Hidden Magnetic Texture in the Pseudogap Phase of High-Tc $YBa{2}Cu{3}O_{6.6}$

Despite decades of intense researches, the enigmatic pseudo-gap (PG) phase of superconducting cuprates remains an unsolved mystery. In the last 15 years, various symmetry breakings in the PG state have been discovered, spanning an intra-unit cell (IUC) magnetism, preserving the lattice translational (LT) symmetry but breaking time-reversal symmetry and parity, and an additional incipient charge density wave breaking the LT symmetry upon cooling. However, none of these states can (alone) account for the partial gapping of the Fermi surface. Here we report a hidden LT-breaking magnetism which is crucial for elucidating the PG puzzle. Our polarized neutron diffraction measurements reveal magnetic correlations, in two different underdoped YBa2Cu3O6.6 single crystals, that settle at the PG onset temperature with i) a planar propagation wave vector (π, 0) ≡ (0, π), yielding a doubling or quadrupling of the magnetic unit cell and ii) magnetic moments mainly pointing perpendicular to the CuO2 layers. The LT-breaking magnetism is at short range suggesting the formation of clusters of 5-6 unit cells that, together with the previously reported IUC magnetism, yields a hidden magnetic texture of the CuO2 unit cells hosting loop currents.

Theory of supercurrent in superconductors

According to the standard theory of superconductivity, the origin of superconductivity is electron pairing. The induced current by a magnetic field is calculated by the linear response to the vector potential, and the supercurrent is identified as the dissipationless flow of the paired electrons, while single electrons flow with dissipation. This supercurrent description suffers from the following serious problems: (1) it contradicts the reversible superconducting-normal phase transition in a magnetic field observed in type I superconductors; (2) the gauge invariance of the supercurrent induced by a magnetic field requires the breakdown of the global [Formula: see text] gauge invariance, or the nonconservation of the particle number; and (3) the explanation of the ac Josephson effect is based on the boundary condition that is different from the real experimental one. We will show that above problems are resolved if the supercurrent is attributed to the collective mode arising from the Berry connection for many-body wavefunctions. Problem (1) is resolved by attributing the appearance and disappearance of the supercurrent to the abrupt appearance and disappearance of topologically protected loop currents produced by the Berry connection; problem (2) is resolved by assigning the non-conserved number to that for the particle number participating in the collective mode produced by the Berry connection; and problem (3) is resolved by identifying the relevant phase in the Josephson effect is that arising from the Berry connection, and using the modified Bogoliubov transformation that conserves the particle number. We argue that the required Berry connection arises from spin-twisting itinerant motion of electrons. For this motion to happen, the Rashba spin–orbit interaction has to be added to the Hamiltonian for superconducting systems. The collective mode from the Berry connections is stabilized by the pairing interaction that changes the number of particles participating in it; thus, the superconducting transition temperatures for some superconductors is given by the pairing energy gap formation temperature as explained in the BCS theory. The topologically protected loop currents in this case are generated as cyclotron motion of electrons that is quantized by the Berry connection even without an external magnetic field. We also explain a way to obtain the Berry connection from spin-twisting itinerant motion of electrons for a two-dimensional model where the on-site Coulomb repulsion is large and doped holes form small polarons. In this model, the electron pairing is not required for the stabilization of the collective mode, and the supercurrent is given as topologically protected spin-vortex-induced loop currents (SVILCs).

On the coupling influence of the relative position of human trunk with respect to the overhead high-voltage power line

<p class="Abstract">In this article, we present our study of the relevance of the relative position of the human torso with respect to the plane of the supporting pylons of various Overhead High-Voltage Power Lines from the perspective of currents induced by the generated magnetic fields. A homogenous model of the human body that considers the trunk as an elliptic cylinder has been developed in CST Studio software. Due to the necessary theoretical brevity, the results obtained by the simulation for the loop currents along the perimeters associated with the large (28 cm) and, respectively, the small (16 cm) axis of the elliptical cross-section of the trunk are presented and discussed. Simulations have been performed for five relative positions (0°, 30°, 45°, 60°, 90°) of the human trunk with respect to the plane of the transmission towers and for two types of symmetric, double three-phase networks (110 kV and 640 A, 220 kV and 960 A, respectively), with the normal supporting poles SN 110252. We present the solutions and the selected boundary conditions with the aim of using CST software in the domain of industrial frequency. The obtained results make it possible to formulate recommendations on the reduction of human exposure to magnetic fields.</p>