Pseudogap and Condensation in Cuprate Superconductors from NMR Shifts

Abstract

The electronic properties of the high-temperature superconducting cuprates are encoded in complex sets of NMR data, but without microscopic theory, reliable NMR phenomenologies are in demand. Early analyses of NMR could only focus on very few materials and discovered spin singlet pairing and the enigmatic pseudogap. However, a coherent phenomenology of shift and relaxation could not be established, as incoming data from other cuprates complicated the picture. Today, due to work of many groups worldwide, planar copper and oxygen NMR data are available for most cuprates. Here, based only on symmetry of the two Cu hyperfine couplings, an anisotropic $A_\alpha$ and isotropic $B$, the Cu shifts are disentangled, and two different shift components emerge. Upon doping the cuprates, metallic B-spins are created above the pseudogap temperature which is shared with metallic A-spins. Further doping decreases the pseudogap temperature and increases the B-spin, but less so the A-spin. The apparent linear rate of increase in density of states of the B-spin with doping increases nearly threefold above about $x=0.20$, where the pseudogap has disappeared and A and B turn into superconducting metals, i.e. they disappear rapidly at $T_\mathrm{c}$. The pseudogap temperature is a measure of the coupling between A and B, which suppresses the shifts but not nuclear relaxation. Spin singlet pairing involves A and B according to three simple rules for condensation which will be discussed. The optimal $T_\mathrm{c}$ demands a special match between A and B and involves systems with a pseudogap. However, the highest $T_\mathrm{c}$ of all cuprates is not encoded in the shift, but rather in nuclear relaxation and charge sharing between planar Cu and O. Relations to other probes are discussed.