# IBM Research Award 2017 - Andrea Cepellotti

Thermal Transport in Low Dimensions, EPFL thesis n°6950 (2016)

Thesis director: Prof. N. Marzari

*"For the discovery of novel exact solutions to the linearized Boltzmann transport equation, and for their application to thermal transport in low dimensional materials."*

The thermal conductivity of insulating crystals originates from the energy transfer through lattice vibrations. Since the pioneering work of Peierls, the prevalent hypothesis is that phonons are the heat carriers, despite some notable shortcomings. For example, in materials of reduced dimensionality or at cryogenic temperatures, the scattering dynamics is dominated by momentum conserving – normal – processes, as opposed to momentum dissipating – Umklapp – processes. Under these circumstances, heat flux is not lost at every scattering event; instead, it is shuttled through multiple phonon states, coupling them and originating unexpected behaviors.

In this Thesis, we proposed that exotic phenomena take place in 2D materials, such as the failure of Fourier’s law and second sound, where temperature propagates as a wave. We rationalised these behaviors introducing the notion of collective phonon excitations, called ‘relaxons’. Defined as the eigenvectors of the scattering matrix, relaxons allow for a simple - yet exact - interpretation of thermal conductivity in terms of a kinetic gas theory, where the relevant gas is made of such relaxons, the true heat carriers, and not phonons. These considerations revise the relevant time and length scale of heat flux dissipation, and provide a new viewpoint on semiclassical transport theories.