I've seen in math and physics lectures delivered in English, that people use to abreviate the commonly very used word "Definition" by "Def n"(Def superscript n). What's the meaning of this n? That is, which sequence of letters of phonemes does this n stand for? And, which other words can be abbreviated in the same way? (I've seen more, I just forgot which)
The n itself does not stand for a sound. The entire abbreviation “Defⁿ” stands for the sound of the word definition.
Could it be you are thinking of “Defⁿ” as a contraction? A contraction is a word in its own right. For example, isn’t is a word, originally coined by contraction of the words is not.
Abbreviations are not contractions. They are still read as the original word. For example, you might abbreviate singular as “sing.” but you would still pronounce it singular.
There really are no general rules for how to abbreviate or how to write an abbreviation, but some words are almost always abbreviated the same way and it is convenient for the reader if you adopt the common abbreviation. For example it is common in academic works to abbreviate pages as “pp.” But that is not a matter of English spelling or grammar, just written style.
Assuming you mean "defn" rather that the literal "def^n", then it's not an exponent it's just an abbreviation using a superscript.
If it's the literal "def^n" then I would think it's a humorous use of "^" alluding to its use indicating a superscript.