e}, suggesting that the masses are heavily renormalized due to electronic correlation. Interestingly, we also find that to match the intensity trend of the correlated plasmon peaks, the quasielectrons need to have alternating charges, that is, the quasielectrons nearest to the walls have −e charge, their immediate neighbours +e charge, and so on, suggesting that the originally itinerant electrons have transformed into quasielectrons and holes distributed alternatingly along the chain due to correlation. This is consistent with previous report of possible formation of charge density wave in SrNbO_{3.4} (refs 18, 19).
The estimated heavy effective mass and the alternating charge arrangement of the quasielectrons should also affect the dephasing time of the correlated plasmons. The heavy effective mass of the quasielectrons can make the confined electrons (and thus the correlated plasmons) much more inertial against scattering, which can significantly enhance the correlated plasmon dephasing time. Furthermore, the redistributed charge arrangement would also alter their scattering profile to be different from that of nearly free bare electrons in metals.
In conclusion, we have demonstrated that depending on the electronic correlation strength, different types of plasmons can be reproducibly excited in Sr_{1−x}NbO_{3+δ} films. In weakly correlated metallic films, conventional plasmons dominate. Meanwhile, in strongly correlated Mottlike insulating films, lowloss correlated plasmons, which have fundamentally different properties and origins from conventional plasmons, are excitable instead. These correlated plasmons arise from the nanometrespaced confinement of extra oxygen planes in the film and, in general, can be tuned by changing the electronic correlation strength. This can be accomplished by changing the extra oxygen plane density, for example, by varying the oxygen pressure during film deposition, and by changing the thickness of the films.
Methods
Materials preparations and characterizations
The Sr_{1−x}NbO_{3+δ} films are deposited on (001) LaAlO_{3} substrates by pulsedlaser deposition. The laser used is a Lambda Physik Excimer KrF ultraviolet laser with a wavelength of 248 nm, energy density of 2 Jcm^{−2}, and pulse frequency of 5 Hz. The three thick mainbatch films are deposited at 750 °C and oxygen partial pressures of 5 × 10^{−6}, 3 × 10^{−5} and 1 × 10^{−4} Torr, respectively. The pulsedlaser deposition target is prepared by solid reactions of Sr_{4}Nb_{2}O_{9} precursor, Nb (Alfa Aesar, 99.99%, −325 meshes) and Nb_{2}O_{5} (Alfa Aesar, 99.9985%, metals basis) powder mixtures with proper molar ratio. The precursor is prepared by calcining SrCO_{3} (Alfa Aesar, >99.99%, metals basis) and Nb_{2}O_{5} powder mixtures in a molar ratio of 4:1. The calcination and sintering is done in air and 5% H_{2}–Ar gas environment for 20 h at a temperature of 1,200 and 1,400 °C, respectively. Different film thicknesses could be achieved by varying the deposition time. Typically, ∼130nmthick film could be obtained with half an hour deposition.
The crystal structures of the mainbatch films are studied using highresolution XRD (Bruker D8 with CuKα1 radiation and wavelength of 1.5406 Å) together with the reciprocal space maps. The XRD results (Supplementary Fig. 1) show that the inplane lattice constants of all three films are 4.04 Å, close to that of bulk SrNbO_{3} (refs 13, 14). The outofplane lattice constant of lpSNO and mpSNO is 4.10 Å, which indicates that these two films have a slight uniaxial anisotropy along the outofplane ([001]) direction. Meanwhile, the outofplane lattice constant of hpSNO is 4.02 Å, closer to the values of the inplane lattice constants. The electronic transport properties of the films are measured using Physical Properties Measurement System (Quantum Design Inc.). The Sr/Nb cationic ratio of the films is measured using Rutherford backscattering spectrometry, and analyses of the obtained spectra using the SIMNRA simulation software yield an Sr/Nb ratio of 0.94 (see Supplementary Note 6 for more details about the stoichiometry of the films).
Spectroscopic ellipsometry
SE measurements are performed with specular reflection geometry at room temperature from 0.6 to 6.5 eV using Woollam VVASE ellipsometer at 50°, 60° and 70° incident angles from the sample normal. The beam spot size is ∼1–3 mm. The resulting ellipsometric parameters of each sample, , where r_{p} and r_{s} are the p and spolarized component of the amplitude reflection coefficients, respectively^{37}, are analysed to extract the complex dielectric function, ɛ(ω)=ɛ_{1}(ω)+iɛ_{2}(ω), of the films using the Woollam WVASE32 and Woollam CompleteEase softwares. Since the samples are strontium niobates thin films on LaAlO_{3} substrate, they are modelled as a twolayer system^{37}. The ɛ(ω) of the thin films is fitted using a combination of Drude^{37} and Herzinger–Johs PSemi–Tri^{38} oscillator functions, while the ɛ(ω) of the underlying LaAlO_{3} substrate is modelled using Lorentz oscillator functions^{37} (all oscillator functions are Kramers–Kronig transformable^{39}). To account for the surface (∼1 nm) and interface (∼3 nm) roughnesses, a Bruggemanmode effective medium approximation is used^{40}. The fitting is performed until a least χ^{2} fit is achieved. Owing to the indications of possible anisotropy from XRD data (Supplementary Fig. 1), the SE data of the films is analysed using two modes: (1) isotropic mode, where the ɛ(ω) along all directions is assumed to be the same, and (2) uniaxial anisotropic mode, where the ɛ(ω) along the outofplane (extraordinary) direction is assumed to be different from the ɛ(ω) along the inplane (ordinary) directions. The fitting analysis of the LaAlO_{3} substrate is performed using isotropic mode and the resulting ɛ(ω) spectra are shown in Supplementary Fig. 2.
The SE data of lpSNO and mpSNO, as well as lpSNO2, mlpSNO2, mpSNO2 and mhpSNO2, cannot be fitted properly using isotropic mode and can only be fitted well at all incident angles using uniaxial anisotropic mode (Supplementary Figs 3 and 12). This indicates that these conducting films have a slight uniaxial anisotropy along the outofplane direction, consistent with XRD data (Supplementary Fig. 1). The resulting ordinary (along inplane directions) ɛ(ω) and LF, −Im [ɛ^{−1}(ω)], of lpSNO and mpSNO films are shown in Fig. 1, while their extraordinary (along outofplane direction) ɛ(ω) and LF spectra are shown in Supplementary Fig. 4. Meanwhile, the resulting ordinary ɛ(ω) and LF of the secondbatch conducting films are shown in Supplementary Fig. 14, while their extraordinary components are shown in Supplementary Fig. 15. Since the features of extraordinary ɛ(ω) of lpSNO and mpSNO are similar to their ordinary ɛ(ω), only the ordinary ɛ(ω) of lpSNO and mpSNO are shown in Fig. 1 for clarity. The SE analyses also show that the thicknesses of lpSNO and mpSNO films are ∼196 nm (with thickness nonuniformity of ∼11%) and ∼218 nm (with thickness nonuniformity of <5%), respectively. The thicknesses of the secondbatch films are shown in Supplementary Table 1.
Meanwhile, the SE data of hpSNO, as well as hpSNO2 and hrpSNO2, can be fitted well at all incident angles using the isotropic mode (Supplementary Figs 5 and 13) and analysis using anisotropic mode yields the same ordinary and extraordinary ɛ(ω) and LF spectra of the film, indicating that hpSNO is optically isotropic and it has little to no anisotropy (see Supplementary Note 7 for more details). This is consistent with XRD data (Supplementary Fig. 1), which shows that the inplane and outofplane lattice constants of hpSNO are much closer to its inplane lattice constants as compared to those of lpSNO and mpSNO. The resulting ɛ(ω) and LF spectra of hpSNO are shown in Fig. 1, while those of hpSNO2 and hrpSNO2 are shown in Supplementary Fig. 14. The SE analysis also shows that the thickness of the thicker hpSNO film is ∼168 nm (with thickness nonuniformity of ∼34%). The SE data of thinner hpSNO films (∼81, ∼52 and ∼20 nm) is similarly analysed using isotropic mode (Supplementary Fig. 10).
From the obtained ɛ(ω), the refractive index (n(ω)), extinction coefficient (κ(ω)), normalincident reflectivity (R(ω)), and absorption coefficient (α(ω)) of the films can be extracted using the Fresnel equations and the following relations:
and
where λ is the photon wavelength. The n(ω), κ(ω), R(ω) and α(ω) of lpSNO, mpSNO and ∼168 nm hpSNO are shown in Supplementary Fig. 6, while the n(ω), κ(ω), R(ω) and α(ω) of thin hpSNO films are shown in Supplementary Fig. 11. It should be noted that since the extraordinary ɛ(ω) of lpSNO and mpSNO are very similar to their ordinary components (Supplementary Fig. 4), for simplicity only the ordinary ɛ(ω) of lpSNO and mpSNO are used to calculate their respective n(ω), κ(ω), R(ω) and α(ω).
Conventional plasmon dephasing time
Based on ɛ(ω) and LF, the free electron scattering, 1/τ, can be estimated by at least two methods. In the first method, by using the Drude model (Supplementary equation 6b), 1/τ can be extracted from the blueshift between the plasmon energy, ω_{p}, and the zerocrossing of ɛ_{1}(ω),
In the second method, the free electron scattering can be estimated from the FWHM, 2ħΓ, of the conventional plasmon peak taken from the LF spectra. The free electron scattering contributes to the dephasing of the conventional plasmon, meaning that the conventional plasmon dephasing time^{3}, T_{2}, can be obtained using
Optical conductivity and spectral weight
Since the ɛ(ω) of lpSNO and mpSNO, as well as lpSNO2, mlpSNO2, mpSNO2 and mhpSNO2, are slightly anisotropic, their optical conductivity, σ_{1}(ω), and spectral weight, W, are also anisotropic because they are both derived from ɛ(ω). The ordinary (o) σ_{1}(ω) of the films are shown in Fig. 2a (main batch) and Supplementary Fig. 16a (second batch), while the corresponding extraordinary (e) components are shown in Supplementary Fig. 7a (main batch) and 17a (second batch). Meanwhile, the evolutions of the ordinary (W_{o}) and extraordinary (W_{e}) components of spectral weight across the three mainbatch films are shown in Supplementary Fig. 7b,c, respectively, while for the secondbatch films they are shown in Supplementary Fig. 17b,c, respectively. The axisaveraged spectral weight shown in Fig. 2b and Supplementary Fig. 16b is obtained using , since the anisotropy of the conducting films is uniaxial with two ordinary inplane axes and one extraordinary outofplane axis. The W is proportional to the number of charges participated in the optical excitation, thus the fsum rule is a charge conservation rule. If the W of a particular energy region increases, it has to be compensated by an equivalent decrease of the W of another energy region, and vice versa.
Transmission electron microscopy
The mainbatch Sr_{1−x}NbO_{3+δ} thin films are prepared for TEM measurements via the liftout method using an FEI Strata 235 dual beam focused ion beam. The samples are then locally ion milled using a Fischione 1040 Nanomill at 900 eV and then 500 eV to remove the focused ion beam damaged surfaces. The TEM and selectedarea electron diffraction (SAED) are performed on a JEOL 3010 operating at 300 kV. Zone axis SAED patterns are collected for all three films (Supplementary Fig. 8) backtoback using identical SAED apertures, magnification and beam illumination (beam fully spread). Distinct Bragg peaks are visible for the Sr_{1−x}NbO_{3+δ} films and LaAlO_{3} substrate in both the outofplane (00l) and inplane (h00) directions indicating at least partial strain relaxation for all three cases. Superlattice reflections along the (101) and (−101) axis surround the main SrNbO_{3} Bragg peaks in the mpSNO and hpSNO SAED patterns, forming Xshaped streaks, due to diffraction from the extra oxygen planar defects. A magnified region around the (100) Bragg peaks for each sample is shown at the bottom of Supplementary Fig. 8 plotted on identical, colorized, intensity scales. To isolate the superlattice reflections the main SrNbO_{3} and LaAlO_{3} peaks are masked out. For consistency the mask locations are determined by a leastsquares fit of a uniform grid to the SrNbO_{3} and LaAlO_{3} Bragg peaks whose positions were determined by Gaussian fit. The background is subtracted as the radial median value from the centre of the diffraction pattern. To quantify the increase in the superlattice peak intensity, the mean value was calculated within the Xshaped region shown overlaid on the (100) peak images in Supplementary Fig. 8 while the mean value outside is taken as the zero value. The resulting value is then normalized by the sample thickness, t/λ (that is, thickness measured in units of the inelastic mean free electron scattering distance, λ, see below and Supplementary Fig. 9) giving a superlattice intensity measure of 19.16, 92.91 and 317.04 for lpSNO, mpSNO and hpSNO, respectively. From this increase in the superlattice reflection intensity from lpSNO, to mpSNO, to hpSNO, it is straightforward to infer an increase in oxygen defect plane density and an increase in oxygen incorporation.
Atomic resolution scanning TEM and energyfiltered TEM are performed on the TEAM0.5, a Cs aberrationcorrected FEI Titan operating at 300 kV. For highresolution scanning TEM, simultaneous images are collected using a highangle annular darkfield (HAADF) detector and a brightfield detector. The former, used in all panels of Fig. 3, produces Zcontrast images with intensities approximately proportional to the square of the atomic number (Z) and atomic nuclei appearing bright. The brightfield images, used in the top half of Fig. 3e, are useful for detecting light elements like oxygen as demonstrated by the visibility of oxygen sites in the planar defects. The brightfield image contrast in Fig. 3e has been inverted to give it a brightatom appearance like the HAADF. Thickness mapping of the TEM crosssections along the electron beam axis (Supplementary Fig. 9) is performed using energyfiltered TEM. To calculate t/λ thickness maps, pairs of images are collected consisting of an unfiltered and an energyfiltered image using a 7 eV slit centred on the zeroloss peak.
Density functional theory calculations
The atomic and electronic structure of SrNbO_{3+δ} compounds are computed by spinpolarized DFT calculations using the Perdew–Burke–Ernzerhof (PBE96)^{41} exchangecorrelation potential and the projectoraugment wave (PAW) method^{42} as implemented in the Vienna ab initio simulation program^{43}. In these calculations, Sr4s4p5s, Nb4p5s4d and O2s2p orbitals are treated as valence states, employing the PAW potentials labelled as Sr_sv, Nb_pv and O in the Vienna ab initio simulation program PBE library. The cutoff energy for the planewave basis set is set to 450 eV, and DFT+U approach^{44} is employed to treat the Nb4d orbitals occupied in the Nb^{4+} ions, with the value of U−J set to 4 eV. SrNbO_{3}, SrNbO_{3.33}, SrNbO_{3.4} and SrNbO_{3.5} are modelled by supercells containing, respectively, 20 atoms with space group Pnam, 64 atoms with space group Ccmm, 54 atoms with space group Pnnm and 44 atoms with space group Cmc2. In the structural relaxations, 8 × 8 × 4, 1 × 4 × 6, 1 × 4 × 6 and 1 × 4 × 6 kpoint meshes are employed for SrNbO_{3}, SrNbO_{3.33}, SrNbO_{3.4} and SrNbO_{3.5}, respectively. The Nb4d valence electron densities of SrNbO_{3} and SrNbO_{3.4} are shown in Fig. 6a,b, while those of SrNbO_{3.33} and SrNbO_{3.5} are shown in Supplementary Fig. 18 and discussed in Supplementary Note 8. The valence electron densities are calculated using electron states with energies ranging from the bottom of the Nb conduction band up to the Fermi level. The samples used in experiments are characterized to have 6% Sr vacancies, and to account for this we estimate that the main effect of Sr vacancies is to shift the Fermi level downward in energy without changing the shape of the valence and conduction bands significantly. For SrNbO_{3.4} (Fig. 6b), the Nb4d electrons occupy only the middle three Nb planes, while those close to the oxygen walls are depleted of electrons. For SrNbO_{3} (Fig. 6a), no such confinement is observed.
The theoretical LF spectra of SrNbO_{3} and SrNbO_{3.4} are calculated as the inverse of the macroscopic complex dielectric function in RPA^{45}. The LF calculations are performed on top of previous DFT+PAW ground state calculations with an increase of the kpoint mesh grid of up to 16 × 16 × 1 and by including 350 bands. In RPA calculations, any short electron–hole interactions are neglected and thus the calculations can only result in conventional plasmons but not correlated plasmons. The conventional plasmons themselves are determined by the zeroes of the real part of the complex dielectric function (Supplementary equation 9). The resulting LF spectra of SrNbO_{3} and SrNbO_{3.4} calculated using this method are shown in Supplementary Fig. 19.
It should be noted that DFT has a limitation in calculating correlated electron systems because it cannot take into account correlation effects properly, in particular the spectral density transfers relevant for Mott physics. This is particularly seen in its inability to calculate LF spectrum that can resemble the experimental LF of the correlated hpSNO film (Supplementary Fig. 19b). Thus, in the future more rigorous theoretical approaches are needed to shed a more complete picture of the electron confinement and its associated correlated plasmon excitations.
Conventional and correlated plasmons theoretical calculations
The theoretical ɛ(ω), LF, and conventional plasmon of lpSNO shown in Fig. 6e,f are calculated using the established Drude model^{3} with the following parameters: m*=m_{e}, , ω_{p}=2 eV, and 1/τ=0.5eV, where m*, V_{cell}, ω_{p} and τ is the electron effective mass, the volume of film unit cell, the plasmon frequency and the lifetime in which electrons can move without experiencing a scattering process, respectively. The V_{cell} is calculated from the lattice constants obtained from XRD (Supplementary Fig. 1) using cubic perovskite structure. With this choice of parameters, the calculation results are in a very good agreement with experimental data up to 4 eV, below the onset energy of the interband transitions, confirming that lpSNO is a metal with conventional plasmonic characteristics.
Meanwhile, the theoretical ɛ(ω), LF and correlated plasmon of hpSNO shown in Fig. 6e,g are calculated using the coupled harmonic oscillator model as a qualitative approach in the low wave vector limit. The thought process regarding this model can be elaborated as follows. In non or weakly correlated metals, the electron–electron repulsions are mostly screened. Thus, when conventional plasmons are excited, the electrons oscillate as a whole against the positive ionic background, and not against each other since the electron–electron interactions are largely suppressed. In this case, the restoring force is only due to the Coulomb attraction with the positive ionic background (Fig. 6c and Supplementary equation 1), resulting in one bulk plasmon frequency that depends only on the free electron density and effective mass. On the other hand, in strongly correlated materials, electron–electron repulsions are unscreened. Thus, when correlated plasmons are excited, the correlated electrons should also oscillate against each other since each electron can now feel the Coulomb repulsions from neighbouring electrons. In this case, the restoring force would also include the electron–electron repulsions, which turns the plasmonic oscillation into a manybody motion with multiple possible natural frequencies (Supplementary equation 10).
Based on this, the correlated plasmon oscillations of Nb4d electrons in hpSNO are modelled as that of a chain of coupled harmonic oscillators bounded by two oxygen walls (Fig. 6d and Supplementary Fig. 20). As a first approximation, the electron–electron interactions are modelled as that of an elastic spring, with the spring constant representing the strength of the electronic correlation. Furthermore, due to correlation effects, the effective masses and charges of the Nb4d electrons might become renormalized^{12} and different from those of bare electron. Thus, in the calculations the effective masses and charges of the correlated electrons along with the number of oscillators in one chain (N) are finetuned as follows to find the set of parameters that can best match the experimental data, especially the three correlated plasmon peaks at ∼1.7, ∼3.0 and ∼4.0 eV (Fig. 1a,d).
First, to tune the peak positions, we set an energy scale of about the lowest energy of the three plasmon peaks, that is, ω_{0}=2.0 eV. We also set a scale for the effective mass values to be m*=Zm_{e}, and a scale for the spring constant values to be . Here, Z is the mass renormalization factor that we initially set to be equal to 1 and adjust it as necessary. As initial guesses, we set m_{1}=m_{2}=⋯=m_{N}=m* and k_{1}=k_{2}=⋯=k_{N+1}=k_{0}, where the indices, i=1, 2, ..., are according to the oscillator arrangement in Supplementary Fig. 20. Finetuning of the peak positions is done by adjusting individually each k_{i}(m_{i}) slightly away from k_{0}(m*). The Z value is also finetuned so that the magnitudes of the calculated ɛ_{1}(ω) and ɛ_{2}(ω) match closely with experimental data, and the optimum Z value is found to be ∼25.
Second, to tune the peak intensity trend which increases as energy increases (see Fig. 1d), we finetune the effective charges of the correlated electrons. If the effective charges are set to be all the same as that of bare electron, the calculation results in a peak intensity trend that decreases as energy increases, which is the opposite trend compared to what was observed experimentally. This happens because the slower vibration mode corresponds to higher polarization, which gives higher peak intensity as energy increases. To improve this, we find that the increasing intensity trend can only be achieved if the charges are assumed to be distributed with alternating signs, that is, q_{1}=−e, q_{2}=+e, q_{3}=−e and so on.
Third, the number of plasmonic peaks appearing in the theoretical ɛ(ω) and LF of hpSNO is tuned by varying the number of oscillators in one chain. In analogy with classical mechanics, an Noscillator system has N natural oscillation modes. Since the number of observed plasmonic peaks in Fig. 1d is three, this gives an indication that N should be an odd number. We start with the case of N=3. A threebody oscillator have three intrinsic oscillation modes, but there is one mode that has zero polarization. This zeropolarization mode cannot show up in ɛ(ω), leaving only two nonzero peaks and inconsistent with the three peaks observed in Fig. 1d. Next, for N=5 the fivebody oscillator has five eigenmodes, but two of them have zero polarization, leaving three nonzero peaks surviving, which is what the experimental results require. The calculation results (Supplementary Figure 21) show that for N=5 the peak positions and the increasing intensity trend are in a rough agreement with experimental results, but the calculated relative peak intensities are not very satisfactory because the first and the second peaks are too low compared to the third peak.
The calculation for the case of N=7 is next performed with the same approach as discussed above. The results show that not only does it give three appearing peaks (Fig. 6e,g and Supplementary Fig. 21), with only an additional negligibly small peak close to 0 eV, but also it provides a peak intensity profile that much better resembles the experimental results. For this particular case, the parameter values are set as follows: ω_{0}=2.0 eV, Z=25, ɛ_{1}(∞)=4.0, 1/τ=0.5 eV, m_{1}=m_{2}=⋯=m_{N}=Zm_{e}, k_{1}=0.4k_{0}, k_{2}=0.5k_{0}, k_{3}=1.0k_{0} and k_{4}=1.1k_{0}, and the rest of the spring constants follow a mirror symmetry, that is, k_{8}=k_{1}, k_{7}=k_{2}, k_{6}=k_{3} and k_{5}=k_{4}.
The calculations are also performed for N=9 and N=11, although Supplementary Fig. 21 shows that these two cases result in too many peaks. In Fig. 1d it can be seen that, in addition to the three main peaks of C_{1}, C_{2} and C_{3}, there is a small peak at ∼2.4 eV that appears in both ɛ(ω) and LF spectra of thick hpSNO, which means this peak is also a correlated plasmon peak. From the analysis of Supplementary Fig. 21, this small peak could come from the excitation of these higherorder modes (that is, N=9 and/or N=11), although its low intensity compared the three main peaks of C_{1}, C_{2} and C_{3} means that the sevenoscillator mode should still be the dominant mode of oscillation.
For more details, the indepth theoretical calculations of the conventional plasmon of lpSNO and correlated plasmons of hpSNO are discussed further in Supplementary Note 3.
Data availability
The data that support the findings of this study are available from the corresponding authors on reasonable request.
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Acknowledgements
This work is supported by Singapore National Research Foundation under its Competitive Research Funding (NRFCRP 8201106), MOEAcRF Tier2 (MOE2015T21099), 2015 PHC Merlion Project and FRC. We thank Centre for Advanced 2D Materials and Graphene Research Centre at the National University of Singapore to provide the computing resource. D.W., Y.Z., B.Y. and T.V. prepared highquality samples and performed transport and structural measurements.
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T.C.A., D.S. and A.R. performed spectroscopic ellipsometry measurements and analysed the resulting spectra. D.W., Y.Z., B.Y. and T.V. prepared highquality samples and performed transport and structural measurements. C.T.N., M.C.S. and A.M. performed highresolution TEM measurements. T.C.A., M.A.M. and A.R. constructed the main theoretical model. M.A.M., Y.C., M.Y., T.Z., P.E.T., M.S., M.A. and A.R. performed theoretical calculations. M.R.M., M.B.H.B. and T.V. performed Rutherford backscattering measurements. A.R. and T.C.A. wrote the paper with input from all coauthors. A.R. and T.V. initiated and lead the project.
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Asmara, T., Wan, D., Zhao, Y. et al. Tunable and lowloss correlated plasmons in Mottlike insulating oxides. Nat Commun 8, 15271 (2017). https://doi.org/10.1038/ncomms15271
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