On the connectedness of planar self-affine sets

In this paper, we consider the connectedness of planar self-affine set $T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with characteristic polynomial $f(x)=x^2+bx+c$ and a digit set $\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only depending on $b,c,m$ are given for the $T(A,\mathcal{D})$ to be connected. Moreover, we also consider the case that ${\mathcal D}$ is non-consecutively collinear.Comment: 18 pages; 18 figure

Superconductivity induced by doping Platinum in BaFe2As2

By substituting Fe with the 5d-transition metal Pt in BaFe2As2, we have successfully synthesized the superconductors BaFe2-xPtxAs2. The systematic evolution of the lattice constants indicates that the Fe ions were successfully replaced by Pt ions. By increasing the doping content of Pt, the antiferromagnetic order and structural transition of the parent phase is suppressed and superconductivity emerges at a doping level of about x = 0.02. At a doping level of x = 0.1, we get a maximum transition temperature Tc of about 25 K. The synchrotron powder x-ray diffraction shows that the resistivity anomaly is in good agreement with the structural transition. The superconducting transitions at different magnetic fields were also measured at the doping level of about x = 0.1, yielding a slope of -dHc2/dT = 5.4 T/K near Tc. A phase diagram was established for the Pt doped 122 system. Our results suggest that superconductivity can also be easily induced in the FeAs family by substituting the Fe with Pt, with almost the similar maximum transition temperatures as doping Ni, Co, Rh and Ir.Comment: 6 pages, 5 figure

Large-gap quantum spin Hall insulators in tin films

The search of large-gap quantum spin Hall (QSH) insulators and effective approaches to tune QSH states is important for both fundamental and practical interests. Based on first-principles calculations we find two-dimensional tin films are QSH insulators with sizable bulk gaps of 0.3 eV, sufficiently large for practical applications at room temperature. These QSH states can be effectively tuned by chemical functionalization and by external strain. The mechanism for the QSH effect in this system is band inversion at the \Gamma point, similar to the case of HgTe quantum well. With surface doping of magnetic elements, the quantum anomalous Hall effect could also be realized