Non-Fermi-liquid behavior in $d$- and $f$-electron metals

A relatively new class of materials has been found in which the basic assumption of Landau Fermi-liquid theory—that at low energies the electrons in a metal should behave essentially as a collection of weakly interacting particles—is violated. These “non-Fermi-liquid” systems exhibit unusual temperature dependences in their low-temperature properties, including several examples in which the specific heat divided by temperature shows a singular $\log T$ temperature dependence over more than two orders of magnitude, from the lowest measured temperatures in the milliKelvin regime to temperatures over 10 K. These anomalous properties, with their often pure power-law or logarithmic temperature dependences over broad temperature ranges and inherent low characteristic energies, have attracted active theoretical interest from the first experimental report in 1991. This article first describes the various theoretical approaches to trying to understand the source of strong temperature- and frequency-dependent electron-electron interactions in non-Fermi-liquid systems. It then discusses the current experimental body of knowledge, including a compilation of data on non-Fermi-liquid behavior in over 50 systems. The disparate data reveal some interesting correlations and trends and serve to point up a number of areas where further theoretical and experimental work is needed.