Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this paper, we demonstrate that PH can be used as a universal framework to identify phases of classical spins on a lattice. This demonstration includes hidden order such as spin-nematic ordering and spin liquids. By converting a small number of spin configurations to barcodes we obtain a descriptive picture of configuration space. Using dimensionality reduction to reduce the barcode space to color space leads to a visualization of the phase diagram.

Dirac and Weyl point- and line-node semimetals are characterized by a zero band gap with simultaneously vanishing density of states. Given a sufficient interaction strength, such materials can undergo an interaction instability, e.g., into an excitonic insulator phase. Due to generically flatbands, organic crystals represent a promising materials class in this regard. We combine machine learning, density functional theory, and effective models to identify specific example materials. Without taking into account the effect of many-body interactions, we found the organic charge transfer salts [bis(3,4-diiodo-3',4'-ethyleneditio-tetrathiafulvalene), 2,3-dichloro-5,6-dicyanobenzoquinone, acetenitrile] [(EDT-TTF-I-2)(2)](DDQ)center dot(CH3CN) and 2, 2', 5, 5'-tetraselenafulvalene-7, 7, 8, 8-tetracyano-p-quinodimethane (TSeF-TCNQ) and a bis-1,2,3-dithiazolyl radical conductor to exhibit a semimetallic phase in our ab initio calculations. Adding the effect of strong particle-hole interactions for (EDT-TTF-I-2)(2)(DDQ)center dot(CH3CN) and TSeF-TCNQ opens an excitonic gap on the order of 60 and 100 meV, which is in good agreement with previous experiments on these materials.

We study the mass fluctuations in gapped Dirac materials by treating the mass term as both a continuous and discrete random variable. Gapped Dirac materials were proposed to be used as materials for dark-matter sensors. One thus would need to estimate the role of disorder and fluctuations on the interband absorption of dark matter. We find that both continuous and discrete fluctuations across the sample introduce tails (e.g., Dirac-Lifshitz tails) in the density of states and the interband absorption rate. We estimate the strength of the gap filling and discuss implications of these fluctuations on the performance as sensors for dark matter detection. The approach used in this work provides a basic framework to model the disorder by any arbitrary mechanism on the interband absorption of Dirac material sensors.

Machine-learning models are capable of capturing the structure-property relationship from a dataset of computationally demanding ab initio calculations. Over the past two years, the Organic Materials Database (OMDB) has hosted a growing number of calculated electronic properties of previously synthesized organic crystal structures. The complexity of the organic crystals contained within the OMDB, which have on average 82 atoms per unit cell, makes this database a challenging platform for machine learning applications. In this paper, the focus is on predicting the band gap which represents one of the basic properties of a crystalline material. With this aim, a consistent dataset of 12 500 crystal structures and their corresponding DFT band gap are released, freely available for download at https://omdb.mathub.io/dataset. An ensemble of two state-of-the-art models reach a mean absolute error (MAE) of 0.388 eV, which corresponds to a percentage error of 13% for an average band gap of 3.05 eV. Finally, the trained models are employed to predict the band gap for 260 092 materials contained within the Crystallography Open Database (COD) and made available online so that the predictions can be obtained for any arbitrary crystal structure uploaded by a user.

Dark Matter particles are commonly assumed to be weakly interacting massive particles (WIMPs) with a mass in the GeV to TeV range. However, recent interest has shifted toward lighter WIMPs, which are more difficult to probe experimentally. A detection of sub-GeV WIMPs will require the use of small gap materials in sensors. Using recent estimates of the WIMP mass, we identify the relevant target space toward small gap materials (100 to 10 meV). Dirac Materials, a class of small- or zero-gap materials, emerge as natural candidates for sensors for Dark Matter detection. We propose the use of informatics tools to rapidly assay materials band structures to search for small gap semiconductors and semimetals, rather than focusing on a few preselected compounds. As a specific example of the proposed strategy, we use the organic materials database () to identify organic candidates for sensors: the narrow band gap semiconductors BNQ-TTF and DEBTTT with gaps of 40 and 38 meV, and the Dirac-line semimetal (BEDT-TTF)center dot Br which exhibits a tiny gap of approximate to 50 meV when spin-orbit coupling is included. We outline a novel and powerful approach to search for dark matter detection sensor materials by means of a rapid assay of materials using informatics tools.

Many functional materials can be characterized by a specific pattern in their electronic band structure, for example, Dirac materials, characterized by a linear crossing of bands; topological insulators, characterized by a "Mexican hat" pattern or an effectively free electron gas, characterized by a parabolic dispersion. To find material realizations of these features, manual inspection of electronic band structures represents a relatively easy task for a small number of materials. However, the growing amount of data contained within modern electronic band structure databases makes this approach impracticable. To address this problem, we present an automatic graphical pattern search tool implemented for the electronic band structures contained within the Organic Materials Database. The tool is capable of finding user-specified graphical patterns in the collection of thousands of band structures from high-throughput calculations in the online regime. Using this tool, it only takes a few seconds to find an arbitrary graphical pattern within the ten electronic bands near the Fermi level for 26,739 organic crystals. The source code of the developed tool is freely available and can be adapted to any other electronic band structure database.