  Odd-frequency superconductivity is an exotic superconducting state in which
the symmetry of the gap function is odd in frequency. Here we show that an
inherent odd-frequency mode emerges dynamically under application of a Lorentz
transformation of the anomalous Green function with the general
frequency-dependent gap function. To see this, we consider a Dirac model with
quartic potential and perform a mean-field analysis to obtain a relativistic
Bogoliubov-de Gennes system. Solving the resulting Gor'kov equations yields
expressions for relativistic normal and anomalous Green functions. The form of
the relativistically invariant pairing term is chosen such that it reduces to
BCS form in the non-relativistic limit. We choose an ansatz for the gap
function in a particular frame which is even-frequency and analyze the effects
on the anomalous Green function under a boost into a relativistic frame. The
odd-frequency pairing emerges dynamically as a result of the boost. In the
boosted frame the order parameter contains terms which are both even and odd in
frequency. The relativistic correction to the anomalous Green function to first
order in the boost parameter is completely odd in frequency. This work provides
evidence that odd-frequency pairing may form intrinsically within relativistic
superconductors.
