Calculations of magnetic field produced by spin-vortex-induced loop currents in Bi₂Sr₂CaCu₂O8+δ thin films using the particle-number conserving Bogoliubov-de Gennes formalism

A theory for cuprate superconductivity predicts the existence of nano-sized loop currents called, `` spin-vortex-induced loop currents (SVILCs)''. We calculate magnetic fields produced by them for a model of Bi₂Sr₂CaCu₂O8+δ (Bi-2212) thin films composed of one surface and two bulk CuO₂ bilayers. In this model, bulk CuO₂ layers host stable spin-vortices around small polarons formed from doped holes; they give rise to a $U(1)$ gauge field described by the Berry connection from many-body wave functions, and generates the SVILCs. The effect of the gauge field is taken into account by the particle-number conserving Bogoliubov-de Gennes (PNC-BdG) formalism. The magnitude of the calculated magnetic field produced by the SVILCs in the vicinity of the surface (10a ≈ 4 nm, where a is the lattice constant of the CuO₂ plane) is in the order of mT; thus, may be detectable by currently available detection methods. The detection of the SVILCs by the magnetic field measurement may bring about the elucidation of the cuprate superconductivity, and may also lead to their quantum device applications, including qubits.