One of the technological aspects of the topological phases have been recognised in creating qubits with long-lasting coherence
One is the subject of the sentence, and one is singular, not plural. So the correct verb is has been recognized. It must be added that this grammatical rule is often violated by native speakers, especially in speech. The multiplicity of plural nouns in the phrases modifying "one" leads the speaker to forget that the actual subject is singular.
"Has" is correct.
The subject of your phrase is the singular noun "One" ("of the..." isn't important.), so your verb must be in agreement (it must also be singular: has).
Also, there may be another error. The sentence is unclear, but it looks like an error. Do you mean that "one of the technological aspects..." has been recognized "as" creating qubits with long-lasting coherence? Did the technological aspect help create qubits with long-lasting coherence?
Or, was it (one of the technological aspects) recognized/identified while you were studying "creating qubits with long-lasting coherence"? Did you find the aspect at that time?