Pressure-induced superconductivity in Li-Te electrides

PHYSICAL REVIEW B 104, 134505 (2021) Pressure-induced superconductivity in Li-Te electrides Xiaohua Zhang ,1,2Fei Li ,1Aitor Bergara,3,4,5,*and Guochun Yang1,2,† 1State Key Laboratory of Metastable Materials Science & Technology and Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University, Qinhuangdao 066004, China 2Centre for Advanced Optoelectronic Functional Materials Research and Key Laboratory for UV Light-Emitting Materials and Technology of Ministry of Education, Northeast Normal University, Changchun 130024, China 3Departamento de Física, Universidad del País Vasco-Euskal Herriko Unibertsitatea, UPV/EHU, 48080 Bilbao, Spain 4Donostia International Physics Center (DIPC), 20018 Donostia, Spain 5Centro de Física de Materiales CFM, Centro Mixto CSIC-UPV/EHU, 20018 Donostia, Spain (Received 2 August 2021; accepted 22 September 2021; published 5 October 2021) Electrides, which accommodate excess of electrons in lattice interstitials as anions, usually exhibit interesting properties and broad applications. Until now, most electrides, especially at high pressures, show semiconducting/insulating character arising from the strong localization of interstitial and orbital electrons. However, modulating their connectivity could turn them into metals and even superconductors. In this work, with the aid of first-principles particle swarm optimization, we have identified a series of pressure-induced Li-rich electrides in the Li-Te system, in which hollow Linpolyhedra accommodate the excess of electrons. With increasing Li content, these electrides undergo an interesting structural evolution. Meanwhile, the connection type of Linpolyhedra experiences transitions from vertexor edge sharing, to face sharing, leading to a diverse distribution and connectivity of interstitial electrons. All identified electrides exhibit anionic electrons-dominated metallicity. More interestingly, Li9Te, with the highest content of Li6octahedra, is superconducting with a critical temperature (Tc) of 10.2 K at 75 GPa, which is much higher than typical electrides (e.g., 12CaO ·7Al2O3,Ca 2N, and Y2C). Its superconductivity mainly originates from the coupling between hybridized electrons (anionic and atomic non-s-state ones) and Te-dominated phonons. DOI: 10.1103/PhysRevB.104.134505 I. INTRODUCTION Electrides are a relatively uncommon class of matter with electrons confined in lattice interstitials that behave as anions, which have recently attracted great attention [1,2]. Based on the topology of localized electrons, electrides can be identified as zero-dimensional (0D) cavities [3], 1D channels [4–6], 2D planes [7,8], and 3D bulk ones [2,9]. However, the concentration, distribution, and connectivity of interstitial electrons in the electrides have a great influence on their electronic properties. For example, as a representative of 0D electrides, 12CaO ·7Al2O3(C12A7 : e−) contains anionic electrons in the interconnected crystallographic cages [3]. With increasing the concentration of anionic electrons, more electrons occupy the free space inside the crystal lattice, inducing a transition from insulator to semiconductor, then to metal, and even superconductor [10,11]. A typical 2D electride can be exemplified by Ca2N, where the anionic electrons are loosely confined in the interlayer space at ambient pressure [7]. Under compression, electronic dimensionality is gradually reduced from 2D to 1D, and then to a 0D electride, resulting in a decrease in the electronic conductivity (e.g., under pressure it shows a transition from metal to semimetal, and then to semiconductor) [12]. On the other hand, *a.berg[email protected] †[email protected] electrides generally display fascinating properties dominated by interstitial electrons, such as a low work function [13,14], high catalytic activity [15,16], superconductivity [10,17], and magnetism [18,19], leading to a variety of applications including catalysts, superconductors, magnetic materials, electrode materials, and in electronic devices [15,20–22]. On the other hand, raising pressure has become an effective method to discover new electrides, especially for allotropes of alkali and alkaline-earth metals [23–26] and their compounds [2,27,28]. This is so because with increasing pressure, the enhancement of the orbital energy at interstitials is smaller than that of the atomic orbital, causing electrons to enter interstitial sites, which lowers their structural energy. Especially for s-block elements, for instance, Li [23], Na [24], K [29], Mg [26], and Al [30] form rich allotropes with an electride character, which are even insulating [25]. On the other hand, alkali metals have been found to be able to form diverse electrides with p-block elements, such as O [31], S [27], C [32], N[2], P [17], Cl [33], I [34], and even with inert gas elements at high pressures [35]. Notably, the pressure-induced Li6P electride shows a superconducting transition temperature (Tc) up to 39.3 K at 270 GPa. Such a high Tcarises mainly from the dumbbell-like connected interstitial electron states that induce a strong Fermi surface nesting and electron-phonon coupling (EPC) [17]. Recently, another interesting electride Li5Cwas predicted to have high Tcof 48.3 K at 210 GPa, in which 2D hexagonal anionic electron topology creates interconnected electronic channels in the lattice interstitials [32]. 2469-9950/2021/104(13)/134505(9) 134505-1 ©2021 American Physical Society ZHANG, LI, BERGARA, AND YANG PHYSICAL REVIEW B 104, 134505 (2021) Tellurium (Te), as the last nonmetallic element in the chalcogens, is isoelectronic to O and S, and shows a low electronegativity, similar to P and I [36]. More importantly, Te has been predicted to be able to form hydrogen-rich compounds, such as H4Te with a high Tcof 104 K at 170 GPa [37]. Considering the similarity of Li with H, the ability of Li forming electrides, and the effect of pressure on stabilizing new materials, it is expected that Li and Te are able to form novel Li-rich electrides under pressure. Herein, potential compounds with LixTe(x=2–12) stoichiometry have been extensively searched from 0 to 100 GPa with the aid of an advanced swarm structural search method. Besides the already known Li2Te, eight new Li-rich tellurides, Pm -3mLi3Te, I4/mmm Li3Te, Imma Li4Te, Cmmm Li5Te, P21/mLi7Te, C2/mLi9Te, C2/mLi10Te, and Cmcm Li12Te, have been predicted to be thermally and dynamically stable. All these Li-rich tellurides are metallic electrides, and present a diverse arrangement of interstitial electrons. More importantly, as Li content increases, superconductivity arises, and Tcgradually increases and peaks at 10.2 K in Li9Te at 75 GPa. They also exhibit a low work function, comparable to C12A7 : e−electride. II. COMPUTATIONAL DETAILS In order to identify thermodynamically stable structures of Li-Te compounds under pressure, structural prediction was implemented with the swarm-intelligence based CALYPSO program (Crystal structure AnaLYsis by Particle Swarm Optimization) [38,39], which can find the most stable structures just knowing the chemical composition [40–43]. We considered various stoichiometries of LixTe(x=2–12) at the selected pressures of 0, 25, 50, and 100 GPa. The details about the structural search method can be found in the Supplemental Material [44]. Structural optimizations and calculations of the electronic properties were carried out within the density-functional theory [45,46] as implemented in the Vienna Ab initio Simulation Pckage (VASP)[47]. Considering both accuracy and computational efficiency, the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA) [48,49] exchange and correlation functional was used. The scalar relativistic projector augmented wave (PAW) [50] pseudopotentials were adopted to describe electron-ion interactions, with 1s22s1and 5s25p4 valence electrons for Li and Te atoms, respectively. The reliability of adopted pseudopotentials for Li and Te is confirmed by the perfect fit of Birch-Murnaghan equation of states derived from PAW and full-potential linearized augmented plane-wave methods as implemented in WIEN2K(Fig. S0) [51]. The cutoff energy was set at 800 eV, and MonkhorstPack [52]k-point grids with a reciprocal space resolution of 2π×0.03 Å–1 in the Brillouin zone were selected to ensure that all enthalpy calculations converged to less than 1 meV per atom. The thermodynamical stability of each lithium telluride stoichiometry with respect to elemental Li and Te solids at each pressure can be evaluated by calculating the formation enthalpy as [53] H(LixTe)=[H(LixTe)−xH(Li)−H(Te)]/(x+1).(1) Here, H(LixTe), H(Li), and H(Te) are the enthalpies of the studied stoichiometry, elemental Li, and Te solids under the corresponding pressure, respectively. The dynamical stability can be determined by calculating phonon frequencies using the supercell finite displacement method [54] with the PHONOPY code [55]. Electron-phonon coupling (EPC) calculations are carried out with the density functional perturbation (linear response) theory as implemented in the QUANTUM ESPRESSO package [56]. The pseudopotential, kpoints, and energy cutoff for wave functions are tested to achieve a pressure consistent with the optimized results obtained with the VASP package, and a good total energy convergence of 0.01 eV/atom. The Tcof all the metallic Li-Te phases is estimated with the McMillanAllen-Dynes formula [57–59]. Details can be found in the Supplemental Material [44]. The work function ()ofametal is calculated considering a surface slab with a thickness of at least ten atoms. The vacuum distance is set to 20 Å, and a slab supercell is made with a,b>10 Å. The value is determined considering the difference between the vacuum potential and the Fermi level of the slab [13]. III. RESULTS AND DISCUSSION A. Phase stability Extensive structural searches are performed on various LixTe(x=2–12) compositions at 0 K and selected pressures of 0, 25, 50, and 100 GPa. The structure with the lowest enthalpy was used to evaluate the stability of different Li-Te compositions according to Eq. (1). The relative thermodynamic stability of the Li-Te compounds with various Li contents at different pressures is shown in the convex hull in Fig. 1(a). Thermally stable phases, represented with filled circles, lie on the global stability line, whereas compositions with hollow circles are metastable in terms of decomposition into other LixTe compounds or elemental Li and Te solids. The emerging stable phases with increasing pressure are highlighted in Fig. 1(a). Furthermore, all thermally stable phases are also dynamically stable, as the calculated phonon spectra do not present any imaginary frequency modes (Fig. S1). In order to determine the stable pressure range of predicted Li-Te compounds, their enthalpy differences are calculated with respect to adjacent stable compositions with a pressure interval of 5 GPa. The pressure-composition phase diagram is shown in Fig. 1(b). In addition to the already known stable antifluorite Li2Te (Fm-3mphase) at 0 GPa [64,65], a continuous phase transition is found from Fm-3mto Pnma at 4.8 GPa, then to the P63/mmc phase at 19.4 GPa, and finally to the P4/nmm structure at 96.5 GPa. The atomic arrangement and electronic bands are shown in Figs. S2 and S3, respectively. All three high-pressure phases of Li2Te are semiconductors with indirect gaps. For Li-rich compositions, two Li3Te phases emerge with increasing pressure: Pm-3mLi3Te is stable between 4 and 85.6 GPa, while I4/mmm Li3Te stabilizes above 85.9 GPa. Imma Li4Te and Cmcm Li5Te start to be stable above 34 and 40 GPa, respectively. For Li-richer compositions, P21/mLi7Te and C2/mLi9Te become stable in the pressure ranges of 28.5–85.6 GPa, and 16.7–64.1 GPa, 134505-2 PRESSURE-INDUCED SUPERCONDUCTIVITY IN Li-Te … PHYSICAL REVIEW B 104, 134505 (2021) FIG. 1. (a) Phase stabilities of various Li-Te compounds at 0, 25, 50, and 100 GPa. The Fm-3m,I-43d,andCmca-24 structures of elemental solid Li were used to calculate the formation enthalpies [60–62]. Elemental solid Te with phases I (P3121), V (Im-3m), VI (I4/mmm), and VII (Fm-3m) were used [63]. (b) Schematic illustration of the pressure stability region of Li-Te compounds. respectively. For C2/mLi10Te and Cmcm Li12Te, their stable pressures are above 82.6 and 35.6 GPa, respectively. Analyzing the interactions between atoms, the electron localization function (ELF) [66] in Fig. S4 indicates that all the stable Li-Te compounds show an electronic depletion near Li atoms and accumulation around Te atoms, revealing a charge transfer from Li to Te, associated with Li–Te ionic bonds. This can be attributed to the large electronegativity difference between Li (0.98) and Te (2.1) [67]. The transferred charge is shown in Table S1, and will be discussed later. Table S2 shows the distance between nearest-neighbor Li atoms (<2.5Å)for Li-rich LixTe (x=3, 4, 5, 7, 9, 10, and 12), which are much smaller than in the most stable body-centered cubic (bcc) Li (3.01 Å) at ambient pressure [68,69], demonstrating a metallic interaction between Li atoms. However, the distances between the nearest-neighbor Te atoms are much higher than that in elemental P3121 Te (2.89 Å) at ambient pressure. Therefore, ionic Li–Te bonds and metallic Li-Li interaction are responsible for the structural stability of Li-Te compounds. B. Crystal structure Figure 2presents the structures of Li-rich LixTe (x=3, 4, 5, 7, 9, 10, and 12) compounds, which exhibit a fairly similar structural characterization, despite having different composition and symmetry. In detail, both Pm-3mand I4/mmm Li3Te are composed of TeLi12 cuboctahedra but with distinct arrangements, causing different symmetries. Li4Te stabilizes into an orthorhombic structure [space group Imma,Fig.2(c)], in which the coordination of Te increases to 13-fold. As xin LixTe increases to 5, 7, and 9, their structures have Cmmm, P21/m, and C2/msymmetries [Fig. 2(d)–2(f)], respectively. In these three structures each Te atom has a 14-fold coordination, despite having different TeLi14 configurations. It is worth noting that although LixTe (x=3, 4, 5, 7, and 9) have different symmetries and basic structural units, all of them contain hollow Li6octahedra, which are surrounded by TeLimpolyhedra with different connection types (Table S3). With a further increase of the Li ratio, e.g., in C2/mLi10Te, the coordination numbers in TeLimand Linpolyhedra increase to 16 and 8 [Fig. 2(g)], respectively. However, in Cmcm Li12Te [Fig. 2(h)], the coordination of Te decreases to 14-fold. Meanwhile, the coexistence of Li6,Li 7, and Li8 polyhedra strengthens the interaction between Li atoms and stabilizes the structure. On the whole, all Li-rich tellurides are composed of interconnected TeLimand Linpolyhedra. The type of connection between TeLimand Linpolyhedra is summarized in Table S3, and discussed in detail below. Among them, Li9Te has the highest content of Li6octahedra (Table S1), and Li10Te has the largest Linpolyhedra (face-sharing Li8enneahedra). Compared to other Li-rich Li-S [27] and Li-I [34] compounds, the same two phases (Li3Te and Li5Te) are found in the Li-Te system, because Te has the same valence electrons as S and similar electronegativity to I. The TeLi14 unit in Li7Te and Li9Te is similar to those in P6/mmm Li5P[70] and R-3m H4Te [37]. C. Electride character The abundant Linpolyhedra provide a great possibility to accommodate additional electrons, forming electrides like other Li-rich compounds (e.g., Li4N[2], Li5P[70], Li6P[17], Li3S[27], Li6O[31], and Li5I[34]). As expected, all Li-rich LixTe show distinct localized interstitial electrons according to the ELF isosurfaces (Fig. S4), confirming their electride character. In order to give an idea of the distribution of these interstitial electrons, we plot the ELF maps of all the electrides in different planes (Fig. 3). In either Pm-3mor I4/mmm Li3Te, interstitial electrons are confined in the vertex-sharing Li6octahedra and distributed in (110) and (001) planes [Figs. 3(a) and 3(b)], forming 0D electrides. In Imma Li4Te, the interstitial electrons are also localized in the Li6octahedra, but relatively concentrated and clearly interconnected [Fig. 3(c)]. This is due to the lumped distribution of the Li6octahedra and the change of connection from vertexto face sharing (Table S3). Cmmm Li5Te contains interstitial electrons linked by the surrounding free-electron gas [Fig. 3(d)][71], which is weaker than in Li4Te, corresponding to edge-sharing Li6octahedra. For clarity, the schematic connectivity of Linpolyhedra in all Li-rich electrides is shown in Fig. S5. Therefore, the connection type between the polyhedra that host anionic electrons determines the connectivity of localized electrons and the 134505-3 ZHANG, LI, BERGARA, AND YANG PHYSICAL REVIEW B 104, 134505 (2021) FIG. 2. Structural features of stable Li-rich tellurides at high pressures. (a) Pm-3mLi3Te at 50 GPa, (b) I4/mmm Li3Te at 100 GPa, (c) Imma Li4Te at 50 GPa, (d) Cmmm Li5Te at 50 GPa, (e) P21/mLi7Te at 50 GPa, (f) C2/mLi9Te at 50 GPa, (g) C2/mLi10Te at 100 GPa, and (h) Cmcm Li12Te at 50 GPa. In all these structures, green and purple spheres represent Li and Te atoms, respectively. dimensionality of the electrides. A similar phenomenon is observed in metallic P63/mSr3CrN3and Ba3CrN3[6]. There are 1D channels made up of face-sharing (SrN)6or (BaN)6 polyhedra arranged along the caxis that accommodate anionic electrons (Fig. S6). R-3m Y2C[72,73] and Ca2N[7,74] contain 2D interstitial regions consisting of edge-sharing Y6 and Ca6octahedra in the ab plane, respectively, where anionic electrons are confined. Such high connectivity of anionic electron is in favor of the electronic conductivity. Interestingly, the anionic electrons in P21/mLi7Te and C2/mLi9Te show a similar distribution: both sunflowerand arc-shaped for them [Figs. 3(e) and 3(f)]. Their anionic electrons are still confined in the Li6octahedra, but the connection type between the Li6octahedra changes to coexistence of faceand edge sharing (Table S3). With further increasing the Li content, the configuration of Linpolyhedra becomes complex. As shown in Table S3 and Fig. S5, the coordination of the Linpolyhedra increases to eightfold in C2/mLi10Te, and six-, seven-, and eightfold in Cmcm Li12Te. The interstitial electrons exhibit a zigzaglike distribution in C2/mLi10Te [Fig. 3(g)], and Uand necklacelike ones in Cmcm Li12Te [Fig. 3(h)]. In general, Li and Te have a formal oxidation state of +1 and −2, respectively. Thus, these Li-Te electrides should have the following theoretical anionic electrons: one e−for Li3Te, two e−for Li4Te, and three e−for Li5Te per formula unit (f.u.), and so on. Based on this, we found that the amount of theoretical anionic electrons is closely associated with that of Li6octahedra: they turn out to be the same except for Li5Te (Table S1). In other words, about one electron could be transferred for each Li6octahedron. Consequently, Li9Te has the highest content of anionic electrons fully confined in Li6 octahedra. In addition, based on the amount of Li8enneahedra in the Li10Te lattice unit (8 in 2 f.u.), each Li8enneahedron might accommodate about two electrons. In order to verify the above assumptions, Bader charge analysis is used to study the charge transfer from Li to Te and lattice interstitials (Table S1). Following our expectations, the anionic electrons increase with the Li content, as observed in Li3Te : 0.25e−,Li 4Te : 0.94e−,Li 5Te : 1.28e−, Li7Te : 2.62e−, and Li9Te : 3.67e–at 50 GPa, showing the highest concentration of anionic electrons in Li9Te. In addition, the average anionic electrons in the Li8enneahedra of Li10Te is almost double that in the Li6octahedra in other Li-Te 134505-4 PRESSURE-INDUCED SUPERCONDUCTIVITY IN Li-Te … PHYSICAL REVIEW B 104, 134505 (2021) FIG. 3. ELF maps of Li-rich tellurides at high pressure. (a) Pm-3mLi3Te at 50 GPa in the (110) plane, (b) I4/mmm Li3Te at 100 GPa in the (001) plane, (c) Imma Li4Te at 50 GPa in the (010) plane, (d) Cmmm Li5Te at 50 GPa in the (010) (left) and (001) (right) planes, (e) P21/mLi7Te at 50 GPa in (hkl =13.978, 1, 58.75) (left) and (hkl =1.276, 0, 1) (right) planes, (f) C2/mLi9Te at 50 GPa in (hkl =−1, 0, 2.089) (left) and (001) planes, (g) C2/mLi10Te at 100 GPa in the (101) plane, and (h) Cmcm Li12Te at 50 GPa in (hkl =1.853, 1, 0) (above) and (100) (below) planes. electrides (Table S1). The presence of slightly less anionic electrons in Li10Te (Li10Te : 3.54e–at 100 GPa) than in Li9Te is mainly attributed to its higher pressure. The average charge lost by each Li atom is in the range of 0.67–0.77 e−. Each Te atom can gain more than two electrons donated by Li atoms, especially in compounds with high Li content, indicating negative oxidation states of Te beyond −2. These extra electrons can occupy Te 5dorbitals, as demonstrated by the projected density of states (PDOS). A similar phenomenon has been reported by Miao’s group [34]intheLi 5I electride. Overall, the charge localized in Linpolyhedra is lower than the theoretical anionic electrons, which is mainly attributed to Bader charge analysis underestimating the amount of charge transfer, as observed in typical ionic compounds, e.g., CsF [41]. In short, the anionic electrons in these Li-Te electrides are closely related to the Li content. For LixTe (x=3, 4, 5, 7, and 9), the anionic electrons are localized in the Li6octahedra, and their connectivity is gradually enhanced with the Li content, due to the transition of Li6octahedra from vertex-, edge-, to face sharing. For Li10Te and Li12Te, the Linpolyhedra accommodating anionic electrons change significantly, leading to a more diverse and complex distribution of anionic electrons. D. Electronic property and superconductivity Considering that electrides can exhibit elusory electronic conductivity, such as a semiconducting character in highpressure Li (C2 and Aba2) [75], Ca2N-II, Sr2N-II, and Ba2N-IV phases [76], as well as superconductivity, as in Li5C [32] and Ca3S[77], we subsequently explored the electronic properties of pressure-induced Li-Te electrides. Unexpectedly, all the Li-Te electrides are metallic (Fig. S7) from the electronic band structures based on the GGA-PBE functional. As representative cases, the electronic band structures of Pm-3mLi3Te, C2/mLi9Te, and C2/mLi10Te are also calculated with the revised Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE06), verifying that they are metallic (Fig. S8). The PDOS obviously indicates that the interstitial electrons make the main contribution at the Fermi level (Fig. S9), which can be attributed to the good connectivity between anionic electrons [17]. Moreover, there appears strong overlap between anionic and atomic non-s-state (Li 2p,Te5p, and Te 5d) electrons. To further confirm this, we have built a hypothetical system by removing seven electrons from Li9Te, [Li9Te]7+. The anionic electrons in ELF are completely absent, which is accompanied by the absence of Fermi surfaces corresponding to the bands crossing the Fermi level of Li9Te [Fig. S10]. Interestingly, Li9Te, with the highest content of Li6octahedra accommodating anionic electrons, not only exhibits a strong hybridization between anionic electrons and atomic orbital electrons (Li 2p,Te5p, and Te 5d), but also has two remarkable van Hove singularities (vHs) dominated by anionic electrons near the Fermi level [Fig. 4(a)]. These features made us explore its superconductivity based on the BardeenCooper-Schrieffer theory [78] and the McMillan-Allen-Dynes equation [79], yielding a Tcof 4.01 K with an EPC parameter (λ) of 0.50 at 50 GPa using a Coulomb pseudopotential of μ∗=0.1 (Table I). Eliashberg spectral function and phonon density of states (PHDOS) show that Te-dominated lowfrequency phonons (0–6.16 THz) contribute ∼38%, and Li vibrations make the main contribution of ∼62% in a wide frequency range (6.16-28 THz) [Figs. 4(b) and 4(c)]. The combination of the PDOS composition at the Fermi level and the contribution of λindicates that the superconductivity of Li9Te is dominated by the coupling between hybridized anionic/atomic non-s-state (Li 2p,Te5p, and Te 5d) electrons and Li-dominated phonons [80]. Subsequently, we explore the pressure-dependent superconductivity of Li9Te at 25, 50, 65, and 75 GPa. As shown in Fig. 4(d),Tcincreases with pressure and reaches 10.2 K at 75 GPa, which is larger than that in typical electrides 134505-5 ZHANG, LI, BERGARA, AND YANG PHYSICAL REVIEW B 104, 134505 (2021) FIG. 4. (a) PDOS of C2/mLi9Te at 50 GPa. PHDOS, Eliashberg spectral function, and frequency-dependent electron-phonon coupling parameters λ(ω)of(b)C2/mLi9Te at 50 GPa and (e) C2/mLi10Te at 100 GPa. (c) The calculated phonon dispersion curves of C2/mLi9Te at 75 GPa. The area of each circle is proportional to the partial electron-phonon coupling, λq,v.(d) Pressure-dependent λ(ω), ωlog,andTcof C2/mLi9Te. (f) The work function of C2/mLi10Te at 100 GPa. The Fermi level is set to zero. The inset displays the corresponding slab with a thickness of at least ten atoms. (e.g., 0.4 K for C12A7 : e−[10], 4.7 K for Ca2N[81], and 0.33–0.59 K for Y2C[82,83]), and comparable to 9.4 K for Nb5Ir3[84]. On the other hand, the pressure-induced increase of Tcshows the same trend as in other electrides C12A7 : e−[85], Ca3Si [86], and Li5C[32], but is opposite to Li6P [17]. Analyzing the pressure dependence of λand the logarithmic average phonon frequency (ωlog), it is apparent that pressure-induced increase of Tcin Li9Te is dominated by the enhancement of λ[Fig. 4(d)]. ωlog shows a smooth trend to first increase and then decrease with pressure, meaning it has a little influence on the Tcevolution of Li9Te. The dominance of λin Tcis very similar to that of the 1D electride Ca3Si [86]. It should be noted that Li9Te is dynamically stable and thermodynamically metastable, with a decomposition enthalpy of only 2.31 meV/atom with respect to Li7Te and Li12Te at 75 GPa. However, it is within the range (50 meV/atom) for experimental synthesis [87]. We now explore the origin of pressure-induced increase of λ. With increasing pressure, the PDOS of anionic electrons at the Fermi level decreases slightly, with an associated small increase of Li 2p,Te5p, and Te 5dcontributions (Fig. S11). This indicates a potential charge transfer from lattice interstitials to these atomic orbitals and, therefore, a stronger interaction between anionic and non-s-state atomic electrons, is expected, which is also confirmed by the Bader charge analysis (Table S4). On the other hand, acoustic branches in the phonon spectra soften with pressure (Fig. S12), which is also associated with the promotion of λand superconductivity, as it is observed in some superconducting hydrides [88–90]. Correspondingly, the Te’s contribution to the total λgradually increases from 35.6% at 25 GPa, to 38.0% at 50 GPa, to 47.0% at 65 GPa, and to 58.2% at 75 GPa (Table S5). Therefore, pressure-induced enhancement of electron hybridization and phonon softening lead to the increasing of λwith pressure. In addition, through electronor hole doping, the Tcvalue is also expected to be enhanced by shifting the Fermi level to adjacent vHs, as shown in H3S[91]. Li10Te, with the largest cavity unit (face-sharing Li8enneahedra), is also expected to be a high-Tcsuperconducting electride. However, unlike Li9Te, the lack of vHs and the low PDOS contribution at the Fermi level [Fig. S9(g)] as well as feeble phonon softening [Fig. S1(j)] lead to relatively weak EPC with λ=0.48 in Li10Te [Fig. 4(e)], corresponding to Tcof ∼4 K at 100 GPa. Te-dominated phonons contribute 40.8% to the total λin the frequency range of 0–6.7 THz, and Li atom contributes 59.2% between 6.7 and 30 THz, which is in contrast with Li9Te. Furthermore, other Li-Te electrides exhibit much lower Tc values (<1 K) than Li9Te and Li10Te (Table I), which can be attributed to that the low concentration and isolated anionic electrons associated with the low content of Li induce a weaker EPC. E. Low work function High interstitial electronic concentrations (Ne) and low work functions are two fascinating properties of electrides. TABLE I. The EPC parameter (λ), ωlog (K), Tc, interstitial electron concentration (Ne) of Li-rich tellurides, and the work function ()on different slabs. Work function (eV) Phase Pressure(GPa) λω log (K) Tc(K) Ne(×1022 cm–3) (100) (010) (001) Pm-3mLi3Te 50 0.15 439.69 0.00 0.59 4.13 4.13 4.13 Imma Li4Te 50 0.25 428.22 0.02 1.89 3.80 3.83 2.83 Cmmm Li5Te 50 0.24 427.90 0.01 2.24 3.93 3.55 4.34 P21/mLi7Te 50 0.32 450.35 0.43 3.54 3.69 3.79 4.03 C2/mLi9Te 50 0.50 333.16 4.01 4.04 3.65 3.82 4.05 C2/mLi10Te 100 0.48 395.15 4.00 4.66 3.74 4.44 2.95 134505-6 PRESSURE-INDUCED SUPERCONDUCTIVITY IN Li-Te … PHYSICAL REVIEW B 104, 134505 (2021) For instance, C12A7 : e−shows a high Neof 2.33 × 1021 cm−3, and a low work function of 2.4 eV [14], leading to important applications such as catalysts and electron field emitters [20]. On the other hand, the low-dimensional localized electrons in the interstitial voids of the electrides easily lead to a low work function [2]. Table Ishows the calculated interstitial electron concentration (Ne) based on the Bader charge analysis, and the work function of Li-rich electrides for a slab with a thickness of ten atoms in different directions. Most of Li-rich tellurides show a Nehigher than in C12A7 : e−and Ca2N(1.33 ×1022 cm–3). More importantly, their work function values are lower than that of elemental Al (4.28 eV). Specifically, the work function of C2/mLi10Te is as low as 2.95 eV in the (001) direction [Fig. 4(f)], and that of Imma Li4Te even reaches 2.83 eV (Table I). Such a low work function is comparable with the R-3m Y2C electride (2.9 eV), [8] and the Li metal (2.9 eV), [93] and is much lower than Y5Si3(3.5 eV), [92] which is an excellent catalyst for ammonia synthesis. Therefore, high interstitial electron concentrations and low work functions may endow Li-rich tellurides with potential applications, such as in catalysis and electric devices. IV. CONCLUSION In summary, we have searched pressure-induced Li-rich tellurides (LixTe, x=2–12) under pressure up to 100 GPa by first-principles calculations. In addition to reproducing the already known Li2Te compound, we have found eight stable Li-rich tellurides. Although presenting different symmetries, they all consist of interconnected TeLimand Lin polyhedra. The hollow Linpolyhedra can accommodate extra electrons, leading to the formation of electrides. The distribution of interstitial electrons depends on the coordination and connection type of the Linpolyhedra, and becomes more diverse and complex with increasing the Li content. Interestingly, all Li-rich electrides are metallic, even for Pm-3mand I4/mmm Li3Te with weakly interconnected anionic electrons. Most of them are superconducting. Li9Te and Li10Te have a much higher Tcthan the others, due to a high content of Li6 octahedra in the former and a large cavity unit (Li8enneahedra) in the latter. In addition, Li-rich tellurides exhibit a high interstitial electron concentration, and a low work function. Our work presents members of pressure-induced electrides with superconductivity and a low work function. ACKNOWLEDGMENTS The authors acknowledge the funding support from the Natural Science Foundation of China under Grants No. 21873017 and No. 21573037, the Postdoctoral Science Foundation of China under Grant No. 2013M541283, the Natural Science Foundation of Jilin Province (Grant No. 20190201231JC), and the Natural Science Foundation of Hebei Province (Grant No. B2021203030). The work was carried out at National Supercomputer Center in Tianjin, and the calculations were performed on TianHe-1 (A). A.B. acknowledges financial support from the Spanish Ministry of Science and Innovation (Grant No. PID2019-105488GB-I00). The authors declare no competing financial interest. [1] J. L. Dye, Science 301, 607 (2003). [2] Y. Tsuji, P. L. V. K. Dasari, S. F. Elatresh, R. Hoffmann, and N. 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