## Transport

Electronic and thermal transport from first-principles: methodological developments and applications to characterize and engineer materials for next-generation technologies (electronics, energy-harvesting, phononics, ...).

## Members

Andrea Cepellotti (now at UC Berkeley)

Francesco Libbi (EPFL)

Nicola Marzari (EPFL)

Michele Simoncelli (EPFL)

Thibault Sohier (EPFL)

## Research:

**Electronic transport in the quantum regime, either in the ballistic (Landauer) formulation, or including electron-phonon interactions in the Keldysh formulation**: the new frontier of our research is to use the non equilibrium Green's function to study electronic transport under a fully quantum framework. The goal of the project is to characterize and improve new generation quantum devices, which are so small that not only the quantum mechanics nature of electrons needs to be taken into account, but also the quantum mechanics nature of the interactions with the environment.**Electronic transport in the semiclassical regime, combining first-principles scattering rates with the Boltzmann transport equation for the electrons:**we have first characterized [1,2,3] the electron–phonon intrinsic contribution to the electronic thermal resistivity of graphene as a function of doping using electronic and phonon dispersions and electron–phonon couplings calculated from first-principles at the level of density-functional theory and many-body perturbation theory (GW).**Ionic adsorption and electron transfer in the Marcus regime:**in the context of energy harvesting devices, the main ambition is to store a large amount of energy in the shortest time possible. Our current research is focused on redox-supercapacitiors, devices which combine two electrostatic energy storage mechanisms: redox electron transfer (as in batteries) and ionic adsorption (as in supercapacitors). We describe quantitatively the adsorption of ions by classical molecular dynamics simulations and electron transfer reactions using diabatic free-energy surfaces computed from ab initio molecular dynamics [4].**Heat transport in the semiclassical regime:**our work [5] concerns a reformulation of semiclassical transport in the basis of the scattering matrix eigenvectors (relaxons), that are identified as the exact carriers of heat (or any other semiclassical quantity obeying the linearized Boltzmann equation); this is especially relevant for the hydrodynamic conditions typical of 2D materials [6,7]. This breakthrough has exposed a plethora of novel phenomena, such as the heat friction [8] and wave-like heat conduction [9]. In particular, our paper [9] provides a firm mathematical and computational ground for the phenomenon of second sound.**Fundamental theory of heat transport in crystals and glasses:**in our last paper [10] we show that a general theory of heat conduction exists, encompassing the emergence and coexistence of all known vibrational excitations in crystal and glasses, and reducing to the Peierls’ phonon Boltzmann transport equation in the semi-classical limit of a simple crystal, or to the Allen-Feldman formulation in the case of a harmonic glass. We show how the two established heat conduction mechanisms — namely the propagation of vibrational waves in anharmonic crystals elucidated by Peierls [Ann. Phys. 395, 1055–1101 (1929)] and the coupling of vibrational modes in harmonic glasses introduced by Allen and Feldman [Phys. Rev. Lett. 62, 645–648 (1989)] — naturally emerge as limiting cases of this more general theory that is built upon the Wigner phase-space formulation of quantum mechanics.

## News

- 27/05/2019: Our work "Unified theory of thermal transport in crystals and glasses" [10] has been published in Nature Physics today!

## Publications

- [1] C. H. Park, N. Bonini, T. Sohier, G. Samsonidze, B. Kozinsky, M. Calandra, and N. Marzari, Electron–Phonon Interactions and the Intrinsic Electrical Resistivity of Graphene, Nano Lett., 14(3), 1113-1119 (2014).
- [2] T. Sohier, M. Calandra, C.H. Park, N. Bonini, N. Marzari, and F. Mauri, Phonon-limited resistivity of graphene by first-principles calculations: Electron-phonon interactions, strain-induced gauge field, and Boltzmann equation., Phys. Rev. B, 90(12), 125414 (2014).
- [3] T. Y. Kim, C.H. Park, and N. Marzari, The electronic thermal conductivity of graphene, Nano Lett. 16.4 2439-2443 (2016).
- [4] P. H.-L. Sit, M. Cococcioni, and N. Marzari, Realistic Quantitative Descriptions of Electron Transfer Reactions: Diabatic Free-Energy Surfaces from First-Principles Molecular Dynamics, Phys. Rev. Lett. 97, 028303 (2006).
- [5] A. Cepellotti and N. Marzari, Thermal Transport in Crystals as a Kinetic Theory of Relaxons, Phys. Rev. X 6, 041013 (2016).
- [6] G. Fugallo, A. Cepellotti, L. Paulatto, M. Lazzeri, N. Marzari, and F. Mauri, Thermal conductivity of graphene and graphite: collective excitations and mean free paths, Nano Lett., 14(11), 6109-6114 (2014).
- [7] A. Cepellotti, G. Fugallo, L. Paulatto, M. Lazzeri, F. Mauri, and N. Marzari, Phonon hydrodynamics in two-dimensional materials Nature communications, 6, 6400 (2015).
- [8] A. Cepellotti and N. Marzari, Boltzmann Transport in Nanostructures as a Friction Effect, Nano Lett., 17 (8), 4675–4682 (2017).
- [9] A. Cepellotti and N. Marzari, Transport waves as crystal excitations, Phys. Rev. Materials 1, 045406 (2017).
- [10] M. Simoncelli, N. Marzari, & F. Mauri, Unified theory of thermal transport in crystals and glasses, Nature Physics, (2019).