Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO₂ planes and the interplay between competing orders with superconductivity. After a short introduction on multi-layered cuprate superconductors, I’ll present a recent study of quantum oscillation and Hall effect in magnetic field up to 88 T in the underdoped trilayer cuprate HgBa₂Ca₂Cu₃O_8+δ. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of multiple competing orders. In particular, our interpretation implies that a metallic antiferromagnetic state extends deep inside the superconducting phase, a key ingredient that supports magnetically mediated pairing interaction in cuprates.

Keywords: high Tc superconductor, electronic properties, high magnetic field