Colloquium: Linear in temperature resistivity and associated mysteries including high temperature superconductivity

Immediately after the discovery of high temperature superconductivity in the cuprates in 1987, properties in the metallic state above T-c were discovered that violated the reigning paradigm in condensed matter physics: the quasiparticle concept due to Landau. The most discussed of such properties is the linear in temperature resistivity down to asymptotically low temperatures, sometimes called Planckian resistivity, above the region of the highest T-c. Similar anomalies have since also been discovered in the heavy-fermion compounds and in the Fe-based superconducting metals, and most recently in twisted bilayer graphene. Innumerable papers in the past three decades have pointed out that the linear in T resistivity and associated properties are a mystery and the most important unsolved problem in condensed matter physics; superconductivity itself is a corollary to the normal state properties. Even in this prolifically investigated field, quantitative experimental results on crucial normal state and superconducting state properties have only recently become available. It is now possible to compare some of the detailed predictions of a theory for the normal and superconductive state in cuprates and in heavy fermions with the experiments. The theory gives the frequency and temperature dependence of various normal state properties and also their measured magnitudes in terms of the same values of two parameters. It also resolves the paradox of d-wave symmetry of superconductivity in the cuprates given that the scattering rate of fermions in the normal state is nearly momentum independent. The same parameters that govern the normal state anomalies are also deduced from the quantitative analysis of data in the superconducting state in cuprates. The simplicity of the results depends on the discovery of a new class of quantum-critical fluctuation in which orthogonal topological excitations in space and time determine the spectra, such that the correlations of the critical spectra are a product of a function of space and a function of time with the spatial correlation length proportional to the logarithm of the temporal correlation length. The fermions scattering with such fluctuations form a marginal Fermi liquid.