Possible pairing symmetries in SrPtAs with a local lack of inversion center

We discuss possible pairing symmetries in the hexagonal pnictide superconductor SrPtAs. The local lack of inversion symmetry of the two distinct conducting layers in the unit cell results in a special spin-orbit coupling with a staggered structure. We classify the pairing symmetry by the global crystal point group D_3d, and suggest some candidates for the stable state using a tight-binding model with an in-plane, density-density type pairing interaction. We may have some unconventional states like s+f-wave and a mixture of chiral d-wave and chiral p-wave. The spin orbit coupling is larger than the interlayer hopping, and the mixing between spin-singlet and triplet states can be seen in spite of the fact that the system has a global inversion center.Comment: 5 pages, 3 figure

Efficient Learning of a One-dimensional Density Functional Theory

Density functional theory underlies the most successful and widely used numerical methods for electronic structure prediction of solids. However, it has the fundamental shortcoming that the universal density functional is unknown. In addition, the computational result---energy and charge density distribution of the ground state---is useful for electronic properties of solids mostly when reduced to a band structure interpretation based on the Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can help to free density functional theory from these limitations. We study a theory of spinless fermions on a one-dimensional lattice. The density functional is implicitly represented by a neural network, which predicts, besides the ground-state energy and density distribution, density-density correlation functions. At no point do we require a band structure interpretation. The training data, obtained via exact diagonalization, feeds into a learning scheme inspired by active learning, which minimizes the computational costs for data generation. We show that the network results are of high quantitative accuracy and, despite learning on random potentials, capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi

Creating better superconductors by periodic nanopatterning

The quest to create superconductors with higher transition temperatures is as old as superconductivity itself. One strategy, popular after the realization that (conventional) superconductivity is mediated by phonons, is to chemically combine different elements within the crystalline unit cell to maximize the electron-phonon coupling. This led to the discovery of NbTi and Nb3Sn, to name just the most technologically relevant examples. Here, we propose a radically different approach to transform a `pristine' material into a better (meta-) superconductor by making use of modern fabrication techniques: designing and engineering the electronic properties of thin films via periodic patterning on the nanoscale. We present a model calculation to explore the key effects of different supercells that could be fabricated using nanofabrication or deliberate lattice mismatch, and demonstrate that specific pattern will enhance the coupling and the transition temperature. We also discuss how numerical methods could predict the correct design parameters to improve superconductivity in materials including Al, NbTi, and MgB