Knot Floer homology is a powerful invariant that carries interesting geometric information of a knot. While the top-term governs the genus and fiberedness, the next-to-top term has recently been shown to detect more subtle properties. For example, for a fibered knot, if the next-to-top term has rank one, then the knot admits a fixed-point-free monodromy, by the work of Ni and Ghiggini-Spano. In this talk, we explore this phenomenon for various classes of positive knots. We show that all prime positive braid knots satisfy this rank-one condition for their next-to-top term. This is joint work with Matthew Hedden.