We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological crystallin
e insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled layer construction.
The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking. Two equally sharp first-order magnetization steps are revealed in a single tempe
rature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium $M(T)$ slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.
