Leavened and unleavened wheat bread are valid matter, but depending on the Church one or the other may be illicit according to the law of that Church. Latin Code of Canon Law requires unleavened bread:
Can. 924 §1. The most holy eucharistic sacrifice must be offered with bread and with wine in which a little water must be mixed.
§2. The bread must be only wheat and recently made so that there is no danger of spoiling.
§3. The wine must be natural from the fruit of the vine and not spoiled.
In the Latin Rite communion bread is primarily in the form of the small individual host. This prevents particles of the sacred species from dropping as crumbs.
In the Eastern Rite Catholic Churches, they use leavened bread per the eastern code of canon law, and the communicant receives it in their mouth via the communion spoon.
A quick scan of pita bread recipes yields ingredients other than wheat and water (leavening is used making it illicit in the Latin Church, but still valid). Salt, Oil, sugar or honey are also listed— which would not be permitted.