We analyze the onset of superconductivity, in a type II superconductor adjacent to a normal material, via a generalized Ginzburg–Landau energy functional, which models the effects of superconducting electron pairs diffusing into the normal part. We consider a superconductor and a normal material, each filling a half-space, in the presence of a constant magnetic field parallel to their interface. Among other results, we show that if the normal state conductivity of the superconductor is less than or equal to the conductivity of the normal material, then normal states are the only global minimizers down to the second critical field $H_{c_2}$. Hence, we analytically confirm experimental predictions that surface superconductivity may be suppressed by coating a superconductor with a normal metal.