  The superconducting proximity effect on two-dimensional massless Dirac
electrons is usually analyzed using a simple model consisting of the Dirac
Hamiltonian and an energy-independent pair potential. Although this
conventional model is plausible, it is questionable whether it can fully
describe the proximity effect from a superconductor. Here, we derive a more
general proximity model starting from an appropriate microscopic model for the
Dirac electron system in planar contact with a superconductor. The resulting
model describes the proximity effect in terms of the energy-dependent pair
potential and renormalization term. Within this framework, we analyze the
density of states, the quasiparticle wave function, and the charge conservation
of Dirac electrons. The result reveals several characteristic features of the
proximity effect, which cannot be captured within the conventional model.
