Band structure reconstruction across nematic order in high quality FeSe single crystal as revealed by optical spectroscopy study

We perform an in-plane optical spectroscopy measurement on high quality FeSe single crystals grown by a vapor transport technique. Below the structural transition at $T_{\rm s}\sim$90 K, the reflectivity spectrum clearly shows a gradual suppression around 400 cm$^{-1}$ and the conductivity spectrum shows a peak at higher frequency. The energy scale of this gap-like feature is comparable to the width of the band splitting observed by ARPES. The low-frequency conductivity consists of two Drude components and the overall plasma frequency is smaller than that of the FeAs based compounds, suggesting a lower carrier density or stronger correlation effect. The plasma frequency becomes even smaller below $T_{\rm s}$ which agrees with the very small Fermi energy estimated by other experiments. Similar to iron pnictides, a clear temperature-induced spectral weight transfer is observed for FeSe, being indicative of strong correlation effect.Comment: 6 page

Optimal three-ball inequalities and quantitative uniqueness for the Lam\'e system with Lipschitz coefficients

In this paper we study the local behavior of a solution to the Lam\'e system with \emph{Lipschitz} coefficients in dimension $n\ge 2$. Our main result is the bound on the vanishing order of a nontrivial solution, which immediately implies the strong unique continuation property. This paper solves the open problem of the strong uniqueness continuation property for the Lam\'e system with Lipschitz coefficients in any dimension

A unified description for dipoles of the fine-structure constant and SnIa Hubble diagram in Finslerian universe

We propose a Finsler spacetime scenario of the anisotropic universe. The Finslerian universe requires both the fine-structure constant and accelerating cosmic expansion have dipole structure, and the directions of these two dipoles are the same. Our numerical results show that the dipole direction of SnIa Hubble diagram locates at $(l,b)=(314.6^\circ\pm20.3^\circ,-11.5^\circ\pm12.1^\circ)$ with magnitude $B=(-3.60\pm1.66)\times10^{-2}$. And the dipole direction of the fine-structure constant locates at $(l,b)=(333.2^\circ\pm8.8^\circ,-12.7^\circ\pm6.3^\circ)$ with magnitude $B=(0.97\pm0.21)\times10^{-5}$. The angular separation between the two dipole directions is about $18.2^\circ$.Comment: 10 pages, 1 figur