We study Skyrmion quantum numbers, charge and statistics, in (2+1) dimension
induced by quadratic band toucing(QBT) fermions. It is shown that induced
charge of Skyrmions is twice bigger than corresponding Dirac particles' and
their statistics are always bosonic. Applying to the Bernal stacking bi-layer
graphene, we show that Skyrmions of quantum spin Hall(QSH) are charge 4e
bosons, so their condensation realizes charge 4e superconductivity(SC). The
phase transition could be a second order, and one candidate theory of the
transition is O(5) non linear sigma model(NLSM) with non-zero
Wess-Zumino-Witten(WZW) term. We calculate renormalization group beta function
of the model perturbatively and propose a possible phase diagram. We also
discuss how QBT fermions are different from two copies of Dirac particles.Comment: 4.5 pages, 2 figures; added reference, extended discussio
