In the present work, we report the new findings on the doping level dependence of the phase coherence between superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+delta}$ (Bi-2212) grains. The experimental results from the strongly underdoped and overdoped regi
mes deviated from the expectation based on the doping level dependence of the superfluid density at $T$ = 0 K. These findings appear to be governed by interplay between competing orders inside the superconducting dome of cuprate superconductors. Two quantum critical points are likely to exist at the underdoped and overdoped regimes beneath the superconducting dome.
We report the synthesis of a new oxychalcogenide HgOCuSe sample. The resistivity decreases as a function of $T^{1.75}$ with decreasing temperature from room temperature down to around 80 K. There exists a very sharp ferromagnetic-like phase transitio
n at around 60 K under a field of $H$ = 100 Oe. Contrary to the usual ferromagnetic materials, the descending and ascending branches of the magnetic hysteresis curve, at 30 K, are reversed in the whole irreversible field range and the reverse irreversibility decreases at 5 K.
