Real-life performance of semiconductors and metals, whether it being in one, two, or three dimensions, is often limited by carrier scattering by phonons. The mobility of charge is a key parameter in the semiconductor industry to describe the electrical performance and the movement under applied electric fields. The traditional approach to calculate phonon-limited mobilities is based on the Boltzmann transport equation in combination with the effective mass approximation and empirical deformation potentials. Recently, predictive parameter-free mobility calculations have been carried out at the density functional theory (DFT) level for the electron-phonon coupling (EPC) [1-6].

EPC may also lead to a Bose-Einstein condensation of electrons near the Fermi surface as Cooper pairs, resulting in conventional superconductivity at sufficiently low temperatures. Also here DFT calculations of EPC have explained the origin of superconductivity in a range of materials and provided quantitative estimates for the critical temperature using Migdal-Eliashberg theory [7-8]. A recent example includes first-principles theory that revealed how high-pressure hydrogen sulfide is a strongly anharmonic superconductor [9].

In a different context, the introduction of Inelastic Electron Tunneling Spectroscopy together with STM/AFM scanning probe techniques have opened up the possibility to study adsorbates with unprecedented resolution and to characterize inelastic scattering against vibrations down to the single-molecule limit. Ab-initio approaches based on DFT and nonequilibrium Green’s functions (NEGF) have been developed to describe the EPC in such nanoscale junctions and to explain the inelastic transport characteristics [10-12].

Despite the common origin of EPC in these three distinct phenomena (phonon-limited resistivity, phonon-mediated superconductivity and IETS) the systems have traditionally been considered separately by different researchers and with different ab initio methods. In this workshop we propose to convene researchers interested in such EPC physics with the view to foster exchange between people with different approaches and methods.

Some key questions for the discussions would be:
· Ab-initio modelling of EPC in 3D materials: How to deal with the computational complexities of very large systems, such as explicit systems with explicit dopants, layered heterostructures, or organic molecular compounds?
. What are the advantages and limitations of currently available calculational schemes? How can scalability issues and applications to novel materials be addressed?
. Harmonic theory is often applied, but what are the impacts and signatures of anharmonicity in EPC in the derived phenomena (resistivity, superconductivity and IETS)?
. Prospects for a first-principles theory of driven BCS superconductivity?
· Beyond the Boltzmann approach: What can NEGF offer for mobility calculations? Which systems would be prone to interference effects that are beyond a semiclassical description? How to address the high-bias regime?
. How can existing ab initio IETS theory be developed further to describe interfaces and excitation of delocalized phonons?