  Topological materials which possess topologically protected surface states
have attracted much attention in recent years. In this work, we study the
critical current of superconductor/inversion symmetry breaking topological
material/superconductor junctions. We found surprisingly that, in topological
materials with broken inversion symmetry, the magnitude of the critical
Josephson currents $|I^{+}_c(B)|$ at fixed magnetic field $B$ is not the same
for critical currents $|I^{-}_c(B)|$ flowing in the opposite direction.
Moreover, the critical currents violate the $| I_{c}^{\pm}(B)| =
|I_{c}^{\pm}(-B)|$ relation and give rise to asymmetric Fraunhofer patterns. We
call this phenomenon asymmetric Josephson effect (AJE). AJE can be use to
detect inversion symmetry breaking in topological materials such as in quantum
spin Hall systems and Weyl semimetals.
