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Note: This article is part of the JCP Special Topic on Electronic Structure Software.

Materials combining both a high refractive index and a wide band gap are of great interest for optoelectronic and sensor applications. However, these two properties are typically described by an inverse correlation with high refractive index appearing in small gap materials and vice-versa. Here, we conduct a first-principles high-throughput study on more than 4000 semiconductors (with a special focus on oxides). Our data confirm the general inverse trend between refractive index and band gap but interesting outliers are also identified. The data are then analyzed through a simple model involving two main descriptors: the average optical gap and the effective frequency. The former can be determined directly from the electronic structure of the compounds, but the latter cannot. This calls for further analysis in order to obtain a predictive model. Nonetheless, it turns out that the negative effect of a large band gap on the refractive index can counterbalanced in two ways: (i) by limiting the difference between the direct band gap and the average optical gap which can be realized by a narrow distribution in energy of the optical transitions and (ii) by increasing the effective frequency which can be achieved through either a high number of transitions from the top of the valence band to the bottom of the conduction or a high average probability for these transitions.Focusing on oxides, we use our data to investigate how the chemistry influences this inverse relationship and rationalize why certain classes of materials would perform better. Our findings can be used to search for new compounds in many optical applications both in the linear and non-linear regime (waveguides, optical modulators, laser, frequency converter, etc.). arXiv:1809.01132v2 [cond-mat.mtrl-sci]

High-power infrared laser systems with broadband tunability are of great importance due to their wide range of applications in spectroscopy and free-space communications. These systems require nonlinear optical (NLO) crystals for wavelength up/down conversion using sum/difference frequency generation, respectively. NLO crystals need to satisfy many competing criteria, including large nonlinear optical susceptibility, large laser induced damage threshold (LIDT), wide transparency range and phase-matchability. Here, we report bulk single crystals of SnP2S6 with a large non-resonant SHG coefficient of d33 = 53 pm V −1 at 1550nm and a large LIDT of 350 GW cm -2 for femtosecond laser pulses. It also exhibits a broad transparency range from 0.54μm to 8.5μm (bandgap of ~2.3 eV) and can be both Type I and Type II phase-matched. The complete linear and SHG tensors are measured as well as predicted by first principles calculations, and they are in excellent agreement. A proximate double-resonance condition in the electronic band structure for both the fundamental and the SHG light is shown to enhance the non-resonant SHG response. Therefore, SnP2S6 is an outstanding candidate for infrared laser applications.

Core-hole induced electron excitations in fullerene molecules, and small-diameter conducting carbon nanotubes, are studied using density functional theory with minimal, split-valence, and triply-split-valence basis sets plus the generalized gradient approximation by Perdew-Burke-Ernzerhof for exchange and correlation. Finite-size computations are performed on the carbon atoms of a C(60) Bucky ball and a piece of (3, 3) armchair cylindrical network, terminated by hydrogen atoms, while periodically boundary conditions are imposed on a (3, 3) nanotube unit cell. Sudden creation of the core state is simulated by replacing a 1s electron pair, localized at a central site of the structures, with the effective pseudo-potentials of both neutral and ionized atomic carbon. Excited states are obtained from the ground-state (occupied and empty) electronic structure of the ionized systems, and their overlaps with the ground state of the neutral systems are computed. These overlaps enter Fermi's golden rule, which is corrected with lifetime and finite-temperature effects to simulate the many-electron response of the nanoobjects. A model based on the linked cluster expansion of the vacuum persistence amplitude of the neutral systems, in a parametric core-hole perturbation, is developed and found to be reasonably consistent with the density functional theory method. The simulated spectrum of the fullerene molecule is found to be in good agreement with x-ray photoemission experiments on thick C(60) films, reproducing the low energy satellites at excitation energies below 4 eV within a peak position error of ca. 0.3 eV. The nanotube spectra show some common features within the same experiments and describe well the measured x-ray photoelectron lineshape from nanotube bundles with an average diameter of 1.2 nm.

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Let E/Q be an elliptic curve over the rational numbers. It is known, by the work of Bombieri and Zannier, that if E has full rational 2-torsion, the number N E (B) of rational points with Weil height bounded by B is exp O log B √ log log B. In this paper we exploit the method of descent via 2-isogeny to extend this result to elliptic curves with just one nontrivial rational 2-torsion point. Moreover, we make use of a result of Petsche to derive the stronger upper bound N E (B) = exp O log B log log B for these curves and to remove a deep transcendence theory ingredient from the proof.