A note on the possible mechanisms of high-temperature superconductivity

Possible mechanisms of high-temperature superconductivity are briefly discussed. In particular, a recent paper by P W Anderson on this problem is criticized as containing a number of incorrect and unfounded statements. One of these — that the static dielectric function $\varepsilon(\mathbf{q},0)$ cannot be negative — is discussed in detail, as is its consequence, a strong limit on the transition temperature $T_c$. Proofs are given that $\varepsilon(\mathbf{q},0)$ not only can but indeed must be negative in many stable systems, including most of the conventional metals. Various types of electron–electron interaction in superconducting cuprates are discussed. The role of the electron–phonon interaction in cuprates is highlighted.