Layered Electride Research Articles

Stoner instability-mediated large magnetoelectric effects in 2D stacking electrides

Strong magnetoelectric effects in single-phase two-dimensional (2D) materials are extremely rare in nature. Here by first-principles calculations, we find a strong magnetoelectric coupling in polar stacking bilayer Hf2S that allows the reversal of net magnetic moments with the reversal of electric dipoles. Further analysis shows that such strong magnetoelectric effects benefit from the Stoner instability of surface Hf atoms triggered by polar stacking. Moreover, an unexpectedly large out-of-plane electric polarization (which is at least two times larger than that of bilayer BN) survives in the material, despite its metallicity. The large electric polarization is ascribed to the delocalized interlayer electrons which generally present in layered electride materials. It is quite interesting that large electric polarization, metallicity and magnetism coexist in one single-phase material. Our findings reveal rich physical phenomena to be explored in 2D stacking multiferroics and suggest an alternative way of searching for strong magnetoelectric materials with ultrathin thickness.

Low thermal expansion of layered electrides predicted by density-functional theory.

Layered electrides are a unique class of materials with anionic electrons bound in interstitial regions between thin, positively charged atomic layers. While density-functional theory is the tool of choice for computational study of electrides, there has to date been no systematic comparison of density functionals or dispersion corrections for their accurate simulation. There has also been no research into the thermomechanical properties of layered electrides, with computational predictions considering only static lattices. In this work, we investigate the thermomechanical properties of five layered electrides using density-functional theory to evaluate the magnitude of thermal effects on their lattice constants and cell volumes. We also assess the accuracy of five popular dispersion corrections with both planewave and numerical atomic orbital calculations.

Thickness-Dependent Superconductivity in a Layered Electride on Silicon.

Layered materials exhibit a plethora of fascinating properties. The challenge is to make the materials into epitaxial films, preferably integrated with mature technological platforms to facilitate their potential applications. Progress in this direction can establish the film thickness as a valuable parameter to control various phenomena, superconductivity in particular. Here, a synthetic route to epitaxial films of SrAlSi, a layered superconducting electride, on silicon is designed. A set of films ranging in thickness is synthesized employing a silicene-based template. Their structure and superconductivity are explored by a combination of techniques. Two regimes of TC dependence on the film thickness are identified, the coherence length being the crossover parameter. The results can be extended to syntheses of other honeycomb-lattice ternary compounds on Si or Ge exhibiting superconducting, magnetic, and other properties.

Surface-induced ferromagnetism and anomalous Hall transport at Zr2S(001)

Two-dimensional layered electrides possessing anionic excess electrons in the interstitial spaces between cationic layers have attracted much attention due to their promising opportunities in both fundamental research and technological applications. Using first-principles calculations, we predict that the layered bulk electride ${\mathrm{Zr}}_{2}\mathrm{S}$ is nonmagnetic with massive Dirac nodal-line states arising from $\mathrm{Zr}\text{\ensuremath{-}}4d$ cationic and interlayer anionic electrons. However, the ${\mathrm{Zr}}_{2}\mathrm{S}(001)$ surface increases the density of states at the Fermi level due to the surface potential, thereby inducing a ferromagnetic order at the outermost Zr layer via the Stoner instability. Consequently, the time-reversal symmetry breaking at the surface not only generates spin-polarized topological surface states with intricate helical spin textures but also hosts an intrinsic anomalous Hall effect originating from the Berry curvature generated by spin-orbit coupling. Our findings offer a playground to investigate the emergence of ferromagnetism and anomalous Hall transport at the surface of nonmagnetic topological electrides.

Periodic trends in the structural, electronic, and transport properties of electrenes.

Two-dimensional layered electrides are a class of atomically thin materials in which the anion is an excess electron rather than a negatively charged ion. These excess electrons form delocalized sheets of charge surrounding each layer of the material. A well-known example is Ca2N; its identification and characterization has triggered an avalanche of studies aimed at broadening applications of electrides. Ca2N is only one member of the M2X family of materials, with M being an alkaline-earth metal and X belonging to the pnictogen group, which can be exfoliated to form single- or few-layer electrenes. The goal of this study is to systematically investigate the monolayer and bilayer properties for this family of materials. Density-functional calculations reveal linear relationships between surface and interstitial charges, work functions, exfoliation energies, and Ewald energies. Using the Landauer formalism, informed by rigorous electron-phonon scattering calculations, we also investigate the electronic transport characteristics of the monolayer and bilayer electrenes. Our findings indicate that the nitrogen-based electrenes (Ca2N, Sr2N, and Ba2N) are more conductive than their counterparts involving heavier pnictogens. The results of this study highlight underlying periodic trends in electrene properties that can help identify which materials would be best suited for particular applications.

Emerging two-dimensional magnetism in nonmagnetic electrides Hf2X (X=S, Se, Te)

Recent experimental discoveries of two-dimensional (2D) magnets have triggered intense research activities to search for atomically thin magnetic systems. Using first-principles calculations, we predict the emergence of 2D magnetism in the monolayers (MLs), few layers, and surfaces of nonmagnetic layered electrides ${\mathrm{Hf}}_{2}X$ $(X=\text{S}, \mathrm{Se}, \mathrm{Te})$ consisting of three-atom-thick $\mathrm{Hf}\text{\ensuremath{-}}X\text{\ensuremath{-}}\mathrm{Hf}$ stacks. It is revealed that each bulk ${\mathrm{Hf}}_{2}X$ hosts a quantum state of Dirac nodal lines with a high density of states arising from $\mathrm{Hf}\text{\ensuremath{-}}5d$ cationic and interlayer anionic electrons around $\ensuremath{-}0.9 \mathrm{eV}$ below the Fermi level ${E}_{F}$. However, for the MLs, few layers, and surfaces of ${\mathrm{Hf}}_{2}X$, such hybridized states are shifted toward ${E}_{F}$ to generate van Hove singularities, leading to a Stoner instability. The resulting surface ferromagnetism gives rise to strongly spin-polarized topological surface states at ${\mathrm{Hf}}_{2}X(001)$, demonstrating that anionic electrons, 2D magnetism, and band topology are entangled with each other. Our findings will open different perspectives for the discovery of 2D magnets via exploiting surface effects in nonmagnetic layered electrides.

First-principles study of two-dimensional electron gas on a layered Gd2C electride surface

Electrides are ionic compounds in which electrons behave as anions in the interior of a positively charged framework. As a layered electride, ${\mathrm{Gd}}_{2}\mathrm{C}$ receives attention because of its ferromagnetism. Although previous research has focused on the bulk properties of ${\mathrm{Gd}}_{2}\mathrm{C}$, few studies have focused on ultrathin layers or surfaces for two-dimensional (2D) characteristics. Here, we report a first-principles study of the electronic properties of few-layer ${\mathrm{Gd}}_{2}\mathrm{C}$ structures. ${\mathrm{Gd}}_{2}\mathrm{C}$ has a work function of 3.35 eV. When a layered electride is exfoliated, the interstitial layer becomes a surface and may be exposed to the outside. Because the interlayer region has changed to the surface, the properties of the electron gases once located in the interlayer in the past will also change. We found that the surface anionic electrons accounted for about 25% of the number of electrons in the interlayer region in the absence of an external electric field. When we applied an external electric field, the number of surface electrons increased, and the increase was proportional to the square of the field intensity. Since the electronic properties of 2D materials can be understood through scanning tunneling spectroscopy (STS), we also performed the STS simulations. At $\ensuremath{-}0.9\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$, the STS image was blurred because of surface anionic electrons. In contrast to the spin-up electron, an interlayer band of the spin-down electron crossed the Fermi level in the ultrathin ${\mathrm{Gd}}_{2}\mathrm{C}$ layers. Our findings open a possibility that the spin-polarized electronic gas in the few-layer electride could be used for spintronics.

Oxidation, Stability, and Magnetic Ground States of Two-Dimensional Layered Electrides

Two-dimensional electrides have emerged as a new class of layered materials, in which excess electrons exist in the interlayer spacing. These anionic electrons cause exotic electronic properties, such as low work function, high electronic mobility, and magnetic anisotropy. However, they render the surface of the electrides remarkably reactive; therefore, the surfaces are prone to oxidation. In this study, we investigated the oxidation mechanisms of two representative electrides, Ca2N and Y2C, using first-principles calculations. The adsorption of atomic and molecular oxygen on Ca2N and Y2C monolayers was observed to be highly exothermic (∼5 eV/atom). Upon adsorption, triplet O2 molecules spontaneously dissociated on both monolayers owing to an enormous charge transfer from the surfaces (∼1.4e/atom). The dissociated O atoms had no magnetic moments, while the electride surfaces exhibited a complex ferrimagnetic ground state caused by the charge transfer and structural deformation accompanying the O2 adsorption. Similar adsorption behaviors were observed even for increased electride thicknesses, implying that our findings are also applicable to the multilayers of the electrides. The present work shed more light on the oxidation mechanism of two-dimensional electrides and may serve as a valuable guide for the synthesis of stable layered electrides.

Theory of Epitaxial Growth of Borophene on Layered Electride: Thermodynamic Stability and Kinetic Pathway

Based on first-principles calculations, we propose that a layered electride Mg2O can serve as an effective substrate, in place of metal substrate, to grow honeycomb borophene (h-borophene). We first confirm the thermodynamic stability of h-B@Mg2O heterostructure by energetics analysis and dynamic stability by absence of imaginary frequency in phonon spectra. Then, kinetically, we identify the atomistic pathways for a preferred 2D growth mode over 3D growth, and reveal a growth transition from 2D compact islands to h-borophene at ~13-atom cluster size, indicating the feasibility of epitaxial growth of h-borophene on Mg2O. The h-borophene is found to be stabilized by nearly one electron transfer from Mg2O to h-borophene based on the Bader charge analysis. Moreover, the intrinsic band structure of the free-standing h-borophene is only weakly perturbed by the Mg2O substrate, a significant advantage over metal substrate. We envision that layered electrides provide an attractive family of substrates for epitaxial growth of a range of 2D materials that can otherwise only be grown on undesirable metal substrates.

Layered electrides as fluoride intercalation anodes

We predict that layered electrides, such as Ca2N and Y2C, can serve as good hosts for fluoride intercalation.

Decisive Role of Interlayer Ionic Couplings for the Electronic Properties of Two-Dimensional Layered Electrides

Two-dimensional (2D) layered electrides have attracted significant attention as a new class of 2D materials owing to the presence of unusual anionic electrons (AEs). The electride layers are more strongly bound by ionic interactions involving AEs compared with van der Waals layers, which is also critical to the physical and chemical properties of the materials. However, to date, the role of interlayer ionic coupling in determining the properties of 2D electrides has been mostly unexplored. Here we use density functional theory calculations to systematically investigate the effect of interlayer ionic couplings associated with AEs on the electronic properties of various existing and proposed layered electrides. A higher density of AEs in the 2D layered spacing leads to stronger localization and interlayer coupling strength, which induces a Stoner-type magnetic instability. In-plane strain can dramatically modify the configuration of AEs, thereby enabling strain engineering of 2D materials. Strikingly, the work function and interlayer binding energy of the layered electrides are distinctly related, which is in stark contrast to those of van der Waals materials. Besides, we suggest Ba2N and Sr2N as promising candidates for new 2D materials owing to their low interlayer binding energies and stable monolayer forms.

Electron—Phonon Interaction, Phonon and Electronic Structures of Layered Electride Ca2N

The phonon and electronic properties, the Eliashberg function and the temperature dependence of resistance of electride Ca2N are investigated by the DFT-LDA (density functional theory in local density approximation) plane-wave method. The phonon dispersion, the partial phonon density of states and the atomic eigenvectors of zero-center phonons are studied. The electronic band dispersion and partial density of states conclude that Ca2N is a metal and the Ca 3p, 4s and N 2p orbitals are hybridized. For the analysis of an electron-phonon interaction and its contribution of the Eliashberg function to resistance was calculated and a temperature dependence of resistance due to electron-phonon interaction was found.

Discovery of Hidden Classes of Layered Electrides by Extensive High-Throughput Material Screening

Despite their extraordinary properties, electrides are still a relatively unexplored class of materials with only a few compounds grown experimentally. Especially for layered electrides, the current research studies mainly focus on several isostructures of Ca2N with similar interlayer two-dimensional (2D) anionic electrons. An extensive screening for different layered electrides is still missing. Here, by screening materials with anionic electrons for the structures in Materials Project, we uncover 12 existing materials as new layered electrides. Remarkably, these layered electrides demonstrate completely different properties from Ca2N. For example, unusual fully spin-polarized zero-dimensional (0D) anionic electrons are shown in metal halides with MoS2-like structures; unique one-dimensional (1D) anionic electrons are confined within the tubes of the quasi-1D structures; and a coexistence of magnetic and nonmagnetic anionic electrons is found in ZrCl-like structures and a new ternary Ba2LiN with both 0D ...

Ultralow Interlayer Friction of Layered Electride Ca2N: A Potential Two-Dimensional Solid Lubricant Material

Dispersion-corrected density functional theory (DFT) calculations reveal that the layered electride of dicalcium nitride (Ca2N) exhibits stronger interlayer binding interactions but lower interlayer friction behavior than that of traditional layered lubricants weakly bonded by van der Waals (vdW) interactions, such as graphite, h-BN, and MoS2. These results are attributed to the two-dimensional (2D) homogeneous conduction electrons distribution in the middle of the interlayer space of Ca2N, which yields a smooth sliding barrier and hence ultralow friction behavior. The interesting results obtained in this study have not only broadened the scope of 2D solid lubricants but also enriched the physical understanding of ultralow friction mechanism for 2D systems.

Probing a divergent van Hove singularity of graphene with a Ca2N support: A layered electride as a solid-state dopant

Layered electrides, as typified by ${\mathrm{Ca}}_{2}\mathrm{N}$, are unconventional quasi-two-dimensional metals with low work functions, in which the conduction electrons are localized between the cation layers as well as outside the surface. We have investigated the electronic structure of the interface between a layered electride and another material, using graphene on ${\mathrm{Ca}}_{2}\mathrm{N}$ as an example. Our first-principles calculation shows that a graphene layer on ${\mathrm{Ca}}_{2}\mathrm{N}$ remains flat and is doped to an extremely high density of $n=5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ with its Fermi level (${E}_{F}$) aligned with the logarithmically divergent van Hove singularity (VHS) at a saddle point of graphene's ${\ensuremath{\pi}}^{*}$ band. This finding shows that graphene/${\mathrm{Ca}}_{2}\mathrm{N}$ is an ideal testing ground for the exploration of the many-body ground states, most notably superconducting states ($p+ip$ wave, $d$ wave, and $f$ wave), predicted to appear when ${E}_{F}$ is close to a VHS. The work function decreases abruptly upon monolayer attachment but reverts to that of ${\mathrm{Ca}}_{2}\mathrm{N}$ upon bilayer attachment. This peculiar behavior is explained in terms of the distinctive electronic structures of the constituent materials and their bonding.

Experimental Demonstration of an Electride as a 2D Material.

Because of their loosely bound electrons, electrides offer physical properties useful in chemical synthesis and electronics. For these applications and others, nanosized electrides offer advantages, but to-date no electride has been synthesized as a nanomaterial. We demonstrate experimentally that Ca2N, a layered electride in which layers of atoms are separated by layers of a 2D electron gas (2DEG), can be exfoliated into two-dimensional (2D) nanosheets using liquid exfoliation. The 2D flakes are stable in a nitrogen atmosphere or in select organic solvents for at least one month. Electron microscopy and elemental analysis reveal that the 2D flakes retain the crystal structure and stoichiometry of the parent 3D Ca2N. In addition, the 2D flakes exhibit metallic character and an optical response that agrees with DFT calculations. Together these findings suggest that the 2DEG is preserved in the 2D material. With this work, we bring electrides into the nanoregime and experimentally demonstrate a 2D electride, Ca2N.

Evidence for Anionic Excess Electrons in a Quasi-Two-Dimensional Ca2N Electride by Angle-Resolved Photoemission Spectroscopy.

Angle-resolved photoemission spectroscopy (ARPES) study of a layered electride Ca2N was carried out to reveal its quasi-two-dimensional electronic structure. The band dispersions and the Fermi-surface map are consistent with the density functional theory results except for a chemical potential shift that may originate from the high reactivity of surface excess electrons. Thus, the existence of anionic excess electrons in the interlayer region of Ca2N is strongly supported by ARPES.