Abstract
The quest to create superconductors with higher transition temperatures is as old as superconductivity itself. One strategy, popular after the realization that (conventional) superconductivity is mediated by phonons, is to chemically combine different elements within the crystalline unit cell to maximize the electron-phonon coupling. This led to the discovery of NbTi and Nb_33Sn, to name just the most technologically relevant examples. Here, we propose a radically different approach to transform a ‘pristine’ material into a better (meta-) superconductor by making use of modern fabrication techniques: designing and engineering the electronic properties of thin films via periodic patterning on the nanoscale. We present a model calculation to explore the key effects of different supercells that could be fabricated using nanofabrication or deliberate lattice mismatch, and demonstrate that specific pattern will enhance the coupling and the transition temperature. We also discuss how numerical methods could predict the correct design parameters to improve superconductivity in materials including Al, NbTi, and MgB_22.
Highlights
Conventional — i.e., phonon-mediated — superconductors include many elemental metals with transition temperatures between 1K and 10K, simple alloys like NbTi and Nb3Sn with transition temperatures up to ∼20K, and MgB2 with a record transition temperature of 39K at ambient pressure [1]
The effort to improve the quality of these conventional superconductors for applications has all but stopped with the discovery of high-temperature superconductors [2,3,4]
The strategy we propose here is similar to creating new superconductors by chemically changing their unit cell as it has been done mainly in the middle of the 20th century [3], but approaching instead from the long-range limit, as current nanofabrication already allows structures of roughly 5 to 50 unit cells [8,9,10,11,12,13,14,15]
Summary
In this Appendix, we describe in more detail our model calculation for a square lattice with a nano-patterned supercell. For illustration and for comparison, we first consider the model for the pristine material with the coupling matrix element gk0q, the resulting coupling constant λ, and the transition temperature Tc. 2. We model the supercell by setting the electron hopping to zero to the sites that are part of the hole, and find the new basis in which the electron Hamiltonian is diagonal. 3. We take the pristine interaction Hamiltonian, but replace the original electron operators by the new basis. We take the pristine interaction Hamiltonian, but replace the original electron operators by the new basis This allows us to obtain the new interaction matrix element gKνqν between the new eigenstates. 4. We calculate the coupling constants λ from the new interaction matrix elements and electron dispersions
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