  Superconductivity is a fascinating quantum phenomenon characterized by zero
electrical resistance and the Meissner effect. To date, several distinct
families of superconductors (SCs) have been discovered. These include
three-dimensional (3D) bulk SCs in both inorganic and organic materials as well
as two-dimensional (2D) thin film SCs but only in $inorganic$ materials. Here
we predict superconductivity in 2D and 3D $organic$ metal-organic frameworks by
using first-principles calculations. We show that the highly conductive and
recently synthesized Cu-benzenehexathial (BHT) is a Bardeen-Cooper-Schrieffer
SC. Remarkably, the monolayer Cu-BHT has a critical temperature ($T_{c}$) of
4.43 K while $T_{c}$ of bulk Cu-BHT is 1.58 K. Different from the enhanced
$T_{c}$ in 2D inorganic SCs which is induced by interfacial effects, the
$T_{c}$ enhancement in this 2D organic SC is revealed to be the out-of-plane
soft-mode vibrations, analogous to surface mode enhancement originally proposed
by $Ginzburg$. Our findings not only shed new light on better understanding 2D
superconductivity, but also open a new direction to search for SCs by interface
engineering with organic materials.
