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Parton distribution functions (PDFs) are important tools for accessing hadron structure. Recently, a twist-4 gluon PDF F(x) has been introduced to explore the gluon condensate and mass structure in the nucleon. In this talk, I will introduce our recent work on the one-loop structure of F(x). Especially, I will present our results about the zero modes contribution. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons and obtained identical results in Feynman and light-cone gauges. The one-loop structure of another twist-4 PDF that is defined with the topological operator will also be discussed.