Cuprates exhibit exceptionally strong superconductivity. To understand why, it is essential to elucidate the nature of the electronic interactions that cause pairing. Superconductivity occurs on the backdrop of several underlying electronic phases, including a doped Mott insulator at low doping, a strange metal at high doping, and an enigmatic pseudogap phase in between -inside which a phase of charge-densitywave order appears. In this Article, we aim to shed light on the nature of these remarkable phases by focusing on the limit as T → 0, where experimental signatures and theoretical statements become sharper. We therefore survey the ground state properties of cuprates once superconductivity has been removed by the application of a magnetic field, and distill their key universal features. arXiv:1807.05074v1 [cond-mat.supr-con] 13 Jul 2018Phase diagram of hole-doped cuprates. a) In zero field, superconductivity exists in a dome below Tc (dashed line). When it is removed by a magnetic field, various underlying ground states are revealed: 1) Doped Mott insulator with antiferromagnetic order, on the far left (brown, AF); 2) Pseudogap (PG) phase below a temperature T (yellow, PG), ending at a T = 0 critical point p (red dot); 3) Charge-density-wave phase (blue, CDW), contained inside the pseudogap phase; 4) a strange metal just above p (white region), which gives way to a Fermi liquid at highest doping (grey region). b) Phase diagram of Nd-LSCO, with the pseudogap temperature T measured by resistivity (circles) and ARPES (square; panels c, d), ending at the critical point p (from ref. (4)). c) ARPES spectra showing the pseudogap in Nd-LSCO measured just above Tc at four dopings, as indicated (5). The pseudogap is seen to close between p = 0.20 and p = 0.24, consistent with p = 0.23. d) ARPES spectra at p = 0.20 vs temperature (5). The pseudogap is seen to close at T = 75 K (square in panel b).