The parent compound of an unconventional superconductor must contain unusual correlated electronic and magnetic properties of its own. In the high-Tc potassium intercalated FeSe, there has been significant debate regarding what the exact parent compo
und is. Our studies unambiguously show that the Fe-vacancy ordered K2Fe4Se5 is the magnetic, Mott insulating parent compound of the superconducting state. Non-superconducting K2Fe4Se5 becomes a superconductor after high temperature annealing, and the overall picture indicates that superconductivity in K2-xFe4+ySe5 originates from the Fe-vacancy order to disorder transition. Thus, the long pending question whether magnetic and superconducting state are competing or cooperating for cuprate superconductors may also apply to the Fe-chalcogenide superconductors. It is believed that the iron selenides and related compounds will provide essential information to understand the origin of superconductivity in the iron-based superconductors, and possibly to the superconducting cuprates.
We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations in exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We focus on fin
ding harmonic cochains cohomologous to a given cocycle. Amongst other things, this allows localization near topological features of interest. We derive a weighted least squares method by proving a discrete Hodge-deRham theorem on the isomorphism between the space of harmonic cochains and cohomology. The solution obtained either satisfies the Whitney form finite element exterior calculus equations or the discrete exterior calculus equations for harmonic cochains, depending on the discrete Hodge star used.
