Deviations from continuum mechanics are always expected in nanoscale structures. We investigate the validity of the plate idealization of ultrathin graphene by gaining insight into the response of chemical bonds to bending deformations. In the monolayer, a bond orbital model reveals the breakdown of the plate phenomenology. In the multilayer, objective molecular dynamics simulations identify the validity margin and the role of discreteness in the plate idealization. Our result has implications for a broad class of phenomena where the monolayer easily curves, and for the design of mass and force detection devices.

We use a hybrid strategy to obtain anharmonic frequency shifts and lifetimes of phonon quasiparticles from first principles molecular dynamics simulations in modest size supercells. This approach is effective irrespective of crystal structure complexity and facilitates calculation of full anharmonic phonon dispersions, as long as phonon quasiparticles are well defined. We validate this approach to obtain anharmonic effects with calculations in ${\mathrm{MgSiO}}_3$ perovskite, the major Earth forming mineral phase. First, we reproduce irregular thermal frequency shifts of well characterized Raman modes. Second, we combine the phonon gas model (PGM) with quasiparticle frequencies and reproduce free energies obtained using thermodynamic integration. Combining thoroughly sampled quasiparticle dispersions with the PGM we then obtain first-principles anharmonic free energy in the thermodynamic limit ($N\to \infty$).

The stability of cubic $\mathrm{Ca}\mathrm{Si}{\mathrm{O}}_3$ perovskite (CaPv) at high temperatures and pressures is investigated by vibrational normal-mode analysis. We compute power spectra of mode autocorrelation functions using a recently developed hybrid approach combining ab initio molecular dynamics with lattice dynamics. These power spectra, together with the probability distributions of atomic displacements, indicate that cubic CaPv is stabilized at $T\sim 600$ K and $P\sim$ 26 GPa. We then utilize the concept of phonon quasiparticles to characterize the vibrational properties of cubic CaPv at high temperature and obtain anharmonic phonon dispersions through the whole Brillouin zone. Such temperature-dependent phonon dispersions pave the way for more accurate calculations of free-energy, thermodynamic, and thermoelastic properties of cubic CaPv at Earth's lower mantle conditions.

We present, for the first time, an atomic-level and quantitative study of a strain-induced pseudomagnetic field in graphene nanoribbons with widths of hundreds of nanometers. We show that twisting strongly affects the band structures of graphene nanoribbons with arbitrary chirality and generates well-defined pseudo-Landau levels, which mimics the quantization of massive Dirac fermions in a magnetic field up to 160 T. Electrons are localized either at ribbon edges forming the edge current or at the ribbon center forming the snake orbit current, both being valley polarized. Our result paves the way for the design of new graphene-based nanoelectronics.

The existence of Bloch flat bands of electrons provides a facile pathway to obtain exotic quantum phases owing to strong correlation. Despite the established magic angle mechanism for twisted bilayer graphene, understanding of the emergence of flat bands in twisted bilayers of two-dimensional polar crystals remains elusive. Here, we show that due to the polarity between constituent elements in the monolayer, the formation of complete flat bands in twisted bilayers is triggered as long as the twist angle is less than a certain critical value. Using the twisted bilayer of hexagonal boron nitride ($h\mathrm{BN}$) as an example, our simulations using the density-functional tight-binding method reveal that the flat band originates from the stacking-induced decoupling of the highest occupied (lowest unoccupied) states, which predominantly reside in the regions of the moiré superlattice where the anion (cation) atoms in both layers are overlaid. Our findings have important implications for the future search for and study of flat bands in polar materials.

We investigated the vibrational property of lead telluride (PbTe) with a focus on lattice anharmonicity at moderate temperatures $(300<T<800$ K) using the phonon quasiparticle approach which combines first-principles molecular dynamics and lattice dynamics. The calculated anharmonic phonon dispersions are strongly temperature dependent and some phonon modes adopt giant frequency shifts, e.g., transverse optical modes in the long-wavlength regime. As a result, we witness the avoided crossing between transverse optical modes and longitudinal acoustic modes at elevated temperature, in good agreement with experimentation and available theoretical studies. These results, together with the large root-mean-square displacements of atoms, reveal a strong anharmonic effect in PbTe. The obtained phonon lifetimes allow studies of transport properties. For considered temperatures, the phonon mean free paths can be shorter than lattice constants at relatively high temperature, especially for optical modes. This finding goes against the widely employed minimal phonon mean free path concept. As such, the calculated lattice thermal conductivity of PbTe, which is indeed relatively small, does not have the prescribed minima at high temperature, showcasing the breakdown of the minimal mean free path theory. Our study provides a basis for delineating vibrational and transport properties of PbTe and other thermoelectric materials within the framework of the phonon gas model.