M2-rank of overpartitions and harmonic weak Maass forms

There has been significant recent interest in constructing many families of harmonic weak Maass forms using rank generating functions of various partitions. In this paper, applying Zwegers' results on Appell-Lerch sums, we provide a new family of harmonic weak Maass forms with the M2-rank generating function of overpartitions. As applications, we prove the modularity of M2-rank differences and Ramanujan-type congruences for such ranks.