Measuring electron-phonon coupling with Scanning Tunneling Microscopy

Electron-boson interactions are~ubiquitous in systems ranging from simple metals to novel materials such as graphene, high-temperature superconductors and topological insulators. Of particular interest is the coupling between electrons and phonons. In general, electron-phonon coupling gives rise to quasiparticles of decreased mobility and increased effective mass. Nearly all information about electron-phonon coupling is contained in the Eliashberg function ($\alpha^{2}F(\omega ;k,E)) $of the material. In this talk I discuss the various methods by which the effects of electron-phonon coupling can be measured by scanning tunneling microscopy. I will present STM data on a variety of systems ranging from metals to topological insulators and discuss the signatures of electron-phonon interactions in different types of STM data. In particular I discuss how high resolution measurements allow us to measure the dispersion and obtain the real part of the self-energy, which can in principle be inverted to obtain the Eliashberg function.