Binds specifically to phosphatidylinositol 3,4-diphosphate (PtdIns3,4P2), but not to other phosphoinositides. May recruit other proteins to the plasma membrane. {ECO:0000269|PubMed:11001876, ECO:0000269|PubMed:11513726, ECO:0000269|PubMed:14516276}. This is the function of PLEKHA1 (pleckstrin homology domain containing A1, Ensembl gene identifier ENSG00000107679).