Kondo semiconductors exhibit a gap in their low-temperature excitation spectra, and can be modeled by the Anderson lattice model at half filling which shows a hybridization gap. The mixed-valent Kondo semiconductor ${\mathrm{SmB}}_{6}$ also shows in-gap magnetic excitations that exhibit the temperature dependence and dispersion that are expected from magnetic excitons. The gaps measured in the Kondo semiconductors are extremely sensitive to doping in which the f ions are substituted by non-$f$ ions. Recent measurements on ${\mathrm{YbB}}_{12}$ shows a feature similar to that of the magnetic exciton in ${\mathrm{SmB}}_{6}.$ Furthermore, the concentration dependence of the features observed in inelastic neutron-scattering spectra of doped ${\mathrm{YbB}}_{12}$ is different from the concentration dependence found in measurements of thermodynamic and transport properties. The impurity concentration dependence of the gap and the spin-exciton features are investigated. The spectroscopic properties are calculated for the Anderson lattice model at half filling, in which the disorder is treated in the coherent potential approximation. The results are compared with the recent experiments.

https://math.temple.edu/~prisebor/CollapseofCoh.pdf

Collapse of the coherence gap in Kondo semiconductors

The intermediate-valence compound ${\mathrm{SmB}}_{6}$ is a well-known Kondo insulator, in which the hybridization of itinerant $5d$ electrons with localized $4f$ electrons leads to a transition from metallic to insulating behavior at low temperatures. Recent studies suggest that ${\mathrm{SmB}}_{6}$ is a topological insulator, with topological metallic surface states emerging from a fully insulating hybridized bulk band structure. Here, we locally probe the bulk magnetic properties of pure and $0.5%$ Fe-doped ${\mathrm{SmB}}_{6}$ by muon spin rotation/relaxation methods. Below 6 K, the Fe impurity induces simultaneous changes in the bulk local magnetism and the electrical conductivity. In the low-$T$ insulating bulk state we observe a temperature-independent dynamic relaxation rate indicative of low-lying magnetic excitations driven primarily by quantum fluctuations.

Quantum spin fluctuations in the bulk insulating state of pure and Fe-doped SmB 6

We examine the presence of nonmagnetic impurities in a hybridization gap model of a Kondo insulator which has band inversion. The model has been used to predict that ${\mathrm{SmB}}_{6}$ is a topological insulator. We show that there are two types of nonmagnetic impurity states in a Kondo insulator. The type of states can be categorized as deep impurity states, similar to the impurity states in an ordinary metal, and impurity states which have energies within the hybridization gap. Unlike the deep impurity states which only form if the impurity potential exceeds a critical value of the order of the conduction bandwidth, the in-gap impurity states form for exceptionally small values of the impurity potential comparable to the hybridization gap. This result may explain why Kondo insulators are found to be exceptionally sensitive to impurities. We show that these in-gap states are caused by band inversion and have properties similar to those expected for impurities in a topological insulator.

https://link.aps.org/accepted/10.1103/PhysRevB.101.094101

Topological nonmagnetic impurity states in topological Kondo insulators

The resistivity, Hall constant, specific heat, and magnetic susceptibility of the doped Kondo insulator ${({\mathrm{Ce}}_{1\ensuremath{-}x}{\mathrm{La}}_{x})}_{3}{\mathrm{Bi}}_{4}{\mathrm{Pt}}_{3}$ are studied as a function of temperature and $x$. Already at $x=0.006$, the alloy behaves like a metal, so that the metal-insulator transition in the impurity band must occur at a lower concentration. Our data allow to determine the effective mass ${m}^{*}$ and the carrier concentration $n$ separately. After a strong initial increase of $n(x)$, the carrier concentration remains nearly constant between $x=0.1$ and 0.5. The effective mass in the metallic state initially increases with $x$ and reaches a maximum of ${m}^{*}\ensuremath{\approx}100{m}_{0}$ at $x=0.3$. The scattering time $\ensuremath{\tau}$ as determined from the Drude formula decreases drastically between $x=0.006$ and 0.1, has a minimum at about $x=0.1$, and then a maximum at $x=0.3$. Surprisingly, ${m}^{*}∕\ensuremath{\tau}$ is nearly constant for the entire alloy range for $x\ensuremath{\geqslant}0.1$.

Kondo-hole conduction in the La-doped Kondo insulator Ce 3 Bi 4 Pt 3

We report the in situ preparation of surfaces of the proposed topological Kondo insulator SmB by controlled cycles of Ar ion sputtering and annealing. The procedure provides a reproducible way for the preparation of Sm- or B-rich surface terminations by low (1080 C) or high (1200 C) temperature annealing. The surface quality and termination were checked by low energy electron diffraction and Auger electron spectroscopy. Photoemission studies were carried out using momentum microscopy and two laboratory light sources providing polarised radiation with an energy of 6 eV (fourth harmonic of a pulsed Ti:Sapphire laser) and unpolarised radiation with an energy of 21.2 eV (He–I line of a gas discharge lamp). Full dispersions of electronic states in a wide two-dimensional momentum space were obtained by momentum microscopy from the in situ prepared Sm-terminated surface. The shape of the Fermi surface is discussed based on the sections through the bulk Brillouin zone sampled by the different photon energies.

Momentum microscopy of single crystals with detailed surface characterisation

The heavy fermion semiconductors such as Ce3Bi4Pt3, YbB12, and SmB6 may be modeled as indirect hybridization gap semiconductors. The magnitudes of the gap are smaller than the gaps predicted by local density functional electronic structure calculations, suggesting strong renormalizations due to electronic correlations. The inelastic neutron scattering spectra Im[χ(q,ω)] are examined within the context of this model. Anomalously sharp and temperature dependent peaks are seen at energies within the indirect gap in the inelastic neutron scattering experiments on SmB6 and YbB12 The in-gap features are identified as excitations of magnetic bound states, which are induced by residual anti-ferromagnetic interactions between the renormalized quasi-particles.

Peter S. Riseborough

Papers

Magnetic bound states in SmB6

Magnetic Bound States in SmB6