Robust UV Plasmonic Properties of Co-Doped Ag₂Te

Abstract

Ag₂Te is a novel topological insulator system and a new candidate for plasmon resonance due to the existence of a Dirac cone in the low-energy region. Although the optical response spectrum of Ag₂Te has been studied by theoretical and experimental methods, the plasmon resonance and stability of Co-doped Ag₂Te remain elusive. Here, we theoretically report a new unconventional UV plasmon mode and its stability in Co-doped Ag₂Te. Through density functional theory (DFT), we identify a deep UV plasmon mode within 15–40 eV, which results from the enhanced inter-band transition in this range. The deep UV plasmon is important for detection and lithography, but they have previously been difficult to obtain with traditional plasmon materials such as noble metals and graphene, while most of which only support plasmons in the visible and infrared spectra. Furthermore, we should highlight that the high-energy dielectric function is almost invariant under different doping amounts, indicating that the UV plasmon of Ag₂Te is robust under Co doping. Our results predict a spectrum window of a robust deep UV plasmon mode for Ag₂Te-related material systems.

1. Introduction

As a class of topological materials, Dirac semimetals have linear band dispersion around the conduction and valence band touching point, the so-called Dirac cone [1,2,3,4]. In recent years, topological Dirac materials have attracted wide attention for their ability to support nearly zero mass fermions around the Dirac cone, which can induce extremely high mobility and make the Dirac material an ideal system to support collective electromagnetic oscillations [5,6,7,8]. Graphene is a 2D topological Dirac material that hosts two pairs of Dirac cones in the Brillouin zone. Its infrared plasmon has been widely studied, but the 2.3% light absorption of monolayer graphene limits its further application [9,10]. A Dirac material system with a stronger light-matter interaction is urgently needed.

Recent reports revealed that the silver telluride material has unique properties for electronic and optical applications [11,12,13]. The Ag₂Te monoclinic phase in particular has been proven to possess an isotropic Dirac cone, which makes Ag₂Te exhibit topological properties [14]. The large number of massless fermions supplied by Dirac cones makes Ag₂Te a promising candidate for collective electromagnetic oscillations [15,16]. The bulk character endows Ag₂Te with a better light–matter interaction than graphene. Previous research on Ag₂Te concentrated on its basic optical properties and topological behavior [11], but the physical picture of plasmon resonance remains unclear.

In recent years, great progress has been made in spintronics devices that use the spin of a semiconductor as a degree of freedom [17,18,19,20,21,22]. By doping a semiconductor with dilute magnetism, materials with both semiconductor and magnetic properties are obtained at room temperature, providing a promising approach for realizing the next generation of spin-based logic electronics [23,24]. Since the realization of room-temperature ferromagnetism of ZnO through Mn doping, doping of semiconductors with transition metals (Mn, In, Co and Cr) to achieve room-temperature ferromagnetism has become a common way to realize dilute magnetic semiconductors [25,26,27,28].

In this work, we comprehensively investigated the electronic structure and optical properties of Ag₂Te through density functional theory (DFT). The reflectivity of Ag₂Te coincides well with previous experimental results [15]. The real part of the dielectric function is negative when the optical energy is below 0.1 eV and in the range of 12–20 eV, in which the former comes from Drude free electrons, while the latter stems from a higher density of states (DOS) in the high-energy region. Surface plasmon polaritons (SPPs) are excited at the material interface where the real part of the dielectric function is negative on one side and positive on the other side. The plasmon of Ag₂Te is supported in both the infrared and UV energy regions. The perturbation applied to the electronic structure through Co atom doping can open a band gap and make the semimetal become a semiconductor, while the UV plasmon is robust to Co atom doping.

2. Methods

We perform first-principles methods using CASTEP to calculate the electronic structure and energy. The generalized gradient approximation (GGA) of Perdew, Burke and Ernzerhof (PBE) is used for the exchange-correlation potential [29,30,31]. The plane-wave basis cutoff energy is 490 eV. SCF (Self Consistent Field) energy tolerance is $1\times {10}^{-6}$ eV/atom. To analyze the electronic properties in the 6.25% doping concentration system, we use a 2 × 1 supercell of Ag₂Te with an Ag atom substituted by a Co atom. For the 12.5% doping concentration, we use a 1 × 1 crystal cell. The geometry optimization energy convergence tolerance is set as $2.0\times {10}^{-5}$ eV/atom. A 3 × 4 × 3 Monkhorst-Pack mesh grid is used to sample the Brillouin zone.

Optical properties are calculated by performing Kubo formula [32]: $\mathsf{\sigma }\left(\mathsf{\Omega }\right)=\frac{2e^2}{\mathsf{\Omega }}{\int }_{\mu -\mathsf{\Omega }}^{\mu }\frac{d\omega }{2\pi }{\int }^{}\frac{d^{2}k}{{\left(2\pi \right)}^2}·Tr\left[{\widehat{v}}_x\widehat{A}\left(k,\omega +\mathsf{\Omega }\right){\widehat{v}}_x\widehat{A}\left(k,\omega \right)\right]$, where $\mathsf{\Omega }$ is the energy of the incident light, $\widehat{A}\left(k,\omega \right)$ derives from Green’s function ${\widehat{G}}_{xx}\left(z\right)={\int }_{-\infty }^{\infty }d\omega {\widehat{A}}_{xx}\left(\omega \right)/\left[2\pi \left(z-\omega \right)\right]$, ${\widehat{G}}_{xx}\left(z\right)$ express from ${\widehat{G}}^{-1}\left(z\right)=z\widehat{I}-\widehat{H}$, $\widehat{I}$ is unit matrix, k integration over Brillouin zone and $\mu$ is the chemical potential set as 150 meV, $\hslash {\widehat{v}}_x=\partial \widehat{H}/\partial k_x$. This means that once we have modelled the material in inverted space and written out its Hamiltonian, the conductivity function can be calculated using the Kubo formula. Dielectric function is obtained by: $\epsilon \left(\omega \right)=1+\frac{i\sigma \left(\omega \right)}{{\epsilon }_0\omega }$. The optical properties of Ag₂Te are calculated by the Kubo formula in CASTEP software. The optical properties of bilayer graphene are calculated by directly performing the Kubo formula. In the calculation of dielectric functions, we also consider the influence of the Drude model while the energy is below 0.25 eV. For the Drude model, the dielectric function can be obtained by $\epsilon \left(\omega \right)=1-\frac{{\omega }_p{}^2}{{\omega }^2+i\gamma \omega }$, where ${\omega }_p=\sqrt{\frac{n{e}^2}{{\epsilon }_{0}m}}$. The $\omega$ is energy of light, ${\omega }_p$ is oscillation energy of free electrons, n is concentration of electrons, m is mass of electrons and $\gamma$ stands for scattering frequency, usually dependent on mobility. In the Drude model, carrier’s concentration and mobility determined the dielectric function. In our calculation of Ag₂Te, the concentration of electrons $n=1.16\times {10}^{18}{\mathrm{cm}}^{-3}$ [15]. According to this concentration of electrons, ${\omega }_p=0.25 \mathrm{eV}$. The mobility of electrons $\mu =\mathrm{22,000}{\mathrm{cm}}^2/\left(\mathrm{V}\mathrm{s}\right)$ [14]. It is close to the mobility of graphene. Therefore, we set the $\gamma$ of Ag₂Te as $\gamma =0.001 \mathrm{eV}$, which is the same order of graphene’s scattering frequency [5]. The dynamic reflectivity spectrum of Ag₂Te is obtained from the dielectric function by $R\left(\omega \right)={\left(\frac{\sqrt{\epsilon \left(\omega \right)}-1}{\sqrt{\epsilon \left(\omega \right)}+1}\right)}^2$.

3. Results and Discussion

3.1. Electronic Structure and Plasmonic Properties

Silver telluride material systems usually have two chemically stable stoichiometric crystals: AgTe and Ag₂Te [33,34]. AgTe has the space group Pmnb with an orthorhombic crystal lattice, while Ag₂Te exhibits a monoclinic phase ($\beta$) at room temperature, as shown in the crystal structure in Figure 1a. The band structure calculated by DFT is illustrated in Figure 1b. Analogous to graphene, the conduction band and valence band touch and form a dispersion-less Dirac point, making Ag₂Te exhibit a high electron mobility of more than 22,000 cm²/Vs [14].

Previous works have predicted that Ag₂Te is a good candidate for plasmon applications [11], which is attributed to the large number of massless free electrons provided by Dirac cones and the semimetal properties, similar to graphene and precious metals. The collective electromagnetic oscillation of free carriers is usually described by the Drude model, and it stems from an intraband transition, in which the number of free electrons dominates the frequency of the oscillation. As shown in Figure 2, the solid purple line represents the density of states (DOS) of Ag₂Te. The DOS is minimized at the charge neutrality point and rapidly increases away from the Dirac point, which means that the optical properties of Ag₂Te away from the Dirac cone are determined by the interband transition. Figure 2 depicts the contribution of the individual orbitals of each atom in Ag₂Te to the DOS. It can be clearly observed that the density of states of silver telluride at −5 eV comes from the contribution of the d-orbital of the Ag and the p-orbital of the Te. The s-orbitals of the Te atom provide the DOS for the inner valence electrons. The doped Co atom introduces DOS in the d orbitals near Dirac, which we analyse later in this section.

The distribution of electrons at different energy scales strongly influences the optical properties of materials. As shown in Figure 3a, the calculated dielectric function $\epsilon \left(\omega \right)$ clearly exhibits a Drude model character in the low-energy region. The real part of the dielectric function is negative below 0.1 eV, namely, plasmon resonance exists in the far-infrared region with wavelengths above 10$\mathsf{\mu }\mathrm{m}$. The dielectric function grows sharply below 0.1, while when the optical energy exceeds 0.1 eV, the real part of the dielectric function decreases, and the imaginary part of the dielectric function increases. This phenomenon demonstrates that other mechanisms offset the Drude model above 0.1 eV. This corresponds to traditional plasmon materials such as metals and graphene, as shown in Figure S1a, and the reason can be attributed to the interband transition. When the optical energy reaches 10 eV, the real part of the dielectric function becomes negative again. This result coincides with the peak at approximately −10 eV in the DOS, from which we can infer that the strong interband transition and inner valence electrons oscillation causes a negative real part of the dielectric function. The calculated dielectric function is consistent with the previous experimental fit [15], which indicates that our calculation method was applied correctly.

The calculated reflectivity spectrum is illustrated in the inset of Figure 3a. It shows that light is strongly reflected in the low energy region (at less than 0.1 eV), after decaying rapidly with increasing energy, then rises again and finally decreases slowly with increasing energy. The small valley at 0.1 eV denotes intraband transition absorption, which is common in precious metals and graphene [16]. This reflectivity spectrum is in good agreement with previous experimental results [15]. Compared to the previous reflectance spectra in ref [11], our calculations are in better agreement with the experiment results.

To analyze the plasmon resonance mode in Ag₂Te, we calculated the SPPs (Surface plasmon polaritons) dispersion at the interface of air and the Ag₂Te material. As we know, a transverse magnetic (TM) mode SPPs exists at the interface when the real part of the dielectric function is opposite in sign in the two media. In other words, a TM mode SPPs is excited at the interface of air and a material with a negative real part of the dielectric function. For precious metals and graphene, the real part of the dielectric function is always negative when the optical energy $\omega$ is less than the plasmon resonance frequency ${\omega }_p$. For the Ag₂Te material, the real part of the dielectric function is negative in the range from 10–20 eV. At the interface of air and Ag₂Te, the TM SPPs dispersion can be described by solving the plasmon loss function [35] $ℒ\left(k,\omega \right)\approx -\mathrm{Im}\left\{\frac{1}{1+i{k}^2{L}_{k,\omega }\frac{\sigma \left(\omega \right)}{\omega }}\right\}$, where $L_{q,\omega }=\frac{2\pi }{k\overline{\epsilon }\left(\omega \right)}$. In the loss function, the optical conductivity is derived by $\epsilon \left(\omega \right)=1+\frac{i\sigma \left(\omega \right)}{{\epsilon }_0\omega }$. The dielectric function $\epsilon \left(\omega \right)$ was produced by CASTEP. Therefore, the loss function $ℒ\left(k,\omega \right)$ can been calculated by giving the value of wavenumber k and energy $\omega$; the calculation result is illustrated in Figure 3b. The white dashed curve denotes the SPPs dispersion relationship, and the red dashed line denotes the dispersion of light in free space. In contrast to graphene and precious metals, the SPPs dispersion in Ag₂Te extends to the ultraviolet energy range, which coincides with the previous theoretical plasmon energy of 17.2 eV [11]. This plasmon resonance mode is very similar to the so-called plasmon $\mathsf{\gamma }$-mode at approximately 0.4 eV in AB stacked bilayer graphene [36], for which the interband transition of inner-shell valence electron dominates the optical properties and makes the real part of the dielectric function negative, as shown in Figure S1b. From the dispersion relation, we can infer that at wavenumber $k=1.5\times {10}^7 {\mathrm{m}}^{-1}$, plasmon resonance occurs at optical energy $\omega =20 \mathrm{eV}$. This plasmon wavenumber can be provided by periodic ribbons with width [37] $w=\frac{\pi }{k}$; for $k=3\times {10}^7 {\mathrm{m}}^{-1}$, $w=105 \mathrm{nm}$, which is consistent with the actual growth of Ag₂Te nanowires, as shown in Figure S2. SPPs can be excited in the UV band by arranging the nanowires in a fixed period, thus greatly improving the interaction between light and the Ag₂Te material.

3.2. Robust UV Optical Properties under Co Doping

In this section, we found that Co doping of Ag₂Te can effectively modulate its low-energy electronic structure and achieve magnetic doping of Ag₂Te while opening a band gap and maintaining its high-energy optical properties.

We perform the geometry optimization to the lattice of Ag₂Te doped with Co. The principle of geometry optimization is to find the lowest energy of the system (see Methods for details). Co doping in Ag₂Te is atomic substitutional doping, in which Co atoms replace Ag atoms. Considering the lattice symmetry of Ag₂Te, there are four kinds of Co substitutions in the Ag₂Te lattice; the positions replaced by Co atoms correspond to the positions of Ag1, Ag2, Ag5 and Ag6 in Figure S3a. We named each doping kind as types A, B, C and D. For each type, the enthalpy required to form a specific lattice structure is −31,427.94 eV, −31,428.53 eV, −31,427.99 eV and −31,426.74 eV, respectively. The differences in enthalpy are not negligible, indicating that only type B exists. The optimized geometry lattice constants are shown in

Table 1. Lattice constants after different types of doping.

	A (nm)	B (nm)	C (nm)	$\mathit{\alpha } \left({}^{\mathbf{°}}\right)$	$\mathit{\beta } \left({}^{\mathbf{°}}\right)$	$\mathit{\gamma } \left({}^{\mathbf{°}}\right)$
Original crystal	0.809	0.448	0.896	90.00	123.33	90.00
Type A doping	0.807	0.445	0.956	93.76	123.01	88.29
Type B doping	0.854	0.437	0.819	92.52	125.81	88.59
Type C doping	0.827	0.453	0.934	89.77	125.75	89.59
Type D doping	0.887	0.443	0.957	85.94	129.03	92.90

. Compared to the original lattice, the doped lattice is slightly displaced to ensure the lowest overall energy. The above four energies are for a doping concentration of 12.5% Co, while the energies for 6.25% and 25% doping are shown in Figure S3.

The DOS of Co is calculated in Figure 2. The doped Co atoms contribute the DOS from the d orbitals, which mainly affects the electronic structure near the Dirac point of Ag₂Te. The energy band structure of Co_0.13Ag_1.87Te are shown in Figure 4a, and the energy band structures for the other doping concentrations are shown in Figure S3b,c. Compared with the energy band structure of undoped Ag₂Te in Figure 1b, the energy band of Co_0.13Ag_1.87Te shows a significant band gap opening at the Dirac point. The highest point of the valence band is higher than the lowest point of the conduction band. Thus, the material can still be considered a half-metal, but the position of the energy valley is shifted. The disappearance of the Dirac cone of Co_0.13Ag_1.87Te is similar to the opening of the Dirac cone in the surface state in the Bi₂Se₃ system, with the difference being that Co doping of Ag₂Te shows that magnetic doping can also change the bulk topological properties [38,39]. Similar to graphene, the existence of a Dirac cone originates from the fourfold degeneracy under the combination of time-reversal symmetry and inversion symmetry. Magnetic doping, in contrast, breaks both the time-reversal symmetry and the inversion symmetry of the material, which leads to opening of a band gap and a change in the topological properties of the material [40,41].

Co doping also changes the optical properties of Ag₂Te. We should highlight that the opening of the Dirac cone leads to changes in the low-energy excitation of the material and a decreased number of Drude electrons. As embodied in the dielectric constant, the real part of the dielectric function of Co_0.13Ag_1.87Te below 0.1 eV is always positive, as shown in Figure 4b, while the real part of the dielectric function of undoped Ag₂Te ranges from negative to positive below 0.1 eV according to the above calculation. A negative real part of the dielectric function of a material is necessary to produce SPPs [10]. Therefore, the far-infrared response of Ag₂Te is affected by Co doping. There is no longer any plasmon resonance in the far-infrared waveband, and the reflectivity in the infrared range is greatly reduced (as shown in Figure 4c). In contrast, in the high-energy range, the electron transition in Ag₂Te is not significantly affected by Co doping. In Figure 4b, the real part of the dielectric function of Co_0.13Ag_1.87Te in the energy range of 8–20 eV is similar to that of undoped Ag₂Te, and they are both negative. This indicates that the UV plasmonic properties of the Ag₂Te material are robust under Co doping. As shown in Figure S3, the dielectric function and reflectivity of Ag₂Te have similar behaviors at higher and lower levels of doping, i.e., the low-energy optical transition is broken for both, but the interaction in the UV band remains.

The above results demonstrate that the low-energy excitation of Ag₂Te materials significantly depends on the Dirac cone, in which a gap is opened under Co magnetic doping, thus affecting the low-energy excitation and infrared properties of the materials. The influence of magnetic doping on the high-energy electron transition of the material is negligible, which indicates that the UV optical properties of the Ag₂Te material system are very stable for Co atom magnetic doping. This offers the possibility of changing the magnetic and semiconducting properties of the material without affecting the UV optical properties. The insensitivity of the high-energy UV properties of Ag₂Te to impurities also provides the possibility of low-cost and reliable material growth.

4. Conclusions

Plasmons have long been a hot topic of the nanophotonics field due to their ability to enhance light-matter interactions at tiny scales. The surface plasmon resonance of metallic materials is generally excited at visible and near-infrared wavelengths, while the surface plasmon of graphene acts at mid-infrared wavelengths. Ag₂Te, a new topological material system, provides a promising approach for realizing plasmon resonance in the UV spectrum because of its unique dielectric response properties. We investigated the optical properties and UV plasmonic properties of Ag₂Te materials through DFT calculations. The reflectivity spectrum is almost consistent with previous experiments, indicating that our study method is correct. We should highlight that under Co doping of Ag₂Te materials, magnetic doping opens the Dirac cone by breaking the time-reversal symmetry and inversion symmetry of the material, but the UV excitation of Ag₂Te materials remains stable, indicating that Ag₂Te is a versatile platform that can possess both magnetic and semiconducting properties while maintaining UV excitation. Our discovery not only reveals a novel material platform for robust UV plasmon resonance but also provides predictions of the doping properties of Ag₂Te materials.