Narrow-gap insulators
The Fermi surface is conventionally thought to be unique to a metallic state. An insulator is not expected to host a Fermi surface. The discovery of 3D topological insulators has demonstrated that a metallic state can exist intrinsically at the surface of a bulk insulator, creating a new state of matter. A more recent and controversial finding made in narrow-gap correlated insulators, namely SmB6 and YbB12, is the realization of a 3D Fermi surface within the insulating bulk of these materials.
Schematic diagram of low-energy electronic structure in SmB6. The hybridization between the itinerant 5d and localized 4f band below the Kondo temperature opens up a bandgap ΔK at the Fermi level.
de Haas-van Alphen quantum oscillations and bulk Fermi surface in SmB6. Figure reference: Science 349, 287
SmB6 and YbB12 are archetypal Kondo insulators (KIs), a class of materials in which the hybridization between the itinerant d-band and localized f-band leads to the formation of a small bandgap ΔK ≈ 5 meV at the Fermi energy. The opening ΔK occurs at the Kondo temperature TK, below which a metal-insulator transition occurs and the resistivity diverges correspondingly. While the electrically insulating behavior at low T is found to be robust in magnetic fields up to 45 T [Science 349, 287 (2015)], in magnetization both SmB6 and YbB12 exhibit prominent quantum oscillations [Science 362, 65 (2018)], the direct manifestation of an underlying Fermi surface, with characteristics consistent with a bulk origin. Furthermore, the heat conduction in SmB6 and YbB12 dramatically violates the Wiedemann-Franz law [Nat. Phys. 14, 166 (2018); Nat. Phys. 15, 954 (2019)], implying the existence of charge-neutral itinerant carriers. The experimental observation of a bulk Fermi surface in an insulating state challenges the conventional distinction between a metal and an insulator, suggesting a new state of quantum matter, whose nature represents an emergent mystery.
To expand the materials universe available for the study of unconventional Fermi surfaces in correlated insulating states, we are currently exploring alternative narrow-gap correlated insulators with similar characteristics as the Kondo-insulating rare-earth borides. FeXn (Xn = Si, Sb2, Ga3) is a family of materials which features an exceptionally high thermoelectric power at cryogenic temperatures, anomalous magnetic properties, and varying sizes of bandgap (Δ = 5 - 300 meV). Furthermore, FeXn shows a resistivity plateau at ~ 10 K which suggests a possible existence of topologically non-trivial surface states. The similarity and distinction between boride KIs and FeXn will provide useful clues for identifying the key characteristics for realizing unconventional metallicity in correlated insulators and the nature of the charge-neutral Fermi surface therein.
Resistivity versus temperature of narrow-gap insulators FeSi and FeGa3. A saturation of resistivity below ~10 K is found in both materials.
Further reading
1. Natalie Wolchover, "Paradoxial crystal baffles physicist", Quanta magazine (2015)
2. L. Li et al., "Emergent mystery in the Kondo insulator samarium hexaboride", Nature Review Physics 2, 463 (2020)
3. J. M. Tomczak et al., "Thermoelectricity in correlated narrow-gap semiconductors", J Phys: Condens. Matter 30, 183001 (2018)