Skyrmions with quadratic band touching fermions: A way to achieve charge 4e superconductivity

Abstract

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.