Thermoelectric materials convert heat into electricity or vice versa through a solid-state process. For the conversion efficiency to be competitive with fluid-based technologies, a thermoelectric material must be a good insulator of heat while, simultaneously, exhibit good electrical properties‒a combination that is hard to find in common materials. Here we present the concept of a locally resonant nanophononic metamaterial (NPM) [1-3] to overcome this natural properties trade-off. One realization of an NPM is a freestanding silicon membrane (thin film) with a periodic array of nanoscale pillars erected on one or both free surfaces. Heat is transported along the membrane portion of this nanostructured material as a succession of propagating vibrational waves, phonons. The atoms making up the minuscule pillars on their part generate stationary vibrational waves, which we describe as vibrons. These two types of waves linearly interact causing a mode coupling for each pair which appears as an avoided crossing in the pillared membrane’s phonon band structure. This in turn (1) enables the generation of new modes localized in the nanopillar portion(s) and (2) reduces the base membrane phonon group velocities around the coupling regions. These two effects in tandem cause a reduction in the in-plane thermal conductivity of the underlying membrane. Given that the number of vibrons scales with the number of degrees of freedom of a nanopillar, this effect intensifies as the size of the nanopillar(s) increases, and in principle may be tuned to influence the entire phonon spectrum (which for silicon extends up to over 17 THz). This novel phenomenon thus provides an opportunity for achieving exceptionally strong reductions in the thermal conductivity. Furthermore, since the mechanisms concerned with the generation and carrying of electrical charge are practically independent of the phonon-vibron couplings, the Seebeck coefficient and the electrical conductivity are at most only mildly affected, if not at all. In this talk, I will introduce the concept of an NMP and present thermal conductivity predictions using lattice-dynamics-based calculations and molecular dynamics simulations as well as preliminary electrical properties predictions using density functional theory. In conclusion, projections of record-breaking values of the thermoelectric energy conversion figure of merit ZT will be provided.

[1] Davis, B.L. and Hussein, M.I., Phys. Rev. Lett. 112, 055505, 2014.

[2] Honarvar, H. and Hussein, M.I., Phys. Rev. B. 93, 081412(R), 2016.

[3] Honarvar, H., Yang, L. and and Hussein, M.I., Appl. Phys. Lett. 108, 263101, 2016.

### Applied Math and Comp Sci Colloquium

Friday, September 22, 2017 - 2:00pm

#### Mahmoud Hussein

University of Colorado, Boulder