Abstract:
Recent experiments established pure graphene as the strongest material known to mankind, further invigorating the question of how graphene fails. Using density functional theory, we reveal the mechanisms of mechanical failure of pure graphene under a generic state of tension. One failure mechanism is a novel soft-mode phonon instability of the $K_1$-mode, whereby the graphene sheet undergoes a phase transition and is driven towards isolated benzene rings resulting in a reduction of strength. The other is the usual elastic instability corresponding to a maximum in the stress-strain curve. Our results indicate that finite wave vector soft modes can be the key factor in limiting the strength of monolayer materials.

Abstract:
Here we propose a new approach for performing a Taylor series expansion of the first-principles computed energy of a crystal as a function of the nuclear displacements. We enlarge the dimensionality of the existing displacement space and form new variables (ie. slave modes) which transform like irreducible representations of the space group and satisfy homogeneity of free space. Standard group theoretical techniques can then be applied to deduce the non-zero expansion coefficients a priori. At a given order, the translation group can be used to contract the products and eliminate terms which are not linearly independent, resulting in a final set of slave mode products. While the expansion coefficients can be computed in a variety of ways, we demonstrate that finite difference is effective up to fourth order. We demonstrate the power of the method in the strongly anharmonic system PbTe. All anharmonic terms within an octahedron are computed up to fourth order. A proper unitary transformation demonstrates that the vast majority of the anharmonicity can be attributed to just two terms, indicating that a minimal model of phonon interactions is achievable. The ability to straightforwardly generate polynomial potentials will allow precise simulations at length and time scales which were previously unrealizable.

Abstract:
Inorganic perovskite oxide ferroelectrics have recently generated substantial interest for photovoltaic applications; however, existing materials suffer from excessive electronic band gaps and insufficient electric polarization. The recent resurgence of hybrid perovskite ferroelectrics addresses the aforementioned deficiencies, but they are highly unstable against environmental effects and an inorganic resolution may still be optimal. Here we use first-principles calculations to design a low band gap, planar ferroelectric by leveraging the complexity of layered double perovskite oxides AA$^\prime $BB$^\prime$O$_6$. We exploit A$\ne$A$^\prime$ size mismatch, a nominally empty $d$-shell on the B-site, and A cations bearing lone-pair electrons to achieve a large ferroelectric polarization. Additionally, B$^\prime\ne$B is chosen to achieve full charge transfer and a Mott susceptible filling on the B$^\prime$-site, yielding a low band gap. These principles are illustrated in BaBiCuVO$_6$, BaBiNiVO$_6$, BaLaCuVO$_6$, and PbLaCuVO$_6$, which could be realized in layer-by-layer growth. This new class of materials could lead to stable, high-efficiency photovoltaic.

Abstract:
The ideal strength of monolayer materials possessing semimetallic, semiconducting, and insulating ground states is computed using density functional theory. Here we show that, as in graphene, a soft mode occurs at the K-point in BN, graphane, and MoS$_2$, while not in silicene. The transition is first-order in all cases except graphene. In BN and graphane the soft mode corresponds to a Kekul{\'e}-like distortion similar to that of graphene, while MoS$_2$ has a distinct distortion. The phase transitions for BN, graphane, and MoS$_2$ are not associated with the opening of a band gap, which indicates that Fermi surface nesting is not the driving force. We perform an energy decomposition that demonstrates why the soft modes at the K-point are unique and how strain drives the phonon instability.

Abstract:
The application of modern layer-by-layer growth techniques to transition-metal oxide materials raises the possibility of creating new classes of materials with rationally designed correlated electron properties. An important step toward this goal is the demonstration that electronic structure can be controlled by atomic composition. In compounds with partially occupied transition-metal d shells, one important aspect of the electronic structure is the relative occupancy of different d orbitals. Previous work has established that strain and quantum confinement can be used to influence orbital occupancy. In this paper we demonstrate a different modality for orbital control in transition-metal oxide heterostructures, using density-functional band calculations supplemented by a tight-binding analysis to show that the choice of nontransition-metal counterion X in transition-metal oxide heterostructures composed of alternating LaNiO3 and LaXO3 units strongly affects orbital occupancy, changing the magnitude and in some cases the sign of the orbital polarization.

Abstract:
A full implementation of the $ab$ $initio$ density functional plus dynamical mean field theory (DFT+DMFT) formalism to perform total energy calculations and structural relaxations is proposed and implemented. The method is applied to the structural and metal-insulator transitions of the rare earth nickelate perovskites as a function of rare earth ion, pressure, and temperature. In contrast to previous DFT and DFT+$U$ theories, the present method accounts for the experimentally observed structure of $La$NiO$_3$ and the insulating nature of the other perovskites, and quantitatively reproduces the metal-insulator and structural phase diagram in the plane of pressure and rare earth element. The temperature dependence of the energetics of the phase transformation indicates that the thermal transition is driven by phonon entropy effects.

Abstract:
A combination of density functional and dynamical mean-field theory is applied to the perovskites SrVO$_3$, LaTiO$_3$ and LaVO$_3$. We show that DFT+DMFT in conjunction with the standard fully localized-limit (FLL) double-counting predicts that LaTiO$_3$ and LaVO$_3$ are metals even though experimentally they are correlation-driven ("Mott") insulators. In addition, the FLL double counting implies a splitting between oxygen $p$ and transition metal $d$ levels which differs from experiment. Introducing into the theory an \textit{ad hoc} double counting correction which reproduces the experimentally measured insulating gap leads also to a $p$-$d$ splitting consistent with experiment if the on-site interaction $U$ is chosen in a relatively narrow range ($\sim 6\pm 1$ eV). The results indicate that these early transition metal oxides will serve as critical test for the formulation of a general \textit{ab initio} theory of correlated electron metals.

Abstract:
Using density functional theory with added on-site interactions (DFT+U), we study the electronic structure of bulk, monolayer, and bilayer of the layered transition-metal dichalcogenide $1T-TaS_2$. We show that a two-dimensional spin--$\frac{1}{2}$ Mott-phase exists for the monolayer in the charge-density wave state (CDW) and that such a phase is systematically destroyed by packing of the distorted layers leading to a one dimensional metal for bulk, CDW-distorted TaS$_2$. The latter finding is in contrast with previous DMFT predictions --disagreement we explain by the weak effective interaction felt by the electrons in the CDW state. Experimental observations of insulating behavior may arise from disorder due to stacking faults.

Abstract:
We have formulated and implemented a fully charge-self-consistent density functional theory plus dynamical mean field theory methodology which enables an efficient calculation of the total energy of realistic correlated electron systems. The density functional portion of the calculation uses a plane wave basis set within the projector augmented wave method enabling study of systems with large, complex unit cells. The dynamical mean field portion of the calculation is formulated using maximally localized Wannier functions, enabling a convenient implementation which is independent of the basis set used in the density functional portion of the calculation. The importance of using a correct double counting term is demonstrated. A generalized form of the standard double counting correction, which we refer to as the $U^\prime$ form, is described in detail and used. For comparison the density functional plus U method is implemented within the same framework including the generalized double counting. The formalism is validated via a calculation of the metal-insulator and structural phase diagrams of the rare-earth nickelate perovskites as functions of applied pressure and A-site rare-earth ions. The calculated density functional plus dynamical mean field results are found to be consistent with experiment. The density functional plus U method is shown to grossly overestimate the tendency for bond-disproportionation and insulating behavior.

Abstract:
A combination of density functional and dynamical mean field theory calculations are used to show that the remarkable metal-insulator transition in the rare earth nickelate perovskites arise from a site-selective Mott phase, in which the $d$-electrons on a half of the Ni ions are localized to form a fluctuating moment while the $d$-electrons on other Ni ions form a singlet with holes on the surrounding oxygen ions. The calculation reproduces key features observed in the nickelate materials, including an insulating gap in the paramagnetic state, a strong variation of static magnetic moments among Ni sites and an absence of "charge order". A connection between structure and insulating behavior is documented. The site-selective Mott transition may be a more broadly applicable concept in the description of correlated materials.