By combining first-principles simulations including an on-site Coulomb repulsion term and Boltzmann theory, we demonstrate how the interplay of quantum confinement and epitaxial strain allows to selectively design $n$- and $p$-type thermoelectric response in (LaNiO$_3$)$_3$/(LaAlO$_3$)$_1(001)$ superlattices. In particular, varying strain from $-4.9$ to $+2.9%$ tunes the Ni orbital polarization at the interfaces from $-6$ to $+3%$. This is caused by an electron redistribution among Ni $3d_{x^2-y^2}$- and $3d_{z^2}$-derived quantum well states which respond differently to strain. Owing to this charge transfer, the position of emerging cross-plane transport resonances can be tuned relative to the Fermi energy. Already for moderate values of $1.5$ and $2.8%$ compressive strain, the cross-plane Seebeck coefficient reaches $sim -60$ and $+100$ $mu$V/K around room temperature, respectively. This provides a novel mechanism to tailor thermoelectric materials.
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