  We show that the current-density functional theory for superconductors
(sc-CDFT) can describe the magnetic-field-induced first-order phase transition
of aluminum from a superconducting state to a normal state. This is
accomplished by introducing a model for the magnetic field dependence of the
attractive interaction between superconducting electrons. This model states
that the surface potential well produced by the penetrating magnetic field
leads to the magnetic field dependence of the attractive interaction.
Specifically, the electron density near the surface increases with the magnetic
field due to the surface potential well, which causes the reduction in the
attractive interaction due to the screening effect. We also develop the
calculation scheme to solve the gap equation of the sc-CDFT with taking into
account the magnetic field dependence of the attractive interaction. It is
shown that calculation results of the magnetic field dependence of the
superconducting gap are in good agreement with experimental results of the
first-order phase transition.
