Enhanced Cooper pairing in nanopatterned metals

Nanopatterning has been shown to be a powerful tool for manipulating the vibrational modes of elastic structures, with applications such as optical-mechanical mode coupling. Inspired by these recent developments in phononic band engineering, we propose a nanopatterning scheme to enhance the superconducting transition temperature ${T}_{c}$ in phonon-mediated nanofilm superconductors, such as aluminum. Using the finite element method, we simulate the lattice vibrational modes of nanopatterned films within the Debye model. Our results show that periodic nanopatterning softens the lattice vibrational modes compared to bulk films. It also increases the density of states at high energies, resulting in a couple of percent enhancement in ${T}_{c}$. Moreover, we investigate connections to Weyl's law and provide an experimental design prescription to optimize nanopatterning for further enhancement of the superconducting transition temperature.