# Dresden 2014 – wissenschaftliches Programm

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# HL: Fachverband Halbleiterphysik

## HL 27: Frontiers of electronic structure theory - Non-equilibrium phenomena at the nano-scale II (organized by O)

### HL 27.4: Vortrag

### Montag, 31. März 2014, 17:00–17:15, TRE Ma

**Breakdown of Fourier law in layered materials** — •Andrea Cepellotti^{1}, Giorgia Fugallo^{2}, Francesco Mauri^{3}, and Nicola Marzari^{1} — ^{1}THEOS, École Polytechnique Fédérale, Lausanne — ^{2}IMPMC, Universite Pierre et Marie Curie, Paris — ^{3}LSI, École Polytechnique, Paris

We compute the thermal conductivity in crystalline layered materials by solving the Boltzmann Transport Equation (BTE) for phonons [1], with the phonon-phonon collision rates obtained from density-functional perturbation theory. We find that in 2D materials, such as graphene and related compounds, and even in 3D layered materials, like bulk graphite, the single-mode relaxation time approximation (SMRTA) cannot describe heat transport correctly, underestimating by one order of magnitude or more thermal conductivities and phonons’ mean free paths. Instead, we show that the exact self-consistent solution of the BTE provides results in excellent agreement with experimental measurements [2]. The shortcomings of the SMRTA lie in the assumption that heat flow is transferred only by individual phonon excitations, whereas in layered materials the transport can only be explained in terms of collective phonon excitations. The characteristic length of these collective excitations is often comparable with that of the experimental sample - as a result, Fourier’s law become questionable, since its statistical nature makes it applicable only to systems larger than a few mean free paths.

[1] G. Fugallo et al., Phys. Rev. B, **88**, 045430 (2013).

[2] A. A. Balandin, Nat. Mater. **10**, 569 (2011).