  The effect of biaxial strain on the superconducting properties of MgB2 thin
films was studied by first-principles calculations. The stability analyses by
phonon dispersions show that biaxial strain as much as 7% can be applied onto
MgB2 without inducing any imaginary frequency. The superconducting property
calculations based on the frame of Migdal-Eliashberg theory successfully
reproduce the two-gap superconductivity of MgB2. The results show that the
tensile biaxial strain can increase the critical temperature of MgB2 while the
compressive biaxial strain would decrease the critical temperature. The
detailed microscopic mechanism of the biaxial strain effect on the
superconducting properties was studied by calculations of electronic structures
and phonon dispersions. The increased Tc is a combining result of the increased
electron density at the Fermi level and the in-plane boron phonon softening. By
means of high-throughput screening of proper substrates, it is found that most
of the substrates would result in tensile strain in MgB2 film, which is in
agreement with many experimental works. The results in this work provide
detailed understanding of the biaxial strain engineering mechanism and
demonstrate that biaxial strain engineering can be an effective way of tuning
the superconducting properties of MgB2 and other similar materials.
