ELEPHANT · First-principles modelling of electron-phonon anisotropy (ELE-PH-ANT) in low-dimensional superconductors

First-principles modelling of electron-phonon anisotropy (ELE-PH-ANT) in low-dimensional superconductors

Prediction of key superconducting properties, such as the critical temperature and the superconducting energy gap remains one of the outstanding challenges in modern electronic structure theory. Owing to the complex nature of the superconducting state, a quantitative understanding of the pairing mechanism in conventional superconductors requires a very detailed knowledge of the electronic structure, the phonon dispersions, and the interaction between electrons and phonons. Up till now, estimation of the critical temperature in conventional superconductors has been done primarily with the semi-empirical McMillan's approach. This approximation relies on the average strength of the electron-phonon coupling making it unsuitable for studying emerging classes of layered and low-dimensional superconductors. The main objective of the project was to develop a computational method which combines the anisotropic Migdal-Eliashberg formalism with electron-phonon interpolation based on maximally-localised Wannier functions. This first objective was achieved within the first year of the fellowship. During this period the Migdal-Eliashberg formalism was implemented on top of the Wannier-function methodology for the study of the electron-phonon interaction existent within the EPW code (see http://epw.org.uk online for further details). EPW is a Fortran90 / MPI programme that comprises about 15 000 lines of code, a third of which was developed within this project. The new computational method enables calculations of the momentum and band-resolved superconducting gap both effectively and accurately using a fine description of electron-phonon scattering processes on the Fermi surface. This implementation allows EPW users to study complex superconductors, such as layered materials, low-dimensional materials, and materials with multiple Fermi surface sheets with unprecedented accuracy, and is certainly an important step forward towards systematic ab initio studies of high-temperature superconductors. Once successfully implemented, the developed computational methodology was tested in the case of two representative superconductors, namely lead and magnesium diboride. This study, published in Physics Review B, validated the approach against previous first-principles calculations, as well as experimental results. The new computational tool is currently used to investigate systems with reduced dimensionality with potential for superconductivity. These studies are in their final stage and will be submitted within the next few months. During the Marie Curie Fellowship, Roxana Margine also worked on two collaborative projects at the University of Oxford. Using her expertise in carbon nanomaterials, she conducted joint work within the Department of Materials on the characterisation of a defect dynamics in graphene. She also became familiar with state-of-the art compound prediction techniques based on the use of genetic algorithms and had the opportunity to take part in four experiments at the Diamond Light Source synchrotron on synthesis and characterisation of a new complex CaB6 compound under extreme pressures (up to 44 GPa) and temperatures. The two collaborative studies were published in Science and Physics Review Letters., respectively. The significant impact of EPW stems from the fact that it implements a cutting-edge computation method for superconductivity research which is absent in standard ab initio packages. The computer code developed within this Marie Curie Fellowship was designed as a post-processing module and interfaced with a major open-source European first principles package 'Quantum-ESPRESSO'. Furthermore, this code will be released under the GNU General Public License, thereby enabling other researchers in the field to directly benefit from the outcomes of this Marie Curie Fellowship. Therefore, the fundamental knowledge acquired in this research is expected to make an important contribution to superconductivity research and have a long-lasting impact on European technological research and development.

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