Résumé
Progress in the fabrication and characterisation low dimensional materials brings new perspectives in condensed matter physics and vast technological opportunities. It also raises new questions on the effects of dimensionality. Our understanding of materials properties relies on the intrinsic quasiparticles of a periodic structure: electrons and phonons. The electron-phonon interaction is thus a fundamental component of condensed matter, and it plays a key role in spectroscopy, electron and heat transport, as well as superconductivity. It is discussed from a modelling and simulation perspective, with a focus on the consequences of reduced dimensions. Mostly 2D and 1D systems are considered, such that the crystal retains some degree of periodicity. Various effects are discussed, from the modification of the joint density of states to more fundamental changes in the nature and behaviour of the electron-phonon interaction itself. Phonons with atomic displacements in the non-periodic direction are obviously specific to low dimensional systems. Because they involve long-range Coulomb interactions, polar phonons are also strongly modified, both in their dispersion (LO-TO splitting) and their coupling to electrons (Fröhlich interaction).A powerful feature of low-dimensional materials is the ability to use the available space in the non-periodic direction to place other materials of device components that will tune the electron-phonon properties of the system. For example, as routinely done in experiments, a gate can be placed around 2D materials to induce large variations in the carrier density. It is then essential to understand the consequences of this electrostatic doping on the electron-phonon interaction. Finally, the emergence remote interactions between electrons and phonons in different components of van der Waals heterostructures will be discussed.