by not only targeting reductions in thermal conductivity, but simultaneous improvements in the power factor as well.'
author:
- Vassilios Vargiamidis
- Neophytos Neophytou
title: |
    Hierarchical nanostructuring approaches for thermoelectric materials\
    with high power factors
---

Introduction
============

Thermoelectric (TE) materials convert heat from temperature gradients into electricity and vice versa. Their performance is quantified by the dimensionless figure of merit $ZT = \sigma S^2 T / (\kappa_{\text{e}} + \kappa_{\ell})$ where $\sigma$ is the electrical conductivity, $S$ is the Seebeck coefficient, $T$ is the operating temperature, $\kappa_e$ is the electronic thermal conductivity, and $\kappa_\ell$ is the lattice thermal conductivity. The product $\sigma S^2$ is known as the power factor ($PF$). Traditional TE materials, which are mostly semiconductor doped alloys of Sb and Bi$_2$Te$_3$ at room temperature, and PbTe or SiGe at higher temperatures, reach $ZT \approx 1$. Over the last several years, however, numerous other materials have been explored, such as transition-metal dichalcogenides (TMDC) [@GDing16; @HHuang16; @WHuang14], skutterudites [@YTang15ncom; @YTang15nmat], phonon-glass-electron crystal structures [@Beek15nmat], half-Heuslers [@Stern16ntech; @CFu15ncom], oxides [@YYin17], etc. A large number of these materials demonstrate $ZT$ above $1$, primarily due to the reduction of their thermal conductivity [@Beretta19].

In order to achieve even further reductions in thermal 