PY-Nodes: An ab-initio python code for searching nodes in a material using Nelder-Mead's simplex approach

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With the discovery of topological semimetals, it has been found that the band touching points near the Fermi level are of great importance. They give rise to many exciting phenomena in these materials. Moreover, these points, commonly known as nodes, are related to several properties of these semimetals. Thus, the proper estimation of their coordinates is extremely needed for better understanding of the properties of these materials. We have designed a Python 3 based code named PY-Nodes for efficiently finding the nodes present in a given material using first-principle approach. The present version of the code is interfaced with the WIEN2k package. For benchmarking the code, it has been tested on some famous materials that possess characteristic nodes. These include – TaAs, a well-known Weyl semimetal, Na3Bi, which is categorized as Dirac semimetal, CaAgAs, classified as a nodal-line semimetal and YAuPb, which is claimed to be non-trivial topological semimetal. In the case of TaAs, 24 nodes are obtained from our calculations. On computing their chiralities, it is found that 12 pairs of nodes having equal and opposite chirality are obtained. Furthermore, for Na3Bi, a pair of nodes are obtained on either side of the Γ-point in the k3 direction. In the case of CaAgAs, several nodes are obtained in the kz=0 plane. These nodes, when plotted in the kx-ky plane, form a closed loop which is generally referred to as a nodal-line. Finally, in the case of YAuPb, large number of nodes are obtained in the vicinity of Γ-point. The results obtained for these materials are in good match with the previous works carried out by different research groups. This assures the reliability and efficiency of the PY-Nodes code for estimating the nodes present in a given material. Program summaryProgram Title: PY-NodesCPC Library link to program files:https://doi.org/10.17632/m97syc9rth.1Licensing provisions: GNU General Public License 3.0Programming language: Python 3External routines/libraries: Math, TimeNature of problem: Searching for the node points corresponding to any given number of bands present in the first Brillouin zone of any material.Solution method: Nelder-Mead's simplex approach is a well-known function-minimization method. This approach is used to minimize the function f(k), which is defined as sum of the absolute energy difference of the adjacent pairs of bands at a given k-point. The local minima will correspond to the node points present in the material.