Prediction of nonlayered oxide monolayers as flexible high-κ dielectrics with negative Poisson’s ratios

During the last two decades, two-dimensional (2D) materials have been the focus of condensed matter physics and material science due to their promising fundamental properties and (opto-)electronic applications. However, high-κ 2D dielectrics that can be integrated within 2D devices are often missing. Here, we propose nonlayered oxide monolayers with calculated exfoliation energy as low as 0.39 J/m2 stemming from the ionic feature of the metal oxide bonds. We predict 51 easily or potentially exfoliable oxide monolayers, including metals and insulators/semiconductors, with intriguing physical properties such as ultra-high κ values, negative Poisson’s ratios and large valley spin splitting. Among them, the most promising dielectric, GeO2, exhibits an auxetic effect, a κ value of 99, and forms type-I heterostructures with MoSe2 and HfSe2, with a band offset of ~1 eV. Our study opens the way for designing nonlayered 2D oxides, offering a platform for studying the rich physics in ultra-thin oxides and their potential applications in future information technologies.


Nonlayered Oxides Exfoliation.
For the extraction of 2D materials from nonlayered bulks, the first step is to determine the promising exfoliated crystal planes.The strategy is to identify the crystal planes with large difference between in-plane and interplanar interactions.A primary tool is the set of interplanar spacing (dhkl) and packing ratio of different planes.We select the close-packed planes and nearly close-packed planes with large dhkl, indicating that there may be a relatively weak out-of-plane interaction and strong in-pane bonding.In the second step, we rotate the selected crystal plane (h k l) to the (0 0 1) plane, in preparation for the subsequent exfoliation calculations.In the last step, we extract 2D material from its bulk precursor by gradually increasing the tensile stress on the selected crystal plane.The specific procedure is as follows: we stretch the crystal along the z-direction in steps of 5% strain, during which the in-plane lattice constants a, b and all the atoms in the system are fully optimized.In addition, to complete the extraction of 2D material from its 3D precursor, it usually takes 22 to 130 stretching steps, for all the exfoliation cases we considered.

Supplementary Discussion
Mechanistic Explanation.Negative Poisson's ratio (NPR) effect of GeO2 (101).When the GeO2 monolayer is stretched in the x-direction, the angle 1  increases, together with the lattice constant in the y-direction decreases, see Supplementary Figure 36(a).The contraction of lattice in the y-direction results in a decrease in the angle 2  , see Supplementary Figure 36 (b), the monolayer thickness in the z-direction thus increases, and vice versa, leading to NPR effect.Red and grey spheres (sticks) denote O and the Ge atoms, respectively.
NPR effect for MO2 (110) (M=Os, Pb, Pd, and Rh).When the MO2 (110) monolayers are stretched in the y-direction, the angle 3  decreases and the lattice in the x-direction contracts, see Supplementary Figure 37(a).The contraction of lattice in the x-direction leads to the out-of-plane angle 4  decreases and the monolayer expands in the z-direction (see Supplementary Figure 37(b)), and vice versa, leading to NPR effect.Red and grey spheres (sticks) denote O and metal atoms, respectively.
Biased-Poisson's ratio effect of WO3 (110).When WO3 (110) monolayer is compressed in the x direction, the angle 5  in the x z plane decreases, making O1 atom move down along the z axis, the WO3 (110) monolayer thus expands in the z-direction, see Supplementary Figure 38(a).In turn, if WO3 (110) monolayer is stretched in the x-direction, WO3 (110) still expands in the zdirection.This is because the lattice expansion in the x-direction will cause the lattice contraction in the y-direction, see Supplementary Figure 38(b), which makes the angle 6  in the yz plane decrease and O2 atom move down along the z-direction, WO3 (110) monolayer thus still expands in the z-direction.The mechanical response in the z-direction to the uniaxial strain in the x and y directions are fully identical due to the structural isotropy in the x and y directions.
Biased-Poisson's ratio effect of AgO/CuO (101).when the AgO/CuO (101) monolayers are compressed in the x-direction, the angle 7  decreases, see the left panel in Supplementary Figure 39(a), which leads to the monolayer expands in the z-direction; while if the MO (101) monolayers are stretched in the x-direction, the lattice in the y-direction contracts, see Supplementary Figure 39(b), and the angle Figure 1.

Table 2 .
Magnetic nonlayered bulk oxides.U values (eV) used for transition metal are given in the second column.The ground-state magnetic configuration (GSMC) is determined by comparing the energy of ferromagnetic (FM) and several antiferromagnetic (AFM) configurations.The corresponding magnetic moment (M) per magnetic atom are given in the last column.
Supplementary Table3.The interplanar spacing (dhkl), close-packed degree and interplanar binding energy (Eb) for 97 crystallographic planes in 47 experimentally stable nonlayered bulk oxides extracted from Materials Project database.The definition of % close-packed can be found from the Methods section in the manuscript.

Table 4 .
Magnetic 2D oxides with b ≤ 3/2.Energy difference per formula between antiferromagnetic and ferromagnetic states ΔE = E(AFM) -E(FM), positive ΔE value means FM is ground-state magnetic configuration (GSMC), and vice versa. Te corresponding magnetic moment (M) per magnetic atom are given in the last column.

Table 23 .
In-plane (‖) and out-of-plane (⊥) static dielectric constants (κ) of 49 2D oxide semiconductors with band gaps ranging from 0.3 to 6.8 eV.κ ∞ denotes the electronic components of the static dielectric constants ( "electronic" + "ionic").And t is the thickness of monolayer.The thickness t is estimated by the interlayer distance of the bilayer.Band gaps (Eg) are calculated with the HSE functional.