Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

Relentless and complex transits from a planetesimal debris disc

This article reports quasi-continuous transiting events towards WD 1054–226 at d = 36.2 pc and V = 16.0 mag, based on simultaneous, high-cadence, multiwavelength imaging photometry using ULTRACAM over 18 nights from 2019 to 2020 March. The predominant period is 25.02 h and corresponds to a circular orbit with blackbody Teq = 323 K, where a planetary surface can nominally support liquid water. The light curves reveal remarkable night-to-night similarity, with changes on longer time-scales, and lack any transit-free segments of unocculted starlight. The most pronounced dimming components occur every 23.1 min – exactly the 65th harmonic of the fundamental period – with depths of up to several per cent, and no evident colour dependence. Myriad additional harmonics are present, as well as at least two transiting features with independent periods. High-resolution optical spectra are consistent with stable, photospheric absorption by multiple, refractory metal species, with no indication of circumstellar gas. Spitzer observations demonstrate a lack of detectable dust emission, suggesting that the otherwise hidden circumstellar disc orbiting WD 1054–226 may be typical of polluted white dwarfs, and detected only via favourable geometry. Future observations are required to constrain the orbital eccentricity, but even if periastron is near the Roche limit, sublimation cannot drive mass loss in refractory parent bodies, and collisional disintegration is necessary for dust production