Novel functional materials have provided the basis for many recent developments in science and technology, and among these materials, electrides are an emerging group with rich physical and chemical properties. Electrides constitute a unique class of ionic compounds, with their excess electrons behaving as anions.1 Owing to their distinct crystal and electronic structures, electrides have a wide range of potential applications as catalysts,2 components of electronic devices,3 magnetic materials,4 and battery electrodes.5 In addition, recent research has predicted an abnormal splitting of longitudinal and transverse acoustic modes (LA–TA splitting) in electrides.6 Exploitation of this phenomenon could lead to further, unprecedented applications of electrides. The organic electrides such as Cs⁺(18-crown-6)₂e⁻, which were the first to be discovered, are usually characterized by poor thermal stability and sensitivity to air and water, which limits their practical applications.7 In 2003, Matsuishi et al.8 succeeded in synthesizing the first inorganic electride, [Ca₂₄Al₂₈O₆₄]⁴⁺ (4e⁻) (C12A7:e⁻), which can be stabilized at room temperature and has highly localized anionic electrons in cage-like interstitial voids in its lattice.9 Subsequently, electrides with two-dimensional layered voids (e.g., Ca₂N10 and Y₂C11) and one-dimensional tubular voids (e.g., [La₈Sr₂(SiO₄)₆]⁴⁺:4e⁻12 and Y₅Si₃13) were discovered. According to the interstitial voids and the distribution of interstitial electrons, electrides are categorized as zero-dimensional (0D), one-dimensional (1D), and two-dimensional (2D).14 In addition, some alkali metals, alkaline earth metals, and compounds containing these elements can also exhibit electride properties under high pressure and are referred to as high-pressure electrides (HPEs). Examples include Na₉B,15 Na-hP4,16,17 and Li₆C.18

Semiconducting electrides have a wide range of applications in infrared (IR) photodetectors, hydrogen storage, and fluorine ion battery electrodes, and they have attracted much research interest in recent years.21 The interstitial electrons are dominantly distributed around the Fermi level, which can significantly influence the electronic structure of these electrides. Three representative classes of semiconducting electrides are shown in Fig. 1. Under pressure, the properties of most of the semiconducting electrides are induced by the loosely bound nature of the interstitial electrons, for example, the metal–semiconductor transitions in Ca₂N,22 Li,23 Na,17 and Na₂He.19 Under ambient conditions, some low-dimensional (0D or 1D) electrides with a high electronegativity difference E_diff, such as Y₂Cl₃20 and C12A7:e⁻,24,25 can also exhibit semiconducting properties. In these electrides, the typical ionic bonding character and low-dimensional interstitial electrons give rise to highly localized energy bands near the Fermi level, separating occupied and unoccupied states. In 2022, McRae et al.21 revealed a unique semiconducting mechanism in 2D electrides, namely, Sc₂C and Al₂C. A higher electronegativity of the cation can enhance the strength of hybridization between interstitial electrons and cation atoms, producing semiconducting properties.

The interstitial electrons can act as ions and form magnetic centers.26 The extremely low work function and unique magnetic properties of magnetic electrides make them promising as spin injection materials and for spintronic device applications.4 Numerous magnetic electrides have been explored so far, such as Y₂C,27 Gd₂C,26 YCl,20 Ba₃MnN₃,4 and Nd₅Pb₃.28 Similar to the typical Mott insulators MnO29 and LaTiO₃,30 magnetic electrides with unpaired interstitial electrons can also exhibit Mott-insulating properties. In 2018, Lu et al. reported that α- and β-Yb₅Sb₃ are Mott-insulating electrides, similar to Sr₅P₃.31,32 However, there are a few known examples of Mott insulator electrides. The interstitial electrons can hybridize with the d/f orbitals of the surrounding real atoms, but unfortunately the influence of this hybridization interaction on the strong correlation effect remains elusive. Among 1D electrides, the Mn₅Si₃ structure represents one of the most common structural types.33,34 To date, at least 87 electrides with this type of structure have been reported in the literature (see Fig. 1), and most of them have been experimentally synthesized.35–37 The low-dimensional nature of the Mn₅Si₃ structure and the abundant number of electrides that possess it provides a broad platform for the search for new Mott insulators.

In the work reported in this article, we investigated a series of Mott-insulating electrides Ae₅X₃ (Ae = Ca, Sr, and Ba; X = As and Sb), all of which have been synthesized experimentally and characterized as potential 1D electrides.4 These materials crystallize in the Mn₅Si₃ configuration with a large interstitial space surrounded by Ae₆ octahedrons, and the anionic electrons are localized in a 1D tubular lattice interstitial void. Considering the formal oxidation states of Ae²⁺ and X³⁻, one extra electron is trapped in each Ae₆ octahedron and arranged in the antiferromagnetic (AFM) configuration. The strong correlation effect between the interstitial electrons induces spin splitting of the energy bands near the Fermi levels, resulting in a greater value of the bandgap (∼0.30 eV). Ca₅As₃, Sr₅As₃, and Sr₅Sb₃ are spin-gapped Mott insulators, similar to Zn(tmdt)₂,38 oxide perovskites,39 and β-Yb₅Sb₃.40 The strong correlation effect between the interstitial electrons can be adjusted through strain–stress and high pressure. The results reveal a great potential of Ae₅X₃ for a wide range of practical applications.

The structures of Ae₅X₃ were obtained from the Inorganic Crystal Structure Database (ICSD).41 First-principles calculations were performed using density functional theory (DFT) in the Vienna Ab initio Simulation Package (VASP)42 for structural optimization43 and electronic structure calculations of Ae₅X₃. Electron exchange-correlation interactions were taken into account using the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE)44 exchange-correlation functional and the projected-augmented plane-wave (PAW) method.45 The plane-wave cutoff energy was set to 500 eV, and the Monkhorst–Pack method46 was used to delineate the Brillouin zone with a K-point grid spacing of 2π × 0.03 Å⁻¹. Spin-polarized calculations were performed by applying an initial magnetic bias on Ae atoms around the voids (4d site). We separately calculated the different AFM and ferromagnetic (FM) settings of Ae₅X₃ and found that the lowest energy was achieved with AFM. The calculated spin polarization energy ΔE of Ae₅X₃ with AFM or FM configuration can be expressed as follows:$$\mathrm{\Delta }E=E_{\text{AFM/FM}}-E_{\text{NM}},$$(1)where E_AFM/FM is the energy of Ae₅X₃ with AFM or FM configuration, and E_NM is the energy of Ae₅X₃ in the nonmagnetic state.

Owing to the more complex space of d/f electron orbitals and the susceptibility to spin-polarized leaps, strongly correlated electronic systems are corrected by the DFT + U method to account for the Coulomb repulsion between the spin electrons.47,48 Although the Hubbard U cannot act directly on the anionic electrons, it can be used to correct the system effectively by acting on the surrounding Ae atoms.49 Lu et al.32 investigated the bandgap of α-Yb₅Sb₃ by applying Coulomb repulsion (Hubbard U) to the Yb_d orbital and found that the system was well described at U = 5 eV. In the present work, different Hubbard U values (3 and 5 eV) were applied to the Ae_d orbital (4d site). The hybrid density functional HSE06 was also tested to correct the structure and electronic structure with a mixing parameter of 25% and a screening parameter of 0.2.31

Figure 2(a) shows the crystal structures of Ae₅X₃ (Ae = Ca, Sr, and Ba; X = As and Sb) with the hexagonal Mn₅Si₃ configuration (P6₃/mcm), with metal Ae atoms occupying the Wyckoff 4d and 6g sites.13 Each Ae atom at the 4d site is coordinated by six X atoms in a linear arrangement along the c direction, and the Ae atoms at the 6g site form the face-sharing Ae₆ octahedron, resulting in a 1D tubular interstitial space along the c axis. It should be noted that this structural feature is common in 1D electrides, such as Sc₅P₃,50 Ca₅Pb₃,36 and Na₃S.51 Two prototypes are usually reported for A₅B₃ electrides, namely, the Mn₅Si₃ configuration mentioned above and the β-Yb₅Sb₃ configuration.32 The β-Yb₅Sb₃ phase crystallizes in an orthorhombic structure (Pnma), with cationic atoms forming 0D voids in a tetrahedral cage; examples include Sr₅Bi₃,52 Yb₅Bi₃,53 and Ca₅Sb₃.54

To investigate the structural preferences of A₅B₃-type compounds, we analyze in detail the structures of A₅B₃-type compounds from the literature. Figure 2(b) shows structural prototypes of A₅B₃ compounds as a function of the radius ratio r_M/r_X and the electronegativity difference E_diff. Here, r_M is the ionic radius of a cation atom with +2 state and Ⅵ coordination, and r_X is the ionic radius of an anion atom with −3 state and Ⅵ coordination. It is found that when r_M/r_X < 1.1, A₅B₃ crystallizes in the β-Yb₅Sb₃ structure (e.g., Ca₅Bi₃55 and Yb₅Bi₃53); in the range 1.1 < r_M/r_X < 1.64, β-Yb₅Sb₃ and Mn₅Si₃ structures coexist (e.g., Yb₅Sb₃32 and Ca₅Sb₃54); when r_M/r_X > 1.64, A₅B₃ prefers the Mn₅Si₃ configuration (e.g., Ba₅Sb₃52 and Eu₅As₃53). Despite the fact that only the Mn₅Si₃ configurations of Ba₅Bi₃ and Dy₅Sb₃ have been reported experimentally, their r_M/r_X values suggest that they may also have a β-Yb₅Sb₃ phase, which might be obtained through high-temperature treatment of Mn₅Si₃ type phases.32 In 2017, through a combination of structural search and experimental validation, Wang et al.31 successfully synthesized a new 1D electride, Sr₅P₃, which crystallizes in the Mn₅Si₃ configuration (r_M/r_X = 2.68) and was shown to be a Mott insulator. The Sc₅P₃ was also theoretically reported to adopt the Mn₅Si₃ structure with r_M/r_X > 1.70 (r_Sc in the +3 state was used here).50 Furthermore, we find that the crystallization type of A₅B₃ is unrelated to E_diff. Considering the stability of Ae₅X₃ in the Mn₅Si₃ configuration, we only discuss Mn₅Si₃-type Ae₅X₃ in this work, although the results can also apply to β-Yb₅Sb₃-type Ae₅X₃.

The formation of anionic electrons is closely related to the volume of the lattice voids. Larger voids usually induce less orbital hybridization between anionic electrons and d orbitals of neighboring atoms.20Figure 2(c) shows the volume of the Ae₆ octahedron along with the Ae ionic radius, and we find that all Ae₆ octahedrons in Ae₅X₃ possess much larger voids (>25 Å³) than those in Sc-based and Y-based electrides,20,50 and thus can hold excess electrons in Ae₅X₃. The volume of the Ae₆ octahedron increases linearly with increasing radius of the Ae ion. In addition, the volume of the Ae₆ octahedron decreases as the electronegativity of the X anion increases. This latter phenomenon is due mainly to the higher electronegativity of X endowing Ae with a lower ionic radius, resulting in a larger lattice void. The volume of the Ba₆ octahedron in Ba₅Sb₃ is the largest octahedron volume among the various Ae₅X₃-type compounds.

To determine the magnetic ground states of these materials, we calculate different magnetic arrangements by applying an initial magnetic bias to different Ae atoms surrounding the voids. The energy differences between the AFM and FM configurations of Ae₅X₃ at U = 0, 3, and 5 eV (Fig. S1, supplementary material) indicate that the most stable magnetic configuration of Ae₅X₃ is the AFM one. Figure 2(d) shows the spin polarization energy ΔE of Ae₅X₃ with AFM configuration, corrected by the Coulomb repulsion between the electrons using U = 0, 3, and 5 eV, respectively. The negative spin polarization energies of Ae₅X₃ with the AFM configuration (U = 5 eV) suggest an energy preference for this configuration. We illustrate the calculations of Ba₅Sb₃, which has been experimentally reported to be an AFM with a bandgap of 0.3 eV.56 When U = 0 or 3 eV, the nonmagnetic (NM) properties of Ba₅Sb₃ are more stable and the material exhibits a metallic character. The calculated result at U = 5 eV reveals a large negative value of ΔE, suggesting an AFM state, and agreeing well with the experimental results. It has been reported that strong orbital hybridization exists in intermetallic electrides Yb₅Sb₃ (in both α and β phases), and the interstitial electrons project onto the other energy bands.32 As shown in Fig. 2(d), all the Ae₅X₃-type compounds discussed here possess lower spin polarization energies at U = 5 eV compared with the intermetallic electride α-Yb₅Sb₃. This suggests that the bonding characteristics of interstitial electrons have a significant influence on the strong correlation effect.

The electron localization function (ELF) has been widely used to investigate bonding characters and lone pairs, and it is able to effectively visualize interstitial electrons.57 On the basis of formal charge states (e.g., Ba²⁺ and Sb³⁻), the presence of one excess electron and large lattice voids in Ae₅X₃ satisfies the criterion for an electride. The 3D ELF map of Ba₅Sb₃ is shown in Fig. 3(a), from which it can be observed that the anionic electrons are distributed in the tubular lattice interstitial voids, exhibiting a quasi-1D electride character. The 2D ELF maps calculated with and without spin polarization for Ba₅Sb₃ compared with those for the intermetallic electride α-Yb₅Sb₃ are shown in Fig. 3(b). When the spin polarization is not included, the half-filled interstitial electrons are linearly distributed along the channel voids, forming a 1D electron gas (left). The strong orbital hybridization in the intermetallic electride α-Yb₅Sb₃ induces delocalization of the interstitial electrons. In the Mn₅Si₃-type structure_, the centers of different Ae₆ octahedrons are equivalent and share the same energy level. According to the Pauli exclusion principle and the Hubbard model, the nearest half-filled electrons prefer an AFM configuration.47,48 As in a traditional strongly correlated system, an energy penalty (U > 0 eV) needs to be imposed when the interstitial electrons transfer to neighboring lattice voids. Consequently, the nearest spin-up and spin-down electrons will avoid being at the same lattice site. This property causes adjacent interstitial electrons to form highly localized magnetic centers [Fig. 3(b), right side]. Compared with α-Yb₅Sb₃, the interstitial electrons are more localized in Ba₅Sb₃, suggesting a weaker orbital hybridization between the half-filled interstitial electrons and the surrounding atoms, and inducing a pronounced strong correlation effect. Given that the interstitial electrons are dominantly distributed around the Fermi level, the electron localization in Ae₅X₃ will have a significant influence on the electronic structure, resulting in a wider bandgap.

The spin-charge density of Ba₅Sb₃ is displayed in Fig. 3(c). Although the initial magnetic bias is applied to the Ae 4d site, the spin-charge density around the Ae 4d site is negligible. The magnetic moment originates mainly from the interstitial electrons with an AFM spin arrangement, and the highest value of the spin-charge density is 0.0043 bohr³ in Ba₅Sb₃. The distribution of spin-polarized interstitial electrons suggests that Ae₅X₃ should be viewed as potential 0D electrides. These results further confirm the validity of altering the basis sets of surrounding atoms to provide an appropriate description of the electronic structures of interstitial electrons. Figure 3(d) shows the maximum values of spin-charge density in the voids of Ae₅X₃ compared with α-Yb₅Sb₃. The Ae₅As₃ possess relatively larger values of spin-charge density [Fig. 3(d)] and lower spin polarization energies [Fig. 2(d)] than the Ae₅Sb₃ and α-Yb₅Sb₃. These results are consistent with the ELF analysis, which implies that high ionic bonding strength can enhance the strong correlation effect.

Both the Coulomb interaction correction and hybrid density functionals have been widely used to calculate the electronic structure of Mott insulator.31,48 To further investigate the effect of the calculation method on the electronic structure of Ae₅X₃, we take Ba₅Sb₃ as an illustrative example in the following discussion. Figures 4(a)–4(d) show the spin-polarized band structures of Ba₅Sb₃ calculated with the HSE06 hybrid functional and with Hubbard U = 0, 3, and 5 eV, respectively. The weighted band structure and partial density of states (Fig. S2, supplementary material) of Ba₅Sb₃ (U = 0 eV) reveal that the interstitial electrons form separate bands and that only a minimal number of electrons are projected to other bands, suggesting that the orbital hybridization between the half-filled interstitial electrons and the surrounding atoms is extremely weak. Since the dominant contribution to the energy bands crossing the Fermi level is from interstitial electrons, these can be regarded as “interstitial bands.”20 The band structures of Ba₅Sb₃ calculated with HSE06, U = 0 eV, and U = 3 eV exhibit a similar character, with half-filled and spin-degenerate “interstitial bands” crossing the Fermi level. In the case of the calculation with U = 5 eV, the energy bands of core electrons remain roughly the same, but the degenerate “interstitial bands” are split and an indirect bandgap of 0.27 eV is opened at the Fermi level, which coincides well with experimental results. Therefore, the semiconducting behavior should be primarily attributed to the Coulomb interactions of the interstitial electrons. Other band structures of Ae₅X₃ are plotted in Figs. S3 and S4 (supplementary material). It is noteworthy that Ca₅As₃, Sr₅As₃, and Sr₅Sb₃ are spin-gapped Mott insulators, and similar phenomena can also be observed in the molecular material Zn(tmdt)₂,38 oxide perovskites,39 NiO,29 and β-Yb₅Sb₃.40 The experimental and calculated bandgaps of Ae₅X₃ are shown in Table I in comparison with Sr₅P₃ and Yb₅Sb₃. The bandgaps of Ae₅X₃ are close to 0.30 eV, except for Ca₅Sb₃ (0.07 eV), about two or three times those of α-Yb₅Sb₃ (0.14 eV)32 and Sr₅P₃ (0.10 eV)31 reported previously. On the other hand, the relatively strong correction effects in Ae₅As₃ endow them with higher bandgaps.

To further uncover the formation mechanism of Mott insulators in Ae₅X₃, we calculated the weighted band structure of interstitial electrons in the nearest Ae₆ octahedron sites A [Figs. 5(a) and 5(c)] and B [Figs. 5(b) and 5(c)] in Ba₅Sb₃. As discussed above [Fig. 4(b)], the energy bands near the Fermi level of Ba₅Sb₃ are spin-degenerate at A–H and L–H when the Coulomb U is not considered When the Coulomb interactions of interstitial electrons are applied with U = 5 eV, the interstitial electrons in site A [Figs. 5(a) and 5(c)] are spin-split, with the spin-up electrons (unoccupied states) lying above the Fermi level and the spin-down (occupied states) electrons lying below the Fermi level. In comparison, the interstitial electrons in site B [Figs. 5(b) and 5(c)] display the opposite behavior. This spin splitting of occupied and unoccupied states opens the bandgap. The partial charge densities of the occupied states are shown in Fig. 5(d), where it is observed that the anionic electrons have a tubular distribution in the interstitial positions, further confirming that Ba₅Sb₃ is a potential 1D electride. The maximum value of the partial charge density is 0.0032 bohr³, which is comparable to the maximum value of 0.0043 bohr³ for the spin-charge density calculated in Fig. 3(c), which suggests that the interstitial electrons, serving as ions and essentially in the spin state, form a local magnetic center.

The bandgap is one of the most critical fundamental parameters for semiconductor-based electronic and optoelectronic devices, and modifying the semiconductor bandgap plays a crucial role in improving the performance of these devices. Common methods of bandgap modification include electric field modulation,58 application of strain–stress,59 atomic doping,37 and the construction of heterostructures.60 Bilayer LaBr₂ can change to become semimetallic under a vertical electric field, and spin polarization conversion can be achieved by reversing the electric field.58 The bandgap of Mott-insulating TiPO₄ can be adjusted through the application of high pressure.61 In experiments on Y₂C weakly magnetic anionic electrons have been observed and it has been found that the magnetic properties of two-dimensional anionic electrons can be modulated by strain–stress and hole doping.27Figure 6(a) shows the bandgap and spin polarization energy of Ba₅Sb₃ under isotropic strain–stress. The bandgap of Ba₅Sb₃ is strongly correlated with the spin polarization energy. The bandgap increases and the spin polarization energy decreases under compression (negative lattice deviation). By contrast, when the spin polarization energy increases under tension (positive lattice deviation), the bandgap decreases, and finally disappears, i.e., the material is in a metallic state.

ELF maps of Ba₅Sb₃ [Fig. 6(b)] show strong localization of anionic electrons at −5% (compression) lattice deviation, while the distribution of anionic electrons is more discrete at 5% (stretch) than at 0% lattice deviation. This suggests that stronger interactions between anionic electrons in electrides with localized magnetic centers are more pronounced and more likely to lead to the formation of Mott insulators. Pressure is an effective way to change the atomic distances between atoms and has essential effects on the behavior of the anionic electrons, such as in the pressure-induced formation of an electron-deficient-type Ca₅Pb₃ electride36 and the metal-to-semiconductor transition in compressed Ca₂N.22 Therefore, we calculated the bandgaps of Ba₅Sb₃ under different pressures [Fig. 6(c)]. As the pressure increases, the bandgap first increases, reaching a maximum value (0.41 eV) at around 6 GPa, and then decreases. The ELF shows that the electron localization becomes more significant with elevation of pressure, indicating that pressure can effectively enhance the strong correlation effect between the interstitial electrons. However, as the pressure continues to increase, the interatomic distance is reduced, and the corresponding energy bands become more dispersed. Thus, the bandgap decreases when the pressure is increased beyond a certain value. Such results can guide the search for other Mott insulators with highly localized magnetic centers induced by pressure (chemical or physical) in electrides.

Elemental doping can change the electronic structure and the mechanical and optical properties of materials. On the other hand, electrides usually possess a strong hydrogen affinity, and hydrogen atoms are generally adsorbed at the sites of the anionic electrons in electrides, thereby changing their electronic structures.20,62 For example, C12A7: H⁻ is converted from an electride to a conventional ionic compound by hydrogen adsorption.63 The addition of H significantly reduces the work functions of YClH and Y₂Cl₃H, and the ferromagnetism of YCl disappears.20 Li et al.37 discovered a series of new ternary electrides by appropriate elemental substitution in Mn₅Si₃-type non-electride materials. As shown in Fig. 6(d), for Ba₅Sb₃, when H atoms are introduced into the Sr₆ octahedron, the electride characteristic and magnetism disappear, but the semiconducting properties remain. The interstitial electrons are transferred to H_1s orbitals and distributed at the deep energy levels.

We have investigated the Mott-insulating properties of Ae₅X₃ electrides with the Mn₅Si₃ configuration. Our results show that the interstitial electrons in Ae₅X₃ adopt an antiferromagnetic configuration and have a quasi-one-dimensional distribution in the face-sharing Ae₆ octahedron. Analysis of the spin-charge density and partial charge density reveals that the half-filled interstitial electrons are essentially in a spin state, forming a localized magnetic center. The strong electron correlations between nearest interstitial electrons induce spin splitting and a separation between occupied and unoccupied states, which is responsible for the semiconducting properties. The calculated indirect bandgap of Ae₅X₃ is about 0.30 eV, which is contributed by the weaker orbital hybridization of the half-filled interstitial electrons with the surrounding atoms. Additionally, Ca₅As₃, Sr₅As₃, and Sr₅Sb₃ are spin-gapped Mott insulators. The bandgaps of Ae₅X₃ are tunable by application of strain–stress or pressure. The unique semiconducting and magnetic properties of these electrides provide new possibilities for their application in spintronic devices, thermoelectric materials, and electron-emitting devices.

Acknowledgment. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12204419 and 12074013) and the China Postdoctoral Science Foundation (Grant No. 2021M702956).