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The electronic density of states (DOS) quantifies the distribution of the energy levels that can be occupied by electrons in a quasiparticle picture, and is central to modern electronic structure theory. It also underpins the computation and interpretation of experimentally observable material properties such as optical absorption and electrical conductivity. We discuss the challenges inherent in the construction of a machine-learning (ML) framework aimed at predicting the DOS as a combination of local contributions that depend in turn on the geometric configuration of neighbours around each atom, using quasiparticle energy levels from density functional theory as training data. We present a challenging case study that includes configurations of silicon spanning a broad set of thermodynamic conditions, ranging from bulk structures to clusters, and from semiconducting to metallic behavior. We compare different approaches to represent the DOS, and the accuracy of predicting quantities such as the Fermi level, the DOS at the Fermi level, or the band energy, either directly or as a side-product of the evaluation of the DOS. The performance of the model depends crucially on the smoothening of the DOS, and there is a tradeoff to be made between the systematic error associated with the smoothening and the error in the ML model for a specific structure. We demonstrate the usefulness of this approach by computing the density of states of a large amorphous silicon sample, for which it would be prohibitively expensive to compute the DOS by direct electronic structure calculations, and show how the atom-centred decomposition of the DOS that is obtained through our model can be used to extract physical insights into the connections between structural and electronic features.
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Semilocal density functionals for the exchange-correlation energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but predicts too-long lattice constants. Recent GGAs for solids yield good lattice constants but poor atomization energies of molecules. We show that the construction principle for one of them (restoring the density gradient expansion for exchange over a wide range of densities) can be used to construct a revised TPSS meta-GGA with accurate lattice constants, surface energies, and atomization energies for ordinary matter.
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What is the difference between space and time? is an ancient question that remains a matter of intense debate. In Newtonian mechanics time is absolute, while in Einsteins theory of relativity time and space combine into Minkowski spacetime. Here, we firstly propose Minkowski fermions in 2+1 dimensional Minkowski spacetime which have two space-like and one time-like momentum axes. These quasiparticles can be further classified as Klein-Gordon fermions and Dirac-Minkowski fermions according to the linearly and quadratically dispersing excitations. Realization of Dirac-Minkowski quasiparticles requires systems with particular topological nodal-line band degeneracies, such as hyperbolic nodal lines or coplanar band crossings. With the help of first-principles calculations we find that novel massless Dirac-Minkowski fermions are realized in a metastable bulk boron allotrope, Pnnm-B16.
In this work an overall electronic structure including the position and formation energies of various intrinsic defects are computed for anatase using Density Functional Theory aided by Hubbard correction (DFT+U). The intrinsic point defects considered here are, oxygen vacancy ($V_O$), oxygen interstitial ($O_i$), titanium vacancy ($V_{Ti}$) and titanium interstitial ($Ti_i$). Out of all the intrinsic defects considered here, $V_{Ti}$ and $Ti_i$ are found to be most stable under equilibrium condition. Whereas, conduction band in anatase is consisted of mainly Ti 3d with a minor component of O 2p states, valence band is found to be mainly composed of O 2p with a minor contribution from Ti 3d states. $V_O$ and $Ti_i$ are found to form localized states in the band gap. Moreover, anisotropy in the effective mass is seen. Finally, an alignment of band diagrams for all the intrinsic defect states is performed using vacuum potential from slab-supercell calculation as reference. This first principle study would help in the understanding of defect-induced insulating to conducting transition in anatase, which would have significant impact in the photocatalytic and optoelectronic area.
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