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.

4.5 pages, 2 figures; added reference, extended discussion

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• The Origin of Families and $SO(18)$ Grand Unification
• Weak-Coupling Theory of Pair Density-Wave Instabilities in Transition Metal Dichalcogenides
• Stripe melting, a transition between weak and strong symmetry protected topological phases
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• Deconfined criticality in bilayer graphene
• Definition and Classification of Fermi Surface Anomalies
• Charge-4$e$ Superconductivity in a Hubbard model
• Charge 4$e$ superconductor: a wavefunction approach
• Topological defects of Néel order and Kondo singlet formation for Kondo-Heisenberg model on a honeycomb lattice
• Topological defects in mixtures of superconducting condensates with different charges
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
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• Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice
• Conserved charges of order-parameter textures in Dirac systems
• Competing Orders and Anomalies
• Local condensation of charge-$4e$ superconductivity at a nematic domain wall
• Andreev reflection in normal metal/charge-4e superconductor junctions
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• Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
• Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order
• Exotic $Z_2$ Symmetry Breaking Transitions in 2D Correlated Systems
• Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Theory of Hofstadter Superconductors