  We theoretically show quasiparticles-driven thermal diode effect (TDE) in an
inversion symmetry-broken (ISB) Weyl superconductor (WSC)-Weyl semimetal
(WSM)-WSC Josephson junction. A Zeeman field perpendicular to the WSM region of
the thermally-biased Weyl Josephson junction (WJJ) induces an asymmetry between
the forward and reverse thermal currents, which is responsible for the TDE.
Most interestingly, we show that the sign and magnitude of the thermal diode
rectification coefficient is highly tunable by the superconducting phase
difference and external Zeeman field, and also strongly depends on the junction
length. The tunability of the rectification, particularly, the sign changing
behavior associated with higher rectification enhances the potential of our WJJ
thermal diode to use as functional switching components in thermal devices.
