The phrase "after a breakthrough" is correct and usable in written English.
It can be used to indicate a point in time or a situation that follows a significant discovery or advancement.
Example: "The team celebrated their success after a breakthrough in the research that could change the industry."
Alternatives: "following a breakthrough" or "subsequent to a breakthrough".
These somewhat lacklustre pieces soon give way to more sensuous abstract watercolours, created after a breakthrough trip to Tunis in 1914.
After a breakthrough success at Ascot, Declaration Of War has since run a fine second to Al Kazeem in the Eclipse at Sandown.
And now, after a breakthrough study by a group of British scientists, it could be used to predict the outcome of trials.
After a breakthrough film role in bratpack hit Footloose in 1984, Parker went on to build a solid career in intelligent comedies.
Washington QB Kirk Cousins, making his first career playoff start after a breakthrough season, was 29 for 46 for 329 yards.
Early in his career, after a breakthrough performance in Israel Horovitz's 1968 play "The Indian Wants the Bronx," Pacino appeared on "The Merv Griffin Show," and, in front of a television audience of millions, he froze.
After signing a breakthrough agreement last month, the North Koreans are stalling again.Meeting in Beijing for the first time since the agreement was signed on February 13th, the same officials started off in upbeat mood.
Nearly a year after announcing a breakthrough joint effort to cut carbon emissions, climate negotiators from the United States and China have convened in Los Angeles to highlight local government efforts to implement the countries' ambitious climate change agenda.
Then, after 11 hours, a breakthrough: the kettle started responding to voice control.
But after finally making a breakthrough in negotiations, the 23-year-old is set to link up with Claudio Ranieri's side before the new season.
"In the case of General Motors, we had a breakthrough after seven years".
