Compound SmB6 Research Articles

Topology of SmB6 revisited by means of topological quantum chemistry

The mixed-valence compound SmB6 with partially filled samarium 4f flat bands hybridizing with 5d conduction bands is a paramount example of a correlated topological heavy-fermion system. In this study, we revisit the topology of SmB6 within the formalism of topological quantum chemistry and symmetry-based indicators. Based on this approach, we reach a detailed classification of the material's topology, and we reformulate the origin of topology in terms of band representations. We corroborate these aspects by constructing a minimal TB model that is consistent with all the symmetries of the system and is able to reproduce the topology of the material. We finally unveil the previously overlooked formation of multiple topological gaps, and we discuss its implications for experiments. Published by the American Physical Society 2024

Probing the bulk valence of Sm in SmB6 by studying the magnetic susceptibility under pressure

For one of the most famous and widely investigated intermediate-valence compound SmB6, we report the results of a precise experimental study of the pressure effect on magnetic susceptibility χ. The measurements of χ(P) were carried out under helium gas pressure P up to 2 kbar at fixed temperatures 78 and 300 K using a pendulum-type magnetometer. The observed pressure effect value, d lnχ/dP ∼ –6 Mbar–1, demonstrates a noticeable decrease in susceptibility under pressure, which is weakly dependent on temperature used. From model analysis of the experimental data, combined with the supplemented LSDA + U calculations of the electronic structure and van Vleck paramagnetism of the band states of SmB6, we have estimated the value of the initial pressure derivative for the intermediate valence of Sm. It is consistent with the literature data obtained by other methods and indicates an increase in valence with increasing pressure. It was shown that the valence of Sm and its pressure dependence are closely related to the detailed characteristics of the conduction band and 4f states.

Classification for a novel antiferromagnetic topological insulating phase in three-dimensional topological Kondo insulator

Antiferromagnetic topological insulator (AFTI) is a topological matter that breaks time-reversal symmetry. Since its proposal, explorations of AFTI in strong-correlated systems are still lacking. In this paper, we show for the first time that a novel AFTI phase can be realized in three-dimensional topological Kondo insulator (TKI). In a wide parameter region, the ground states of TKI undergo a second-order transition to antiferromagnetic insulating phases which conserve a combined symmetry of time reversal and a lattice translation, allowing us to derive a -classification formula for these states. By calculating the index, the antiferromagnetic insulating states are classified into AFTI or non-topological antiferromagnetic insulator (nAFI) in different parameter regions. On the antiferromagnetic surfaces in AFTI, we find topologically protected gapless Dirac cones inside the bulk gap, leading to metallic Fermi rings exhibiting helical spin texture with weak spin-momentum locking. Depending on model parameters, the magnetic transitions take place either between AFTI and strong topological insulator, or between nAFI and weak topological insulator. By varying some model parameters, we find a topological transition between AFTI and nAFI, driving by closing of bulk gap. Our work may account for the pressure-induced magnetism in TKI compound SmB6, and helps to explore richer AFTI phases in heavy-fermion systems as well as in other strong-correlated systems.

Kondo-like behavior near the magnetic instability in SmB6 : Temperature and pressure dependences of the Sm valence

We report a systematic study of Sm valence in the prototypical intermediate valence compound SmB$_6$. Sm mean valence, $v_{\rm Sm}$, was measured by X-ray absorption spectroscopy as functions of pressure ($1<P<13$ GPa) and temperature ($3<T<300$ K). Pressure induced magnetic order (MO) was detected above $P_c = 10$ GPa by resistivity measurements. A shift toward localized $4f$ state with increasing $P$ and/or $T$ is evident from an increase in $v_{\rm Sm}$. However $v_{\rm Sm}$ at $P_c$ is anomalously far below 3, which differs from the general case of nonmagnetic-magnetic transition in Yb and Ce compounds. From the $T$ dependence of $v_{\rm Sm}(P,T)$, we found that $v_{\rm Sm}(P,T)$ consists of two different characteristic components: one is associated with low-energy electronic correlations involving Kondo like behavior, and the other with high-energy valence fluctuations.

Ultrafast terahertz spectroscopy study of a Kondo insulating thin-film SmB6 : Evidence for an emergent surface state

We utilize terahertz time domain spectroscopy to investigate thin films of the heavy fermion compound SmB6, a prototype Kondo insulator. Temperature dependent terahertz (THz) conductivity measurements reveal a rapid decrease in the Drude weight and carrier scattering rate at ~T*=20 K, well below the hybridization gap onset temperature (100 K). Moreover, a low-temperature conductivity plateau (below 20K) indicates the emergence of a surface state with an effective electron mass of 0.1me. Conductivity dynamics following optical excitation are also measured and interpreted using Rothwarf-Taylor (R-T) phenomenology, yielding a hybridization gap energy of 17 meV. However, R-T modeling of the conductivity dynamics reveals a deviation from the expected thermally excited quasiparticle density at temperatures below 20K, indicative of another channel opening up in the low energy electrodynamics. Taken together, these results suggest the onset of a surface state well below the crossover temperature (100K) after long-range coherence of the f-electron Kondo lattice is established.

Temperature and pressure dependences of Sm valence in intermediate valence compound SmB6

We report the results of the X-ray absorption spectroscopy (XAS) on the intermediate valence compound SmB6. The XAS measurements were performed near the nonmagnetic-magnetic phase boundary. Mean Sm valence vSm was estimated from absorption spectra, and we found that vSm near the boundary (P≥10GPa and T∼12K) is far below a trivalent state with magnetic characteristics. Although the result is markedly different from the cases of pressure induced magnetic orders in Yb and Ce compounds, it is likely that the large deviation from the trivalent state seems to be common in some Sm compounds which possess electronic configuration between 4f5 and 4f6 with multi 4f electrons.

Quantum spin fluctuations in the bulk insulating state of pure and Fe-doped SmB6

The intermediate-valence compound SmB6 is a well-known Kondo insulator, in which 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 SmB6 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 SmB6 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-temperature insulating bulk state we observe a temperature-independent dynamic relaxation rate indicative of low-lying magnetic excitations driven primarily by quantum fluctuations.

Electronic states in the pressure-induced magnetically ordered phase in SmB6

We have carried out the high-pressure measurement of X-ray absorption spectroscopy on the intermediate valence compound SmB6 which shows magnetic ordering as well as an insulator-metal transition at critical pressure Pc ∼ 10 GPa. The valence of Sm atom at room temperature increases with increasing pressure, however it is far below a trivalent state at Pc. In contrast to cases of pressure-induced nonmagnetic-magnetic transition in Yb compounds, which mostly occurs in the scheme of well localized 4f electrons, the present observation suggests that electronic system in SmB6 still possesses strong delocalized characters at Pc.

Irreversible proliferation of magnetic moments at cleaved surfaces of the topological Kondo insulator SmB6

The compound SmB$_6$ is the best established realization of a topological Kondo insulator, in which a topological insulator state is obtained through Kondo coherence. Recent studies have found evidence that the surface of SmB$_6$ hosts ferromagnetic domains, creating an intrinsic platform for unidirectional ballistic transport at the domain boundaries. Here, surface-sensitive X-ray absorption (XAS) and bulk-sensitive resonant inelastic X-ray scattering (RIXS) spectra are measured at the Sm N$_{4,5}$-edge, and used to evaluate electronic symmetries, excitations and temperature dependence near the surface of cleaved samples. The XAS data show that the density of large-moment atomic multiplet states on a cleaved surface grows irreversibly over time, to a degree that likely exceeds a related change that has recently been observed in the surface 4f orbital occupation.

One-dimensional edge state transport in a topological Kondo insulator

Topological insulators, with metallic boundary states protected against time-reversal-invariant perturbations, are a promising avenue for realizing exotic quantum states of matter including various excitations of collective modes predicted in particle physics, such as Majorana fermions and axions. According to theoretical predictions, a topological insulating state can emerge from not only a weakly interacting system with strong spin-orbit coupling, but also in insulators driven by strong electron correlations. The Kondo insulator compound SmB6 is an ideal candidate for realizing this exotic state of matter, with hybridization between itinerant conduction electrons and localized $f$-electrons driving an insulating gap and metallic surface states at low temperatures. Here we exploit the existence of surface ferromagnetism in SmB6 to investigate the topological nature of metallic surface states by studying magnetotransport properties at very low temperatures. We find evidence of one-dimensional surface transport with a quantized conductance value of $e^2/h$ originating from the chiral edge channels of ferromagnetic domain walls, providing strong evidence that topologically non-trivial surface states exist in SmB6.

Racah materials: role of atomic multiplets in intermediate valence systems.

We address the long-standing mystery of the nonmagnetic insulating state of the intermediate valence compound SmB6. Within a combination of the local density approximation (LDA) and an exact diagonalization (ED) of an effective discrete Anderson impurity model, the intermediate valence ground state with the f-shell occupation 〈n4f〉 = 5.6 is found for the Sm atom in SmB6. This ground state is a singlet, and the first excited triplet state ~3 meV higher in the energy. SmB6 is a narrow band insulator already in LDA, with the direct band gap of ~10 meV. The electron correlations increase the band gap which now becomes indirect. Thus, the many-body effects are relevant to form the indirect band gap, crucial for the idea of “topological Kondo insulator" in SmB6. Also, an actinide analog PuB6 is considered, and the intermediate valence singlet ground state is found for the Pu atom. We propose that [Sm, Pu]B6 belong to a new class of the intermediate valence materials with the multi-orbital “Kondo-like" singlet ground-state. Crucial role of complex spin-orbital f n–f n+1 multiplet structure differently hybridized with ligand states in such Racah materials is discussed.

Incomplete protection of the surface Weyl cones of the Kondo insulatorSmB6: Spin exciton scattering

The compound SmB$_6$ is a Kondo Insulator, where the lowest-energy bulk electronic excitations are spin excitons. It also has surface states that are subjected to strong spin-orbit coupling. It has been suggested that SmB$_6$ is also a topological insulator. Here we show that, despite the absence of time-reversal symmetry breaking and the presence of strong spin-orbit coupling, the chiral spin texture of the Weyl cone is not completely protected. In particular, we show that the spin-exciton mediated scattering produces features in the surface electronic spectrum at energies separated from the surface Fermi energy by the spin-exciton energy. Despite the features being far removed from the surface Fermi energy, they are extremely temperature dependent. The temperature variation occurs over a characteristic scale determined by the dispersion of the spin exciton. The structures may be observed by electron spectroscopy at low temperatures.

Tuning bulk and surface conduction in the proposed topological Kondo insulator SmB(6).

Bulk and surface state contributions to the electrical resistance of single-crystal samples of the topological Kondo-insulator compound SmB_{6} are investigated as a function of crystal thickness and surface charge density, the latter tuned by ionic liquid gating with electrodes patterned in a Corbino disk geometry on a single (100) surface. By separately tuning bulk and surface conduction channels, we show conclusive evidence for a model with an insulating bulk and metallic surface states, with a crossover temperature that depends solely on the relative contributions of each conduction channel. The surface conductance, on the order of 100 e^{2}/h, exhibits a field-effect mobility of 133 cm^{2}/Vs and a large carrier density of ∼2×10^{14} cm^{-2}, in good agreement with recent photoemission results. With the ability to gate modulate surface conduction by more than 25%, this approach provides promise for both fundamental and applied studies of gate-tuned devices structured on bulk crystal samples.

Pressure-Induced Localization of 4f Electrons in the Intermediate Valence Compound SmB6

We report high-pressure studies of X-ray diffraction and 11 B-nuclear magnetic resonance (NMR) in the intermediate- valence compound SmB6. The pressure dependence of the lattice constant was precisely determined and no anomaly was observed up to 9.1 GPa. The temperature dependence of the nuclear quadrupole resonance frequencyQ, obtained from the 11 B-NMR measurements, is predominantly contributed by on-site charge distribution. Using the relationship betweenQ and Sm valence at ambient pressure reported previously, we estimate the pressure dependence of the Sm valence up to 6 GPa as well. The increase in the Sm valence accelerates with pressure and reaches an increase of about 10% at 6 GPa. The pressure-induced localization of Sm 4f -holes may be responsible for the long-range magnetic order under pressure.

Pulsed magnetic field study of the spin gap in intermediate valence compound SmB 6

In this work, we report the behavior of electrical resistivity of SmB6 at temperatures between 2.2 and 70 K in pulsed magnetic fields up to 54 T. A strong negative magnetoresistance was detected with increasing magnetic field, when lowering the temperature in the range To30 K. We show that the amplitude of negative magnetoresistance reaches its maximum dR/R� 70% at B ¼ 54 T, in the vicinity of phase transition occurring in this strongly correlated electron system at TC� 5 K. The crossover from negative magnetoresistance to positive magnetoresistance found at intermediate temperatures at T430 K is discussed within the framework of exciton–polaron model of local charge fluctuations in SmB6 proposed by Kikoin and Mishchenko. It seems that these exciton–polaron in-gap states are influenced both by temperature and magnetic field.

Evidence for gap anisotropy in [formula omitted

Resistivity measurements under uniaxial stress have been performed on the intermediate valence compound SmB 6 for various directions of the crystal. The experimental technique allows us to explore a limited pressure area (basically 0–3 kbar). Nevertheless, the results clearly show an anisotropy; indeed, the effect of the stress in the decrease of the residual resistivity is much higher in the < 1 1 1 > direction than in the < 1 0 0 > and the < 1 1 0 > orientations. This change is witness to the gap anisotropy which must be linked to the theory of excitonic semiconductors.

Magnetoresistance anomaly at the transition to coherent state in SmB 6

To shed more light on the nature of puzzling “metallic” state observed in intermediate-valence compound SmB 6 below T * ∼ 5 K, precise measurements of transport and magnetic properties have been carried out on single crystals of SmB 6 in a wide range of temperatures (1.8–30 K) in magnetic fields up to 7 T. A strong enhancement of negative magnetoresistance to the maximum value of Δρ/ρ B 2∼−2.2×10 −3 T −2 at T∼T * has been detected when temperature decreases below 14 K. This effect is attributed to the features of anomalous scattering of short-range (<10 Å) exciton-polaronic complexes resulting from fast charge fluctuations on Sm-sites. The anomalies of transport and magnetic characteristics are discussed in terms of electron phase transition to the coherent state of interacting many-body complexes below T * ∼ 5 K.

An observation of electron phase transition in SmB 6 at low temperatures

In order to reveal the nature of the ground state of archetypal intermediate-valence compound SmB 6, a comprehensive study of its transport and magnetic properties was carried out on high-quality single crystals at temperatures of 1.8–300 K in magnetic fields up to 7 T. A drastic enhancement of negative magnetoresistance was observed below 14 K, with the maximum absolute value of Δ ρ/ ρB 2∼2.2×10 −3 T −2 at T≈5.2 K. This effect seems to be attributable to anomalous magnetic scattering of many-body (exciton–polaronic) complexes induced by fast valence fluctuations on Sm sites. The observed anomalies of magnetotransport, thermoelectric and magnetic characteristics are discussed in terms of electron phase transition to the coherent state of interacting many-body complexes occurring at T *∼5 K.

Ground state formation in intermediate valent SmB 6

Electrical resistivity measurements have been carried out on the intermediate valent small gap compound SmB 6 at temperatures between 90 and 0.08 K. From the local activation energy we were able to determine directly the width of the hybridization gap which controls the conductivity between 70 and 15 K, and the distance between the bottom of the conduction band and in-gap states which are formed in this energy gap and provide extrinsic conduction in the temperature range 15–3 K. Below about 3 K the activation energy of all the samples decreases rapidly to values which are much lower than the available thermal energy. This result implies that the residual conductivity of SmB 6 is of non-activated (metallic) nature. The metallic behaviour can be attributed to a many-particle ground state formed from the in-gap states of this compound.

Nature of the low-temperature anomalies in the physical properties of the intermediate-valent compound SmB6

The transport properties (Hall coefficient, thermopower, and resistivity) of high-quality single-crystal samples of the classical mixed-valent compound SmB6 are investigated over a broad temperature range (1.6–300 K) in magnetic fields up to 45 T for the first time following the quasioptical measurements in the 0.6–4.5 meV frequency range [B. Gorshunov, N. Sluchanko, A. Volkov et al., submitted to Phys. Rev. B (1998)]. Measurements in the intrinsic conduction region permit determination of the gap width Eg≈20 meV and evaluation of the behavior of the mobility and concentration of light and heavy charge carriers, as well as the temperature dependence of the carrier relaxation time, in samarium hexaboride. The results of experimental investigations in the “impurity” conduction region (Eex≈3.5 meV) are discussed within the Kikoin-Mishchenko exciton-polaron model of charge fluctuations. Arguments supporting the formation of a metallic state with an electron-hole liquid in SmB6 at liquid-helium temperatures are presented.