  It is necessary to break both time-reversal and parity symmetries to realize
a Josephson, or superconducting, diode exhibiting nonreciprocal critical
direct-currents (DC). In fact, these conditions are still insufficient. The
dependencies of the free energy on the phase difference across the junction and
the magnetic field are classified, exhibiting the current-reversion (JR),
field-reversion, and field-current reversion conditions, respectively. To
exhibit the DC Josephson diode effect, all symmetries satisfying the JR
condition need to be broken. The relations of critical currents with respect to
the magnetic field are classified into five classes, including three exhibiting
the diode effect. These symmetry considerations are applied to concrete
examples. Our work reveals that the DC Josephson diode effect is a natural
consequence of the JR symmetry breaking, hence, providing a guiding principle
to understand or design a DC Josephson diode.
