A review of the Kondo insulator materials class of strongly correlated electron systems: Selected systems and anomalous behavior

Studies of strongly correlated electron systems have been at the forefront of research in condensed matter physics ever since the discovery of the co-existence of strong Pauli-paramagnetism and superconductivity in the archetypal heavy-fermion compound CeCu 2 Si 2 in 1979. The construct of correlated electron physics typifies the behavior of thermal and electronic properties of a material when the Coulomb interaction between conduction electrons exceeds the electron kinetic energy at a given thermal energy and redefines in remarkable ways our understanding of the behavior of a metal near its ground state. While correlated electron behavior has by now been demonstrated in a variety of different types of materials, Kondo systems in particular are arguably the most intensively studied among these. The Kondo interaction is used to describe the effect that a spin-magnetic ion has on its environment when immersed in the conduction electron sea of a metal. The localized spin of the Kondo ion polarizes nearby conduction electrons to form a so-called Kondo cloud, which acts to screen and magnetically (partially) neutralize the localized spin. In Kondo systems, the low-temperature behavior is prone to the formation of heavy fermions, which is the term given to quasiparticle excitations that define the emergence of effective electron masses that can be up to three orders of magnitude greater than that of a free electron. The Kondo effect presents itself in three guises: first, the single-ion Kondo state which is found in a metal having only a small amount of magnetic ions dissolved into it; second, the incoherent Kondo state in materials where there is a Kondo ion in every crystallographic unit cell of the material, but the Kondo ions remain incoherent or uncoupled from each other; and third, the coherent Kondo lattice state which manifests itself toward low temperatures where the interaction between Kondo ions becomes comparable to the thermal energy of conduction electrons that mediate magnetic exchange between Kondo ions. In a small number of cases, the outcome of a material condensing into the Kondo state turns out to be the peculiar formation of a very narrow energy band gap at the metallic Fermi energy. Such a band gap has significant consequences in practically all of the physical properties of a material that stem from the behavior of conduction electrons in proximity of the Fermi energy. This is most readily seen in electrical resistivity, heat capacity, and magnetic susceptibility. The band gapping gives cause to the term Kondo insulator (also referred to as Kondo semimetal or heavy-fermion semiconductor) that is used to describe this exceptional variety of Kondo systems. The term Kondo insulator is in general use although most Kondo insulators have a small but finite electrical conduction in the low-temperature limit where Kondo screening may be accomplished to its full extent. While the Kondo lattice ground state is exemplified by a very high density of electronic states at the Fermi energy, Kondo insulators, on the other hand, have, by virtue of narrow band gapping, a low density of electronic states. It remains a counter-intuitive observation, therefore, that despite their low density of states, Kondo insulators have curiously strong spin polarization energy scales and accompanying high values of their Kondo temperature, being the defining quantity which acts as an organizing principle in their temperature-dependent physical properties. In this article, we review the fundamentals of the Kondo insulating state, and we discuss the theoretical principles of what is presently understood about the formation of a Kondo insulator. The experimental results of a selected number of examples that have gained prominence in this class of materials are compared to each other in order to seek out similarities that may help deepen our understanding of the Kondo insulating state.