What can cause a breach in time?
There is no such thing as a breach in time.
Atoms can be accelerated to high speeds but they can never reach the speed of light. Particle accelerators have already accelerated atoms to close to the speed of light. There were no consequences to time.
The concept of a breach in time is pure science fiction. The Newtonian view of time as a continuum sparked the imagination of writers into views of time as a corridor which can be breeched.
We now know that time is simply the fourth dimension of four dimensional spacetime. Time is simply the distance between two spacetime events along the time dimension.
High speed atoms can have no significant effect on spacetime. A huge mass can cause a region of spacetime where time has stopped. It is called a black hole.
Wormholes which are tubes connecting different points in space time, which can be at different times, is theoretically possible but has not been observed.