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

TL;DR

This paper explores how quadratic band touching fermions induce Skyrmions with charge 4e and bosonic statistics, proposing a mechanism for charge 4e superconductivity in bilayer graphene through Skyrmion condensation.

Contribution

It demonstrates that quadratic band touching fermions lead to charge 4e bosonic Skyrmions and proposes a second-order phase transition to charge 4e superconductivity in bilayer graphene.

Findings

Skyrmions have doubled charge compared to Dirac fermions

Skyrmions are always bosonic in this context

Proposed phase diagram includes a second-order transition to charge 4e SC

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.