Within the framework of the full potential projector-augmented wave methodology, we present a promising low-scaling $GW$ implementation. It allows for quasiparticle calculations with a scaling that is cubic in the system size and linear in the number of $k$ points used to sample the Brillouin zone. This is achieved by calculating the polarizability and self-energy in the real-space and imaginary-time domains. The transformation from the imaginary time to the frequency domain is done by an efficient discrete Fourier transformation with only a few nonuniform grid points. Fast Fourier transformations are used to go from real space to reciprocal space and vice versa. The analytic continuation from the imaginary to the real frequency axis is performed by exploiting Thiele's reciprocal difference approach. Finally, the method is applied successfully to predict the quasiparticle energies and spectral functions of typical semiconductors (Si, GaAs, SiC, and ZnO), insulators (C, BN, MgO, and LiF), and metals (Cu and ${\mathrm{SrVO}}_3)$. The results are compared with conventional $GW$ calculations. Good agreement is achieved, highlighting the strength of the present method.

Traditional strengthening ways, such as strain, precipitation and solid-solution, come into effect by pinning the motion of dislocation. Here, through first-principles calculations we report on an extra-electron induced covalent strengthening mechanism, which alters chemical bonding upon the introduction of extra-valence electrons in the matrix of parent materials. It is responsible for the brittle and high-strength properties of Al₁₂W-type compounds featured by the typical fivefold icosahedral cages, which are common for quasicrystals and bulk metallic glasses (BMGs). In combination with this mechanism, we generalize ductile-to-brittle criterion in a universal hyperbolic form by integrating the classical Pettifor's Cauchy pressure with Pugh's modulus ratio for a wide variety of materials with cubic lattices. This study provides compelling evidence to correlate Pugh's modulus ratio with hardness of materials and may have implication for understanding the intrinsic brittleness of quasicrystals and BMGs.

Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zirconia, an important transition metal oxide. This machine-learned potential accurately captures the temperature-induced phase transitions below the melting point. We further showcase the predictive power of the potential by calculating the heat transport on the basis of Green–Kubo theory, which allows to account for anharmonic effects to all orders. This study indicates that machine-learned potentials trained on the fly offer a routine solution for accurate and efficient simulations of the thermodynamic properties of a vast class of anharmonic materials.

Vertical three-dimensional integration of two-dimensional (2D) semiconductors holds great promise, as it offers the possibility to scale up logic layers in the z axis^1–3. Indeed, vertical complementary field-effect transistors (CFETs) built with such mixed-dimensional heterostructures^4,5, as well as hetero-2D layers with different carrier types^6–8, have been demonstrated recently. However, so far, the lack of a controllable doping scheme (especially p-doped WSe₂ (refs. ^9–17) and MoS₂ (refs. ^11,18–28)) in 2D semiconductors, preferably in a stable and non-destructive manner, has greatly impeded the bottom-up scaling of complementary logic circuitries. Here we show that, by bringing transition metal dichalcogenides, such as MoS₂, atop a van der Waals (vdW) antiferromagnetic insulator chromium oxychloride (CrOCl), the carrier polarity in MoS₂ can be readily reconfigured from n- to p-type via strong vdW interfacial coupling. The consequential band alignment yields transistors with room-temperature hole mobilities up to approximately 425 cm² V⁻¹ s⁻¹, on/off ratios reaching 10⁶ and air-stable performance for over one year. Based on this approach, vertically constructed complementary logic, including inverters with 6 vdW layers, NANDs with 14 vdW layers and SRAMs with 14 vdW layers, are further demonstrated. Our findings of polarity-engineered p- and n-type 2D semiconductor channels with and without vdW intercalation are robust and universal to various materials and thus may throw light on future three-dimensional vertically integrated circuits based on 2D logic gates.

We present quasiparticle (QP) energies from fully self-consistent $GW\left(\mathrm{sc}GW\right)$ calculations for a set of prototypical semiconductors and insulators within the framework of the projector-augmented-wave methodology. To obtain converged results, both finite basis-set corrections and $k$-point corrections are included, and a simple procedure is suggested to deal with the singularity of the Coulomb kernel in the long-wavelength limit, the so-called head correction. It is shown that the inclusion of the head corrections in the $\mathrm{sc}GW$ calculations is critical to obtain accurate QP energies with a reasonable $k$-point set. We first validate our implementation by presenting detailed results for the selected case of diamond, and then we discuss the converged QP energies, in particular the band gaps, for a set of gapped compounds and compare them to single-shot $G_0{W}_0$, QP self-consistent $GW$, and previously available $\mathrm{sc}GW$ results as well as experimental results.