  The duality between coherent quantum phase slip and Josephson junction in
nanosheets was investigated using the dual Hamiltonian method. This is
equivalent to the duality between superconductivity and superinsulator in the 2
+ 1 dimension at zero temperature. This method proved to be reliable within the
Villain approximation. The possibility of the dual Ginzburg-Landau theory,
which is the phenomenology of superinsulators and the dual BCS theory, which is
a microscopic theory, is also shown.
