We are studying a reaction that forms only one kind of product. But due to recent literature that described the reaction with no invertion of the product configuration at all, this doubt emerged.
Yes it is possible. if you generate carbocation and you have some sort auxiliary that blocks one face of carbocation you could get one stereoisomer over the other.
The very well-established mechanism for SN1 reaction starts by the leaving group firstly getting out after which, say, a tertiary flat carbocation forming which is attacked by the nucleophile in a medium (the favored cases are weak nucleophile & polar protic solvent).
There is bound to be a mixture of retention and inversion products since the nucleophile can attack from either face of the flat carbocation with 50:50 chances.
It is difficult to get shielding for one of the faces of the planar carbocation while allowing the other face to be exposed to the nucleophilic attack given the conditions of such reaction.
Nizar Matar, your definition of SN1 is very correct but is textbook. Modern organic chemistry pushes the bounds of what is possible in synthesis so you shouldn't conclude that obtaining one enantiomer is not possible through SN1 conditions.
I am not sure what conditions Matheus Murmel Guimarães is using, but based on the question asked, it seemed like he was asking if it was even theoretically possible and to that I say yes. Is that whats happening in Matheus Murmel Guimarães case? Dont know. Would need to know the conditions.
Greg Petruncio , thanks for the reference you kindly provided. It seems that low temperature, that the authors applied, have contributed to some selectivity but not to total control since they mentioned product distribution.
Well, this is a good start which needs further "good" research.