Pairing symmetries in the Zeeman-coupled extended attractive Hubbard model

By introducing the possibility of equal- and opposite-spin pairings concurrently, we show that the ground state of the extended attractive Hubbard model (EAHM) exhibits rich phase diagrams with a variety of singlet, triplet, and mixed parity superconducting orders. We study the competition between these superconducting pairing symmetries invoking an unrestricted Hartree–Fock–Bogoliubov–de Gennes (HFBdG) mean-field approach, and we use the d-vector formalism to characterize the nature of the stabilized superconducting orders. We discover that, while all other types of orders are suppressed, a non-unitary triplet order dominates the phase space in the presence of an in-plane external magnetic field. We also find a transition between a non-unitary to unitary superconducting phase driven by the change in average electron density. Our results serve as a reference for identifying and understanding the nature of superconductivity based on the symmetries of the pairing correlations. The results further highlight that EAHM is a suitable effective model for describing most of the pairing symmetries discovered in different materials.

Geometrical prediction of cleavage planes in crystal structures

Cleavage is the ability of single crystals to split easily along specifically oriented planes. This phenomenon is of great interest for materials' scientists. Acquiring the data regarding cleavage is essential for the understanding of brittle fracture, plasticity and strength, as well as for the prevention of catastrophic device failures. Unfortunately, theoretical calculations of cleavage energy are demanding and often unsuitable for high-throughput searches of cleavage planes in arbitrary crystal structures. A simplified geometrical approach (GALOCS = gaps locations in crystal structures) is suggested for predicting the most promising cleavage planes. GALOCS enumerates all the possible reticular lattice planes and calculates the plane-average electron density as a function of the position of the planes in the unit cell. The assessment of the cleavage ability of the planes is based on the width and depth of planar gaps in crystal structures, which appear when observing the planes lengthwise. The method is demonstrated on two-dimensional graphene and three-dimensional silicon, quartz and LiNbO3 structures. A summary of planar gaps in a few more inorganic crystal structures is also presented.

Exploring the epoch of hydrogen reionization using FRBs

We describe three different methods for exploring the hydrogen reionization epoch using fast radio bursts (FRBs) and provide arguments for the existence of FRBs at high redshift (z). The simplest way, observationally, is to determine the maximum dispersion measure (DMmax) of FRBs for an ensemble that includes bursts during the reionization. The DMmax provides information regarding reionization much like the optical depth of the CMB to Thomson scattering does, and it has the potential to be more accurate than constraints from Planck, if DMmax can be measured to a precision better than 500 pccm−3. Another method is to measure redshifts of about 40 FRBs between z of 6-10 with$\sim 10\%$ accuracy to obtain the average electron density in 4 different z-bins with $\sim 4\%$ accuracy. These two methods don’t require knowledge of the FRB luminosity function and its possible redshift evolution. Finally, we show that the reionization history is reflected in the number of FRBs per unit DM, given a fluence limited survey of FRBs that includes bursts during the reionization epoch; we show using FIRE simulations that the contributions to DM from the FRB host galaxy & CGM during the reionization era is a small fraction of the observed DM. This third method requires no redshift information but does require knowledge of the FRB luminosity function.

Atomic and molecular properties of nonclassical bioisosteric replacements of the carboxylic acid group

Aim: Drug design is fraught with challenges as small differences in the structure of a drug molecule can significantly affect its biological activity. Bioisosteres are interchangeably used to adjust pharmacokinetic and pharmacodynamic properties without affecting the biological activity of the drug. While electrostatic potential maps (EPMs) are typically used to show the similarity in the ‘key & lock’ interactions between a drug and its receptor, they are limited to qualitative comparisons. Methodology & results: Using the quantum theory of atoms in molecules, quantitative similarities among nonclassical bioisosteres of carboxylic acid were evaluated. Conclusion: The similarity in the bioisosteric groups was captured with the average electron density tool which generated remarkably close average electron densities regardless of the capping group, the isodensity values or the protonation state of the molecule. The similarities among bioisosteres was less obvious using the EPM tool.

X-ray phase determination by the principle of minimum charge

When the electron density in a crystal or a quasicrystal is reconstructed from its Fourier modes, the global minimum value of the density is sensitively dependent on the relative phases of the modes. The set of phases that maximizes the value of the global minimum corresponds, by positivity of the density, to the density having the minimum total charge that is consistent with the measured Fourier amplitudes. Phases that minimize the total electronic charge (i.e. the average electron density) have the additional property that the lowest minima of the electron density become exactly degenerate and proliferate within the unit cell. The large number of degenerate minima have the effect that density maxima are forced to occupy ever smaller regions of the unit cell. Thus, by minimization of the electronic charge, the atomicity of the electron density is enhanced as well. Charge minimization applied to simulated crystalline and quasicrystalline diffraction data successfully reproduces the correct phases starting from random initial phases.