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Register a new userFrom bad metal to Kondo insulator: temperature evolution of the optical properties of SmB$_{6}$
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The recent rekindling of interest in the mixed valent Kondo insulator SmB$_{6}$ as candidate for a first correlated topological insulator has resulted in a wealth of new experimental observations. In particular, angle-resolved photoemission experiments have provided completely new insights into the formation of the low temperature Kondo insulating state starting from the high temperature correlated metal. Here, we report detailed temperature and energy dependent measurements of the optical constants of SmB$_6$ in order to provide a detailed study from the point of view of a bulk sensitive spectroscopic probe. We detect a previously unobserved infrared active optical phonon mode, involving the movement of the Sm ions against the boron cages. The changes taking place in the free carrier response with temperature and their connection to changes in optical transitions between different bands are discussed. We find that the free charge density starts to decrease rapidly below approximately 200 K. Below 60 K a small amount of spectral weight begins to accumulate in low lying interband transitions, indicating the formation of the Kondo insulating state; however, the total integrated spectral weight in our experimental window ($sim 4.35$ eV) decreases. This indicates the involvement of a large Coulomb interaction ($>$ 5 eV) in the formation of the Kondo insulator.
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The predicted interplay between Kondo physics and non-trivial topology in SmB$_{6}$ has stimulated many experimental reports, some of which are in apparent contradiction. The origin of the dispute may lie on the fragility of the Kondo insulating phase in the presence of Sm vacancies (Kondo holes) and/or natural impurities, such as Gd$^{3+}$. In this work, we locally investigated this fragility for Al-flux grown Sm$_{1-x}$Gd$_{x}$B$_{6}$ single crystals (0 $leq$ $x$ $leq$ 0.02) by combining electron spin resonance (ESR) and complementary bulk measurements. The Gd$^{3+}$ ESR spectra in a highly dilute regime ($x$ $sim 0.0004$) display the features of an insulating cubic environment. Remarkably, a metallic ESR lineshape is observed for more concentrated samples ($x$ $geq$ 0.004), even though these systems are still in a reasonably dilute regime and show insulating $dc$ electrical resistivity. Our data indicate that the Kondo insulating state is destroyed locally around impurities before a global percolation occurs. This result not only explains the discrepancy between $dc$ and $ac$ conductivity, but also provides a scenario to explain the presence of quantum oscillations in magnetization in the absence of quantum oscillations in electrical resistivity.
We used the inverted resistance method to extend the bulk resistivity of SmB$_{6}$ to a regime where the surface conduction overwhelms the bulk. Remarkably, the bulk resistivity shows an intrinsic thermally activated behavior that changes ten orders of magnitude, suggesting that it is an ideal insulator that is immune to disorder. Non-stoichiometrically-grown SmB$_{6}$ samples also show an almost identical thermally activated behavior. At low temperatures, however, these samples show a mysterious high bulk resistivity plateau, which may arise from extended defect conduction in a 3D TI.
We study the transport properties of the Kondo insulator SmB$_6$ with a specialized configuration designed to distinguish bulk-dominated conduction from surface-dominated conduction. We find that as the material is cooled below 4 K, it exhibits a crossover from bulk to surface conduction with a fully insulating bulk. We take the robustness and magnitude of the surface conductivity, as is manifest in the literature of SmB$_6$, to be strong evidence for the topological insulator metallic surface states recently predicted for this material.
Several technical issues and challenges are identified and investigated for the planar tunneling spectroscopy of the topological Kondo insulator SmB$_6$. Contrasting behaviors of the tunnel junctions prepared in two different ways are analyzed and explained in detail. The conventional approach based on an AlO$_text{x}$ tunnel barrier results in unsatisfactory results due to the inter-diffusion between SmB$_6$ and deposited Al. On the contrary, plasma oxidation of SmB$_6$ crystals produces high-quality tunnel barriers on both (001) and (011) surfaces. Resultant conductance spectra are highly reproducible with clear signatures for the predicted surface Dirac fermions and the bulk hybridization gap as well. The surface states are identified to reside on two or one {it distinguishable} Dirac cone(s) on the (001) and (011) surface, respectively, in good agreement with the recent literature. However, their topological protection is found to be limited within the low energy region due to their inevitable interaction with the bulk excitations, called spin excitons, consistent with a recent theoretical prediction. Implications of our findings on other physical properties in SmB$_6$ and also other correlated topological materials are remarked.
The true topological nature of the Kondo insulator SmB$_6$ remains to be unveiled. Our previous tunneling study not only found evidence for the existence of surface Dirac fermions, but it also uncovered that they inherently interact with the spin excitons, collective excitations in the bulk. We have extended such a spectroscopic investigation into crystals containing a Sm deficiency. The bulk hybridization gap is found to be insensitive to the deficiency up to 1% studied here, but the surface states in Sm-deficient crystals exhibit quite different temperature evolutions from those in stoichiometric ones. We attribute this to the topological surface states remaining incoherent down to the lowest measurement temperature due to their continued interaction with the spin excitons that remain uncondensed. This result shows that the detailed topological nature of SmB$_6$ could vary drastically in the presence of disorder in the lattice. This sensitiveness to disorder is seemingly contradictory to the celebrated topological protection, but it can be understood as being due to the intimate interplay between strong correlations and topological effects.
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