1. Introduction

Plasmonics has demonstrated to be one of the most exciting fields of nanotechnology, with possible applications in leading markets such as those of energy or biotechnology [1–3]. This interest is based on the ability of plasmonic nanostructures to enhance, filter, harvest, confine, guide or re-direct light with high efficiency at the nanoscale [4].

The simplest plasmonic nanostructure that we can picture consists of a deeply subwavelength nanosphere with a photon energy-dependent dielectric function ε(E) = ε₁(E) + jε₂(E) embedded in a dielectric medium (permittivity ε_m). A resonance occurs for the nanosphere polarizability at the photon energy E for which the condition ε₁(E) = −2ε_m is fulfiled, if ε₂(E) is small enough. It is thus clear that this resonance, which is responsible for the plasmonic properties of the nanosphere (such as near-field enhancement or enhanced light absorption), occurs in a spectral region that is primarily driven by the dielectric function ε. Note that the achievement of this resonance and the corresponding plasmonic properties requires ε₁(E) to be negative, since ε_m of a dielectric should be positive.

Plasmonic properties are conventionally linked with the coupling of the material’s free carriers to light. The response of these so-called “Drude carriers” is described by the Drude dielectric function, for which ε₁ decreases from 1 to markedly negative values when E decreases. Therefore for a nanosphere described by a Drude dielectric function, the nanosphere resonance condition is fulfiled at a single photon energy, at which a localized surface plasmon resonance occurs. This photon energy increases with the free carrier density/relative effective mass ratio.

The free carrier - based picture of plasmonic properties stands on the earliest known and most studied plasmonic materials: noble metals (Au and Ag). Au and Ag present a near-Drude dielectric function with a Drude carrier density/relative effective mass ratio N* in the 10²² - 10²³ cm⁻³ range, and fulfil the nanosphere resonance condition at a single wavelength in the visible [5, 6]. Note that N* values of 10¹⁸ cm⁻³ and above 10²³ cm⁻³ would make the resonance condition be fulfilled in the far-infrared and ultraviolet ranges, respectively [7]. Therefore in order to achieve plasmonic properties beyond the visible, a quest has started to identify alternative plasmonic materials presenting a dielectric function different from those of Au and Ag [5–12]. In addition novel/enhanced plasmonic performance is sought including lower optical losses and/or specific physico-chemical functionalities. Among the alternative plasmonic materials are especially attractive those refered as switchable, i.e. presenting reversibly tunable properties as a response to external stimuli.

Plasmonic properties were predicted early in non-noble elemental metals: alkaline, transition, and p-block metals [6]. The potential of these metals for applications is being currently revisited under the light of the newly acquired knowledge [8–12]. Upon adequate selection of the metal nature, localized surface plasmon resonances can be achieved in the ultraviolet, visible, or near-infrared. Al and In are particularly adequate for achieving sharp resonances and strong near-field enhancement in the far and near-ultraviolet [13–15]. Furthermore the plasmonic properties of non-noble metallic compounds can be broadly tuned through their composition, as shown for titanium nitride-based compounds that are interesting alternatives to Au for applications in the visible [9,16,17]. Plasmonic properties can also be achieved for non-metallic compounds such as transparent conducting oxides [9,18]. Their plasmonic properties originate from the introduction of a controlled density of free carriers in the material’s empty conduction band, though impurity doping or carrier transfer [18]. By such means, the range of plasmonic properties can be tuned from the far-infrared to the near- infrared, and switched dynamically. In a similar way, high impurity doping in semiconductors such as Si or Ge also permits to achieve plasmonic properties that can be driven from the far- infrared to the mid-infrared [9].

All these examples show that plasmonic properties are achieved in a very broad range of materials, well beyond noble metals, and they suggest that plenty of materials showing a plasmonic behaviour remain to be discovered. In this context, it is worth insisting on the fact that plasmonic properties are not necessarily induced by free carriers. Negative ε₁ values can be achieved at the high energy side of resonances with high oscillator strength in the ε₂ spectrum [9], in virtue of the Kramers-Kronig relations. Such a behaviour is well known in the mid-infrared and far-infrared for a broad range of materials in relation with phonon modes [19], and in the vacuum-ultraviolet for semiconductors such as Si and Ge in relation with excitonic transitions. Similar observations have been reported in organic materials [20] and in confined noble metal alloyed nanoparticles [21] where negative ε₁ values are induced by excitonic transitions and by interband transitions, respectively.

At present, there is a marked interest in the development of nanostructures from materials showing ultraviolet - visible plasmonic properties induced by electronic transitions with high oscillator strength [22–26]. Especially, such properties have been demonstrated with organic materials due to excitonic [22–24] or interlevel [25] transitions, and in inorganic topological insulators (Bi₁.₅Sb₀.₅Te₁.₈Se₁.₂) due to interband transitions [26]. These materials are particularly attractive because they promise a much broader tunability in their plasmonic properties than Drude materials, based on the tuning of the occupancy of their electronic energy levels or bands [22–26].

In this context, the plasmonic properties of some of the p-block elemental materials such as Bi, Sb and Ga, which are attracting a growing attention for their applications, are of strong interest. In their solid state, they show a complex electronic band structure and a dielectric function that cannot be expressed by a Drude dielectric function. In particular in our group we have been recently attracted by the peculiar electronic and optical properties of Bi and its potential for switchable plasmonics. So far, switching with Bi is based on the change in its electronic structure and thus in its dielectric function upon an external excitation [27], heating or laser irradiation, that induces the melting of the material. In the case of Bi nanostructures, this change in dielectric function translates into a change in their plasmonic properties and thus in their optical absorption and scattering at selected photon energies. Solid Bi is a semi-metal for which plasmonic properties have been reported in both the mid-infrared [28] and the ultraviolet - visible. Especially, in the latter spectral region, optical resonances with properties mimicking those of localized surface plasmon resonances have been reported for Bi nanostructures [27, 29]. Hereafter such resonances will be called “localized surface plasmon-like resonances”. Let us remark that this “dual” plasmonic behaviour is not compatible with a Drude behaviour that imposes a single spectral region for the plasmonic properties. A similar behaviour arises for solid Sb, a semi-metal, which presents plasmonic properties in the mid-infrared [30], together with an evident metallic aspect that suggests plasmonic properties in the visible and a volume plasmon in the vacuum- ultraviolet that has been probed by electron energy loss spectroscopy [31]. Also particularly interesting is Ga whose nanostructures have been studied in detail recently [12,32–35] in relation with switchable plasmonics, based on their phase transition upon heating or laser irradiation. The most stable solid Ga phase (α-Ga) presents plasmonic properties in the ultraviolet - visible (localized surface plasmon-like resonances in nanostructures) [32] while being known as a molecular metal in which covalent and metallic behavior coexist [35–37].

Given the increasing relevance that nanostructures made of these elemental materials have demonstrated at this point, it is necessary to achieve a deeper understanding of the origin of their plasmonic properties in the solid state. First we will start by performing a comprehensive review of their dielectric functions available in the literature. We have gathered the data in a broad photon energy range that covers the spectrum from the far-infrared to the vacuum-ultraviolet. Second we will present a comparative analysis of the data in relation with the electronic structure of the elemental materials. This analysis shows that the plasmonic properties observed in the ultraviolet - visible are fully and almost fully induced by interband transitions for Bi, Sb and Ga, respectively.

2. Dielectric functions of solid Bi, Sb and Ga

We will center our discussion on the reported dielectric functions that were obtained by optical spectroscopy. The data are very dispersed and varied [28–32, 38–56]. So far, the dielectric functions of solid Bi, Sb and Ga have been studied on samples synthesized by different methods e.g. polished bulk crystals, thin films grown by evaporation, pulsed laser deposition. This list of methods is not exhaustive. Moreover, the samples presented different nanostructures, such as different crystallinity, surface roughness or thickness. In particular the monocrystals present optical anisotropy, in relation with their anisotropic crystalline structure and energy band diagram [38–40]. Bi and Sb present a rhomboedral cristalline structure while that of Ga is monoclinic. The optical anisotropy is particularly marked for Ga. Moreover, in each report, the characterization has been realized in a limited photon energy range with a specific characterization method. Especially, reflectance or transmittance spectroscopy or spectroscopic ellipsometry were used in the different works, and the measurement were done at different angles of incidence and polarizations. In Fig. 1, we gather the results given in the collected reports [28–30, 38, 39, 42, 43, 45–56]. Despite a significant data scattering that appeals at a broadband characterization of model samples, especially for Bi and Ga, general trends can be drawn for the dielectric functions of Bi, Sb and Ga, showing that the three elemental materials share common optical features.

 

Fig. 1 Optically-determined dielectric functions of solid Bi, Sb and Ga gathered from the literature, real part ε₁ (top row) and imaginary part ε₂ (bottom row). The reported data have been obtained from the following references. Bi crystals: Lenham [45], Tediosi (290 K) [46], Hodgson [47], Markov [48]; Bi films: Harris [49], Khalilzadeh [28], Toudert [29], Hunderi (70 K) [38], Toots [50]. Sb crystals: Lenham [45]; Sb films: Fox [42], Harris [51], Cleary [30], Lemonnier [39], Toots [50]. Ga crystals: Lenham [43], Lenham [52], Kofman [53]; Ga films: Hunderi [54], Bor [55], Jezequel [56]. The regions where free carriers (region I) and interband transitions (region II) have a strong contribution to the dielectric function are depicted in the bottom row by blue and red arrows, respectively.

Download Full Size | PDF

Upon decreasing the photon energy E from 24 eV (vacuum-ultraviolet) to 0.03 eV, (far- infrared): the ε₁ function first decreases to reach a local minimum in the visible - near-infrared, then increases until reaching a maximum, and finally abruptly decreases. Therefore we can define two regions where ε₁ is negative and suitable to fulfil an optical resonance condition: one located in the infrared (region I) and another in the ultraviolet - visible (region II). This behaviour strongly departs from that of a simple Drude metal for which ε₁ would only decrease upon decreasing the photon energy in the whole 24 eV - 0.03 eV range.

Instead, the Bi, Sb and Ga show rich dielectric functions that include both contributions from free carriers and interband transitions. The free carriers in these materials have been probed optically, yielding typical density/relative effective mass ratio N* (Bi [41], N* ~3x10¹⁹ cm⁻³, Sb [42], N*~6x10²⁰ cm⁻³, Ga [43], N* between 10²² and 2.10²² cm⁻³, maximum in the basal a-b plane). Note the very low N* values for Bi and Sb, in relation with the semi-metallic behavior of these materials. From these values, it is expected that the free carriers in Bi, Sb and Ga induce a negative ε₁ up to a photon energy located in the far-infrared for Bi [44], in the mid- infrared for Sb, and in the red part of the visible for Ga. The high photon energy side of region I in Fig. 1 follows nicely this trend, suggesting that the contribution of free carriers dominate the response of the three materials in this region.

In region II, interband transitions contribute in a determinant way to the dielectric function of Bi, Sb and Ga. These transitions have been identified by Hunderi for Bi [38] and Ga [54] based on electronic structure calculations, and by Lemonnier et al. for Sb [39]. They induce the dominant peaks shown in the ε₂ spectra of Fig. 1, located close to 0.8 eV for Bi, 0.3 eV for Sb, 2 eV for Ga, at slightly lower photon energies than the negative ε₁ minima. Such a behavior is typical of Kramers-Kronig consistency and the causality principle [9,57]. This suggests that the interband transitions at these photon energies (0.8 eV for Bi, 0.3 eV for Sb, 2 eV for Ga) may have a high enough oscillator strength to induce negative ε₁ in region II at their high energy side. In the next section, we examine this possibility by estimating the contribution of free carriers and interband transitions in this region.

3. Interband origin of the negative ε₁ in the near-ultraviolet - visible

In order to estimate the contribution of free carriers and interband transitions in region II, we have selected the dielectric functions we consider the most reliable for the three materials (for Bi [38], for Sb [39] and [42] and for Ga [54]). Our main criteria for assessing the reliability of the dielectric functions of Bi, Sb and Ga found in the literature were: the inferred material quality (ideally surface roughness should be as low as possible), the optical measurement method (ellipsometry is recommended) and suitability of the model used for the analysis of the optical measurement (transfer matrix formalism for thin films). Then we fitted the selected dielectric functions by using a linear sum of a Drude dielectric function and Kramers- Kronig Lorentz oscillators accounting for interband transitions. The corresponding formulae are given in the Appendix. The choice of using Lorentz oscillators for describing the contribution of interband transitions in each material is purely phenomenological, as well as the number of these oscillators. Different Kramers-Kronig consistent oscillators, not necessarily Lorentzian, might have to be used to account in a more meaningful physical way for the individual interband transitions in each material. This is however beyond the scope of this work, in which we are interested in evaluating the total contribution of interband transitions, which can be described equally by several different sets of oscillators with the only mandatory requirement that they fulfil the Kramers-Kronig relations. Figure 2 shows the resulting fit. It has been performed as follows: the parameters of the Drude dielectric function (free carrier density/relative effective mass ratio N* and collision frequency τ) have been set to values taken from the literature and fixed at these values during the fit procedure, while the parameters of the Kramers-Kronig consistent oscillators were used as only fit parameters. The values used for the parameters (N* and τ) of the Drude dielectric function for Bi, Sb and Ga are given in the captions of Fig. 2. We recall here, for the sake of clarity, the N* values that drive the spectral range in which free carriers play a significant role in the material’s optical response: 3x10¹⁹ cm⁻³ for Bi, 6x10²⁰ cm⁻² for Sb, 2x10²² cm⁻³ for Ga. The very low N* values for Bi and Sb (related with the semi-metallic behavior of these materials) already point toward an unsizable role of free carriers on the optical response of these materials in the ultraviolet visible. As expected, it can be seen that the dielectric functions of Bi and Sb (“Exp” in Fig. 2) in region II are fully ruled by the Lorentz oscillators (“All Oscillators” in Fig. 2). The Drude function (“Drude” in Fig. 2) has a sizeable contribution only at much lower photon energies, in the infrared. Therefore, it is shown that the negative ε₁ and the plasmonic properties of Bi and Sb in the ultraviolet - visible region are induced fully by interband transitions.

 

Fig. 2 Fit of the dielectric functions (black dots, “Exp”) taken from [38] (Bi) [39], and [42] (Sb) and [54] (Ga). The fit has been done using a sum of a Drude dielectric function (green lines) and Kramers-Kronig consistent Lorentz oscillators (purple dotted lines for individual oscillators (“Oscillators”) - 3 oscillators for Bi, 7 for Sb, 4 for Ga - and purple full lines for the sum of all the oscillators, “All Oscillators”). The parameters of the Lorentz oscillators were used as fit parameters whereas those of the Drude dielectric function were fixed at values taken from the literature: Bi - N* ~3x10¹⁹ cm⁻³, τ = 300 fs [41], Sb - N*~6x10²⁰ cm⁻³, τ = 31 fs [42], Ga - N* = 2.10²² cm⁻³, τ = 21 fs [43].

Download Full Size | PDF

For Ga, both the Lorentz oscillators and Drude dielectric function play a role in region II. Therefore, both interband transitions and free carriers contribute to the negative ε₁ and plasmonic properties of Ga in the ultraviolet – visible. However, in the 2.5 – 4 eV spectral region, the main contribution is by far that of interband transitions. This observation is in line with the particular spectral shape of the ε₂ function on the high energy side of the 2 eV peak, which suggests that transitions between parallel bands dominate the response in the visible [54]. The important role of interband transitions in the visible is further supported by the electronic density of states of a-Ga, for which the Fermi level is located in a ~2 eV gap with a low sub-gap density of states [35–37, 58]. Note that the balance between the contributions of interband transitions and free carriers in the ultraviolet - visible may depend on the sample crystallinity (a lower collision frequency for the free carriers makes their contribution stronger in the visible). For an accurate quantification of these contributions, it will be necessary to perform a broadband characterization of a sample of interest.

4. Interband-induced localized surface plasmon-like resonances

Finally, we estimate the contribution of interband transitions and free carriers on the ultraviolet - visible plasmonic properties of Bi, Sb and Ga by simulating the optical response of nanostructures made of these elemental materials, and of modelled materials accounting for their interband transition and free carrier contributions taken separately.

Figure 3 shows simulated spectra of the extinction efficiency Q_ext of nanospheres embedded in a transparent medium, as a function of their diameter (D = 20 nm, 40 nm and 60 nm). Simulations have been performed with a Mie calculation software [59, 60], using several dielectric functions for the nanospheres: the best-fit dielectric functions to the literature data of Fig. 2 (i.e. the actual dielectric functions of Bi, Sb and Ga, “All Oscillators + Drude” in Fig. 3), the corresponding contribution of free carriers only (“Drude” in Fig. 3) and the corresponding contribution of interband transitions only (“All Oscillators” in Fig. 3). Note that these dielectric functions were measured on films with thicknesses above 100 nm, and can be considered as representative of the “bulk” properties of the corresponding materials. We have chosen to use these “bulk” dielectric functions in order to provide a simple and qualitative approximation on the physics that explain the (near) ultraviolet – visible plasmonic properties of solid Bi, Sb and Ga nanospheres. The possible role played by the so-called finite size effects (change in the dielectric function of the material due to the confinement of charge carriers in the nanosphere) will be discussed later in the manuscript.

 

Fig. 3 Simulated extinction efficiency (Q_ext) spectra of nanospheres of different diameters D = 20 nm, 40 nm, 60 nm, embedded in a transparent medium (ε_m = 6.25). The simulations have been performed using a Mie calculation program [59]. Different dielectric functions have been used for the nanospheres: the best-fit dielectric function to the literature data (actual dielectric functions of solid Bi, Sb and Ga - same as in Fig. 2, “All Oscillators + Drude,” black dashed lines), the corresponding contribution of free carriers only (same as in Fig. 2, “Drude,” green lines), the corresponding contribution of interband transitions only (same as in Fig. 2, “All Oscillators,” purple lines). The black vertical arrows show the position of the dipolar localized surface plasmon – like resonances.

Download Full Size | PDF

Simulations done with the contribution of free carriers only show a low Q_ext over the whole ultraviolet - visible range (4 eV to 1.7 eV) for Bi and Sb whatever the value of D. In the case of Ga, sharp surface plasmon resonance modes are observed around 1.5 eV. Note that these resonance modes occur because the “Drude” component of Ga (green line in Fig. 2) fulfils the nanosphere resonance condition (ε₁ = −2ε_m) around this photon energy. Moreover, the low ε₂ value of the “Drude” component around the photon energy of 1.5 eV allows the resonances to be particularly intense and sharp. This confirms that the free carriers taken separately cannot induce a resonance in the ultraviolet - visible neither for Bi and Sb nor for Ga. In contrast, the simulations done with the contribution of interband transitions only show a dipolar localized surface plasmon-like resonance for D = 20 nm, the maximum Q_ext being reached in the near-ultraviolet. This maximum shifts from the near-ultraviolet to the red upon increasing D from 20 nm to 60 nm, while a quadrupolar localized surface plasmon-like resonance grows in the near-ultraviolet. These simulations are identical (for Bi and Sb) and very similar (for Ga) to those done with the best-fit dielectric functions to literature data. This supports the fact that the resonances for Bi and Sb in the ultraviolet - visible are induced by interband transitions only, whereas that for Ga are driven by interband transitions with a very small contribution of free carriers. In that sense, the localized surface plasmon-like resonances of solid Bi, Sb and Ga nanospheres should be named “interband-polaritonic resonances”. Furthermore, note that the sharp surface plasmon resonances that were observed around 1.5 eV when considering only the “Drude” component of Ga in the simulation are not seen anymore when both “Drude” and “All Oscillators” components are taken into account. This is because the sum of these two components is characterized by a positive ε₁ and a high ε₂ in the 1-2 eV spectral region thus prohibiting the occurrence of any plasmon resonance. Note that the positive ε₁ is due to the fact that interband transitions yield a positive contribution to ε₁ in this spectral region overcoming in absolute value the negative contribution of the free carriers. In other words, the interband transitions “screen” the free carriers in the 1-2 eV spectral region in a similar way to what happens in the 2-3 eV region for Au or Cu.

Despite the different origin of these resonances when compared with metals, they share similar spectroscopic features with these traditional plasmonic materials. This trend can be examplified qualitatively using again the “bulk” dielectric functions of solid Bi, Sb and Ga for Mie calculations. As seen in Fig. 3, the peak energy of the dipolar resonance shifts toward the red upon increasing the nanosphere diameter in a similar way as with noble or poor metals [5, 6, 11]. Furthermore in a similar way to traditional plasmonic materials, the spectral position of the dipolar resonance is also sensitive to other parameters such as the nanostructure shape, and the dielectric function ε_m of the surrounding medium. Such trends have been already shown in the case of Bi nanostructures (shape [29, 61], size [11], ε_m [29]), and of Ga nanostructures (size [6, 11]). In Fig. 4, we further examplify this sensitivity for Bi and Ga nanostructures and explore it for the first time for Sb nanostructures. This figure shows the evolution of the dipolar resonance photon energy for solid Bi, Sb and Ga nanospheres as a function of their diameter D and of the dielectric function ε_m of the surrounding medium, varied in a realistic range. For the three materials, the resonance shifts toward lower photon energy upon increasing D or ε_m. Especially, by proper choice of the D and ε_m values for Bi or Sb nanospheres, it is possible to bring the resonance at any photon energy in the near ultraviolet - visible. In contrast, with D and ε_m in the same range, for Ga nanospheres the resonance cannot reach photon energies in the red, however it can be shifted towards the far ultraviolet region.

 

Fig. 4 Simulated photon energy of the dipolar localized surface plasmon-like resonance of solid Bi, Sb and Ga nanospheres as a function of their diameter D and the dielectric function of the surrounding medium ε_m. The simulations have been performed using a Mie calculation program [59], and the dielectric functions of solid Bi, Sb and Ga were the best-fit to the literature data (same as in Fig. 2).

Download Full Size | PDF

As mentioned above, the actual plasmonic response of Bi, Sb and Ga nanospheres in the ultraviolet-visible may depart from the simple pictures shown in Figs. 3 and 4. This is especially true in the case of Bi for which quantum confinement effects have been broadly reported in nanostructures. These quantum confinement effects, observed for nanostructure sizes of a few tens of nm consist in a semimetal to semiconductor transition [62,63] and spectral signatures of confinement-induced intersubband and interband transitions [64–66] in the mid infrared spectral region. Other works have also reported the volume plasmon (measured by EELS) of Bi nanowires and nanoparticles in the vacuum ultraviolet [67–69] but it seems that there is no consensus concerning the existence of strong quantum confinement effects in this spectral region. In the near ultraviolet – visible, one report claims the observation of strong quantum confinement in Bi nanoparticles with a 3 nm diameter [44]. In addition theoretical studies predict a large bandgap opening in nanowires for diameters of tens of nm [62]. However we have observed that the main experimental plasmonic features measured for embedded Bi nanoparticles with diameters between 20 nm and 100 nm are rather well described by classical models (i.e. using the dielectric function of bulk Bi) without the need to invoke quantum confinement effects [29]. This leads us to infer that quantum confinement is not playing a major role on the (near) ultraviolet - visible optical properties of these embedded Bi nanoparticles with 20 to 100 nm diameters. Due to the semimetal to semiconductor transition in Bi for the nanostructures a few tens of nm in size, it is expected that the free carrier density and thus their contribution to the dielectric function of Bi in the ultraviolet – visible will decrease with the size. Therefore it can be inferred that the plasmonic properties of Bi in this spectral region will be dominated by interband transitions even for relatively small nanostructures. To be determined is the dependence of these interband transitions and the dielectric function ε(E) on the nanostructure size (in a similar way to what has been done in the past for Au or Al nanoparticles). To the best of our knowledge, no reliable spectral information about the dielectric function of Bi nanostructures has been reported so far in the ultraviolet - visible. This lack of information appeals at further investigation in which optical measurements will be performed in the ultraviolet - visible on Bi nanostructures of controlled size, shape and organization. The results of these measurements will be compared with classical simulations as those shown in Figs. 3 and 4 to seek for possible deviations that could be ascribed to quantum confinement effects on interband transitions in the ultraviolet - visible.

Despite of the lack of data about the dielectric function of Bi nanostructures in the ultraviolet – visible, we can still draw a qualitative picture of the effect of a quantum confinement on the plasmonic properties of a Bi nanosphere in this spectral region. Assuming that quantum confinement induces a blue – shift of the 3 interband transition – related Lorentz oscillators shown in Fig. 3 in a bandgap opening fashion, the localized surface plasmon – like resonance of a Bi nanosphere of a given size would appear blue-shifted compared with the data shown in Figs. 3 and 4. In addition, a finite size – induced damping of the interband transition – related oscillators would also affect the localized surface plasmon – like resonance. It could be shifted when compared to the data shown in Figs. 3 and 4 and also present a different width and amplitude. Moreover, it could vanish if the oscillator strength of the interband transitions became too small to induce negative enough ε₁ values for a resonance condition to be fulfilled.

5. Conclusions: Interband plasmonics - a new paradigm in photonics?

In the previous section we have proposed that solid Bi, Sb and Ga nanospheres show dipolar surface plasmon-like resonances that can be tuned by design through the ultraviolet - visible region. This behaviour is very convenient for the design of functional Bi, Sb, and Ga nanostructures in a similar way as with noble metal nanostructures. However, in contrast with noble metals, the plasmonic properties of Bi and Sb in the ultraviolet - visible are induced by interband transitions, with no need of free carrier contribution. Interband transitions also play a key role in the case of Ga, where they induce the plasmonic properties in conjunction with a small contribution of the free carriers. This completely differs from the most frequently encountered plasmonic scheme in the ultraviolet - visible, in which interband transitions are a damping channel for plasmonic effects [70, 71]. On the contrary, when strong enough, they allow generating or facilitating plasmonic properties. The fact that plasmonic effects can be generated by interband transitions, i.e. involving electron-hole pair excitation instead of free carriers, is interesting for many reasons. It probably plays a role in the recently demonstrated photocatalytic properties of Bi nanoparticles [72, 73] and more generally has implication for energy conversion schemes involving the collection of photogenerated carriers [1]. Furthermore, it is appealing for the design of novel nanostructures and metamaterials with a much higher tunability and switchability than those standing solely on noble metals, based on the tailoring of band structure [74] and the dynamic control of band occupancy, as already underlined in refs. 23, 25 and 26. For instance, for nanostructures in which the plasmonic properties are based on interband, interlevel or excitonic transitions, it is foreseen that plasmonic switching will be possible without phase transition, by driving optically the nanostructures to an excited state. A change in the nanostructures dielectric function (and thus in their plasmonic properties) will be due in this case to the change in the population of energy bands (material brought to an excited state). Actually, such a behaviour has been evidenced recently [75] although with non-plasmonic nanostructures (ε₁ >0).

Ultraviolet - visible plasmonic properties based on interband or other electronic transitions (excitonic or interlevels) have been demonstrated in other recent works, using organic materials [22–25] or the topological insulator Bi_1.5Sb_0.5Te_1.8Se_1.2 [26]). There are certainly many materials presenting similar properties. For the sake of example, we can cite here compounds including p-block elements [76–80] such as tetradymites [79] or GSTs [80]. These latter materials however show significant losses (comparable with Bi, Sb and Ga) in the ultraviolet-visible thus making them candidates for applications in which losses are not a severe drawback or even can be turned into a valuable and useful property [81].