The three central phenomena of cuprate superconductors are linked by a common doping p*, where the enigmatic pseudogap phase ends, around which the superconducting phase forms a dome, and at which the resistivity exhibits an anomalous linear dependence on temperature as T → 0 (ref. 1). However, the

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Since its experimental discovery, many phenomenological theories successfully reproduced the rapid rise of the Hall number nH , going from p at low doping to 1 + p at the critical doping p * of the pseudogap in superconducting cuprates. Further comparison with experiments is now needed in order to narrow down candidates. In this paper, we consider three previously successful phenomenological theories in a unified formalism-an antiferromagnetic mean field (AF), a spiral incommensurate antiferromagnetic mean field (sAF), and the Yang-Rice-Zhang (YRZ) theory. We find a rapid rise in the specific heat and a rapid drop in the Seebeck coefficient for increasing doping across the transition in each of those models. The predicted rises and drops are locked, not to p * , but to the doping where anti-nodal electron pockets, characteristic of each model, appear at the Fermi surface shortly before p * . While such electron pockets are still to be found in experiments, we discuss how they could provide distinctive signatures for each model. We also show that the range of doping where those electron pockets would be found is strongly affected by the position of the van Hove singularity.

Antiferromagnetism and d-wave superconductivity are the most important competing ground-state phases of cuprate superconductors. Using cellular dynamical mean-field theory (CDMFT) for the Hubbard model, we revisit the question of the coexistence and competition of these phases in the one-band Hubbard model with realistic band parameters and interaction strengths. With an exact diagonalization solver, we improve on previous works with a more complete bath parametrization which is carefully chosen to grant the maximal possible freedom to the hybridization function for a given number of bath orbitals. Compared with previous incomplete parametrizations, this general bath parametrization shows that the range of microscopic coexistence of superconductivity and antiferromagnetism is reduced for band parameters for Nd 2−x Ce x CuO 4 , and confined to electron-doping with parameters relevant for YBa 2 Cu 3 O 7−X .

In scanning tunneling microscopy (STM) conductance curves, the superconducting gap of cuprates is sometimes accompanied by small sub-gap structures at very low energy. This was documented early on near vortex cores and later at zero magnetic field. Using mean-field toy models of coexisting d-wave superconductivity (dSC), d -form factor density wave (dFF-DW), and extended s-wave pair density wave (s PDW), we find agreement with this phenomenon, with s PDW playing a critical role. We explore the high variability of the gap structure with changes in band structure and density wave (DW) wave vector, thus explaining why sub-gap structures may not be a universal feature in cuprates. In the absence of nesting, non-superconducting results never show signs of pseudogap, even for large density waves magnitudes, therefore reinforcing the idea of a distinct origin for the pseudogap, beyond mean-field theory. Therefore, we also briefly consider the effect of DWs on a pre-existing pseudogap.