Topological Kondo insulators represent a unique class of materials where strong electron correlations and topological order intertwine to produce exotic electronic states. Among these, samarium hexaboride (SmB6) has emerged as a prototypical example, exhibiting a hybridization gap and conducting surface states that defy conventional insulating behavior. The material’s peculiar properties arise from the interplay between localized f-electrons and itinerant d-electrons, leading to a bulk insulating state with topologically protected surface conduction.

At the heart of SmB6’s behavior lies the hybridization gap, a consequence of strong correlations between the localized 4f electrons of samarium and the delocalized 5d electrons. The hybridization opens a gap at the Fermi level, typically on the order of 10–20 meV, transforming SmB6 into a Kondo insulator at low temperatures. This gap is temperature-dependent, emerging below the Kondo temperature, which for SmB6 is approximately 50 K. Below this threshold, the bulk resistivity increases exponentially, a hallmark of Kondo insulating behavior. However, unlike conventional insulators, SmB6 exhibits a saturation of resistivity at the lowest temperatures, signaling the presence of residual conduction channels.

The residual conductivity is attributed to topologically protected surface states, a consequence of the material’s inverted band structure. Theoretical models suggest that SmB6 belongs to the class of strong topological insulators with an odd number of Dirac cones on the surface. Angle-resolved photoemission spectroscopy (ARPES) measurements confirm the existence of these Dirac-like surface states, which remain robust against non-magnetic perturbations. The surface conduction is further evidenced by transport experiments where the bulk contribution is suppressed at low temperatures, leaving only surface-dominated conduction.

Transport properties of SmB6 reveal a complex interplay between bulk and surface contributions. At high temperatures, the material behaves like a poor metal due to thermally activated carriers. As the temperature drops below the Kondo temperature, the bulk resistivity rises sharply, but below approximately 5 K, it plateaus, indicating the dominance of surface conduction. The surface conductivity is highly sensitive to sample quality and surface preparation, with mobilities ranging from 100 to 1000 cm²/Vs depending on experimental conditions. Quantum oscillations observed in magnetoresistance measurements further corroborate the existence of well-defined Fermi surfaces associated with the surface states.

The strong electron correlations in SmB6 introduce additional complexity to its topological properties. Unlike weakly correlated topological insulators, where band inversion alone dictates the topological phase, SmB6 requires consideration of many-body effects. Dynamical mean-field theory (DMFT) calculations reveal that electron-electron interactions renormalize the band structure, enhancing the effective mass of surface states. This renormalization leads to heavy Dirac fermions, distinguishing SmB6 from conventional topological insulators with light surface carriers.

Another intriguing aspect is the role of magnetic fields in perturbing the surface states. While non-magnetic impurities have little effect, applied magnetic fields can disrupt the topological protection, leading to deviations from ideal surface conduction. Experiments show that high magnetic fields induce a crossover from surface-dominated to bulk-dominated transport, suggesting a delicate balance between correlation effects and topological order.

The interplay between topology and correlations also manifests in the material’s response to impurities and defects. Unlike dilute magnetic semiconductors, where magnetic doping introduces spin-polarized carriers, SmB6’s surface states are robust against non-magnetic disorder but sensitive to magnetic perturbations. This distinction highlights the unique nature of correlated topological phases, where interactions modify the protection mechanisms of surface states.

Recent advances in thin-film growth and nanostructuring of SmB6 have opened new avenues for probing its topological properties. Epitaxial films exhibit similar hybridization gaps and surface states as bulk crystals, but with additional tunability via strain and substrate effects. Nanowire geometries, in particular, provide a platform for studying one-dimensional transport channels derived from surface states, offering insights into the interplay of dimensionality and topology.

Despite significant progress, several open questions remain regarding the exact nature of SmB6’s surface states and their relationship to bulk correlations. Some studies suggest the possibility of additional exotic phases, such as Majorana zero modes, arising at defects or edges under specific conditions. However, conclusive evidence for such states requires further experimental verification.

The study of topological Kondo insulators like SmB6 bridges the gap between strongly correlated systems and topological materials, offering a rich playground for discovering new quantum phenomena. By understanding the hybridization gap, surface states, and transport properties in these materials, researchers can uncover deeper connections between correlation-driven ordering and topological protection. Future work will likely focus on manipulating these states for potential applications in quantum computing and low-power electronics, where the combination of robustness and tunability is highly desirable.

In summary, SmB6 exemplifies how strong electron correlations can coexist with topological order, producing a bulk insulator with conducting surfaces that challenge traditional classifications. Its unique transport behavior, heavy Dirac fermions, and sensitivity to magnetic fields provide valuable insights into the broader class of correlated topological materials. As experimental techniques and theoretical models continue to advance, the exploration of topological Kondo insulators will remain a vibrant frontier in condensed matter physics.