Session B28: Topological Kondo Insulators

Surface conductance and one-dimensional edge state transport in topological Kondo insulator SmB$_6$

The Kondo insulator compound SmB$_6$, with hybridization between itinerant conduction electrons and localized $f$-electrons driving an insulating gap and metallic surface states at low temperatures, is an ideal candidate for realizing the topological Kondo insulator state. By exploiting the presence of a time reversal symmetry breaking surface ferromagnetic state, we investigate the topological nature of metallic surface states, finding evidence of one-dimensional surface transport with conductance values approaching the quantized value of $e^2/h$ and originating from the chiral edge channels of ferromagnetic domain walls. We will review our milliKelvin magnetotransport measurements of the edge state transport phemonemon in SmB6, as well as thickness and surface gating studies that conclusively prove the surface nature of low temperature conductance.   

Effect of Sm valence variation on hybridization gap and in-gap excitons in SmB6 studied by Raman spectroscopy

SmB$_6$ is a proposed topological Kondo insulator where the presence of topological nontriviality can be tuned by variations in the Sm valence. A range of samples where Sm valence was varied by increasing numbers of Sm vacancies was investigated using Raman spectroscopy over a temperature range of 10 to 300 K. We show a possibility to characterize the presence of Sm vacancies on the order of 1% by correlating with the intensity of defect-induced Raman scattering. At temperatures below 50 K features due to hybridization gap and four in-gap excitons at energies between 128 and 140 cm$^{-1}$ appear in the Raman spectra of samples with low number of Sm vacancies. The narrow 4 cm$^{-1}$ line width of the excitons is associated with their long life time due to the hybridization gap. A presence of Sm vacancies leads to an appearance of the impurity states in the gap and a respective decrease of the exciton life time. As much as estimated 1% of Sm impurities leads to quenching of the in-gap excitons.   

Origin of bulk quantum oscillations in the bulk Kondo insulating ground state of SmB$_6$

I will discuss our recent observation of quantum oscillations corresponding to a bulk Fermi surface in the Kondo insulator SmB$_6$, and consider their possible origin. New complementary experimental results will be presented which raise the interesting question of whether the underlying ground state corresponds to a novel Kondo regime in which the spin channel is gapless while the charge channel is gapped.   

Angular Dependence of Quantum Oscillations in SmB$_6$

Recent proposals of low-dimensional electronic states in the Kondo insulator, SmB$_6$ have lead to renewed interest in the material. In this study we present quantum oscillation measurements of high quality single-crystals of SmB$_6$. Magnetic torque was measured in magnetic fields up to 40 T, allowing the observation of quantum oscillation frequencies ranging from 50 T to 15,000 T in multiple samples prepared by different groups. The size and the angular dependence of the oscillations indicate the striking concurrence of an electronically insulating bulk and a large, bulk Fermi surface. Comparison of the measured oscillations with similar measurements of metallic rare-earth hexaborides supports such a Fermi surface. Our model, previously employed for the metallic hexaborides, describes large ellipsoidally distorted spheres centred at X-points of the Brillouin zone, and smaller ellipsoids positioned at neck points, and gives a good account of the observed frequencies.   

Effect of Gap on Quantum Oscillations

One of the manifestations of the quantization of energy levels in a magnetic field is quantum oscillations. In a metal, oscillations in several physical observables occur each time a Landau level crosses the Fermi level, and is, therefore, a Fermi surface property. In a gapped system, since there is no Fermi surface, such oscillations are not expected. One can ask, what happens to these oscillations as a metal is slowly turned into an insulator by introducing a gap at the Fermi level. To address this, we consider a simple model of two overlapping bands that hybridize to open a gap, and investigate how the oscillations change as the gap is slowly increased, both at zero and non-zero temperature. We show that the oscillations in such gapped systems show marked deviation from the canonical Lifshitz-Kosevich results routinely used to study quantum oscillations in metals.   

Quantum oscillation in narrow-gap topological insulators

The canonical understanding of quantum oscillation in metals is challenged by the observation of de Haas-van Alphen effect in an insulator, SmB$_{6}$ [Tan \emph{et al}, Science {\bf349}, 287 (2015)]. Based on a two-band model with inverted band structure, we show that the periodically narrowing hybridization gap in magnetic fields can induce the oscillation of low-energy density of states in the bulk, which is observable provided that the activation energy is small and comparable to the Landau level spacing. Its temperature dependence strongly deviates from the Lifshitz-Kosevich theory. The nontrivial band topology manifests itself as a nonzero Berry phase in the oscillation pattern, which crosses over to a trivial Berry phase by increasing the temperature or the magnetic field. Further predictions to experiments are also proposed.   

Reduction of the low-temperature bulk gap in the topological Kondo insulator samarium hexaboride under high magnetic fields

The mixed-valent insulator samarium hexaboride exhibits a narrow bandgap at low temperatures, formed by strong-correlation interactions between itinerant $d$ electrons and $f$ states localized to the Sm ions, and surface states accessible to transport below about 2 K. Spectroscopic measurements of the bandgap suggest a gap size of 15-20 meV, but transport measurements of thermally-activated carriers suggest the Fermi energy is about 3 meV below the conduction band edge. Here, we study the activated transport gap in pulsed magnetic fields up to 60 T between 1.5 K and 4 K. The magnetoresistance of the surface states, which has only very weak temperature dependence, is distinct from that of the bulk states, which exhibit thermally-activated behavior. The activation energy shrinks by 50\% at fields up to 60 T. Data up to 93 T suggest that the transport gap continues to close, but is only fully-closed at even higher fields. We compare the measured reduction to theoretically-expected behavior due to Zeeman shifts of the Sm ion $f$-state transition energies. Meanwhile, the surface state shows no hints of Shubnikov--de Haas oscillations, which places constraints on any 2D surface carrier's mobility.   

Magnetotransport Measurements on SmB$_6$ - Cornering the Parameter Space for Carrier Density and Mobility

There is growing interest in studying the conducting surface of SmB$_6$, which is believed to originate from its nontrivial band topology. Up to date, different measurement techniques, including ARPES, dHvA, and Hall bar transport still disagree on important parameters such as the carrier density. In order to find the carrier density ($n$) and mobility ($\mu$) for the Dirac pockets participating in transport, we measure magnetotransport on Corbino devices fabricated on (100), (110), and (111) surfaces grown by floating zone and flux methods. Our samples do not exhibit Shubnikov-de Haas oscillations at high field pulsed measurements up to 90 Tesla, which provides an upper bound of $\mu$ of each channels. Also, angle-dependent magnetotransport up to 35 T allows us to extract an effective $n$ and $\mu$ of the combined channels. Together, a parameter space that confines the possible $n$ and $\mu$ of each channel is constructed, and appears to be in agreement with ARPES reports. Additionally, the effective $n$ and $\mu$ change up to 20 percent when applying magnetic field up to 35 T. We will discuss how the Landau fan diagram can be nonlinear by this effect.   

Kondo Interactions from Band Reconstruction in YbInCu$_{\mathrm{4\thinspace }}$

We combine resonant inelastic x-ray scattering and model calculations in the Kondo lattice compound YbInCu$_{\mathrm{4}}$, a system characterized by a dramatic increase in Kondo temperature and associated valence fluctuations below a first-order valence transition at T $\simeq $ 42 K. The bulk-sensitive, element-specific, and valence-projected charge excitation spectra reveal an unusual quasigap in the Yb-derived state density which drives an instability of the electronic structure and renormalizes the low-energy effective Hamiltonian at the transition. Our results provide long-sought experimental evidence for a link between temperature-driven changes in the low-energy Kondo scale and the higher-energy electronic structure of this system.   

Temperature-dependent Helicity of In-gap states of SmB$_6$

Mixed-valent SmB$_6$ with a temperature (T) dependent bulk gap is the first candidate example of a new class of strongly correlated topological insulators with $f$-$d$ band inversion. Previous angle-resolved photoemission (ARPES) on cleaved \textless 100\textgreater\ surfaces of SmB$_6$ have quantified the T-evolution of (i) the Sm 4$f$ state coherence, (ii) the X-point $f$-conduction band energy and many-body gap destabilization, and (iii) the intimately connected fate of in-gap states. In this work we additionally characterize the T-evolution of the in-gap state orbital angular momentum helicity using circular dichroism. We show that the onset of dichroism, above 100K, coincides with the dimensional crossover from high T 3D non-helical bulk $d$-band states crossing $E_{\mathrm{F}}$ to low T 2D in-gap surface states where the dichroic asymmetry reaches 100$\%$. With the assumption of topological surface state anti-parallel spin-momentum locking, this result can be viewed as supporting previous spin-resolved ARPES measurements of in-gap state helical spin structure.   

In-gap states on the non-polar (110) surface of SmB$_{6}$

Mixed-valent SmB$_6$ with a temperature-dependent bulk gap is the first candidate example of a new class of strongly correlated topological insulators with $f$-$d$ band inversion. The topological origin of in-gap states on cleaved (001) surfaces as measured by angle-resolved photoemission (ARPES) is not without controversy, since the $\overline{X}$ states span the full $\sim$20 meV hybridization gap at low temperature without exhibiting any clear Dirac point. Furthermore, reports exist of band-bending due to the polarity of the (001) surface and depth-dependent deviations from bulk stoichiometry or Sm valency. In this work we explore ARPES of the $non$-$polar$ (110) surface of SmB$_6$ prepared by polishing and high-temperature annealing. We find in-gap states at $\overline{X}$ and $\overline{Y}$ points with very similar properties as the (001) $\overline{X}$ states. We discuss the relevance of these findings to the TI and other proposed models, and to the recent discrepancy between 2D [1] and 3D [2] interpretations of dHvA Fermi surface orbits.\newline [1] G. Li, $et\ al.$, Science \textbf{346}, 1208 (2014).\newline [2] B.S. Tan, $et\ al.$, Science \textbf{349}, 287 (2015).   

Effect of Magnetic Substitution on Topological Kondo Insulator SmB6

The Kondo topological insulator SmB6 is an ideal candidate to realize protected metallic surface states driven by strong electron correlations. Recent experiments [1] provide evidence for one-dimensional electron transport on the surface of SmB6, associated with the existence of topologically nontrivial chiral edge states at the boundaries of intrinsic surface ferromagnetic domains. If these surface states are indeed topologically nontrivial they will be destroyed by the introduction of time reversal symmetry breaking magnetic impurities. We investigate the effect of magnetic impurities on SmB6 through transport measurements in Fe and Ni substituted SmB6 at very low temperatures. [1]Nakajima et. al., arXiv:1312.6132