  Odd-frequency superconductivity, originally proposed by Berezinskii in 1974,
is an exotic phase of matter in which Cooper pairing between electrons is
entirely dynamical in nature. The pair potential is an odd function of
frequency, leading to a vanishing static superconducting order parameter and
exotic types of pairing seemingly inconsistent with Fermi statistics. Motivated
by recent experimental progress in the realization of Majorana zero modes in
semiconducting nanowires, we show that odd-frequency superconductivity
generically appears in a spin-polarized nanowire coupled to Majorana zero
modes. We explicitly calculate the superfluid response and show that it is
characterized by a paramagnetic Meissner effect.
