Second-principles method including electron and lattice degrees of freedom

Abstract

We present a first-principles-based (second-principles) scheme that permits large-scale materials simulations including both atomic and electronic degrees of freedom on the same footing. The method is based on a predictive quantum-mechanical theory, e.g., Density Functional Theory, and its accuracy can be systematically improved at a very modest computational cost. Our approach is based on dividing the electron density of the system into a reference part - typically corresponding to the system's neutral, geometry-dependent ground state - and a deformation part - defined as the difference between the actual and reference densities. We then take advantage of the fact that the bulk part of the system's energy depends on the reference density alone; this part can be efficiently and accurately described by a force field, thus avoiding explicit consideration of the electrons. Then, the effects associated to the difference density can be treated perturbatively with good precision by working in a suitably chosen Wannier function basis. Further, the electronic model can be restricted to the bands of interest. All these features combined yield a very flexible and computationally very efficient scheme. Here we present the basic formulation of this approach, as well as a practical strategy to compute model parameters for realistic materials. We illustrate the accuracy and scope of the proposed method with two case studies, namely, the relative stability of various spin arrangements in NiO and the formation of a two-dimensional electron gas at the interface between band insulators LaAlO${}_3$ and SrTiO${}_3$. We conclude by discussing ways to overcome the limitations of the present approach (most notably, the assumption of a fixed bonding topology), as well as its many envisioned possibilities and future extensions.

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• Spin wave dispersion based on the quasiparticle self-consistent $GW$ method: NiO, MnO and $\alpha$-MnAs
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Cited by in corpus (32)

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• First-principles study of two-dimensional electron and hole gases at the head-to-head and tail-to-tail 180${}^{\circ }$ domain walls in PbTiO${}_3$ ferroelectric thin films
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• Giant voltage amplification from incipient ferroelectric states
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• Parameter-free prediction of phase transition in PbTiO3 through combination of quantum mechanics and statistical mechanics
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• Anisotropy-driven thermal conductivity switching and thermal hysteresis in a ferroelectric
• Polar morphologies from first principles: PbTiO${}_3$ films on SrTiO${}_3$ substrates and the $p(2\times \Lambda )$ surface reconstruction
• Strain game revisited for complex oxide thin-films: Substrate-film thermal expansion mismatch in PbTiO${}_3$
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• Ab initio electron-lattice downfolding: potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials
• Liquid-crystal-like dynamic transition in ferroelectric/dielectric superlattices
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