Abstract
Quantitative prediction of the gap behavior via first-principles calculations has thus far been restricted to temperature dependence. Here, we present a gap equation developed based on the current-density functional theory for superconductors. This equation is applicable to superconductors immersed in a magnetic field and enables us to quantitatively describe the magnetic-field and temperature dependence of the superconducting gap. We also develop a practical scheme in which the gap equation is solved simultaneously with a proposed relation between the energy gain of the superconducting state at zero magnetic field and that at a finite magnetic field. The presented scheme is applied to aluminum immersed in a magnetic field, and successfully reveals the temperature and magnetic-field dependences of the superconducting gap. The critical magnetic field thus obtained shows good agreement with experimental results.
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