Topological Kondo Insulator SmB6 Research Articles

Extraordinary bulk-insulating behavior in the strongly correlated materials FeSi and FeSb2

4f electron-based topological Kondo insulators have long been researched for their potential to conduct electric current via protected surface states, while simultaneously exhibiting unusually robust insulating behavior in their interiors. To this end, we have investigated the electrical transport of the 3d-based correlated insulators FeSi and FeSb2, which have exhibited enough similarities to their f electron cousins to warrant investigation. By using a double-sided Corbino disk transport geometry, we show unambiguous evidence of surface conductance in both of these Fe-based materials. In addition, by using a four-terminal Corbino inverted resistance technique, we extract the bulk resistivity as a function of temperature. Similar to topological Kondo insulator SmB6, the bulk resistivity of FeSi and FeSb2 is confirmed to exponentially increase by up to 9 orders of magnitude from room temperature to the lowest accessible temperature. This demonstrates that these materials are excellent bulk insulators, providing an ideal platform for studying correlated 2D physics.

Breakdown of bulk-projected isotropy in surface electronic states of topological Kondo insulator SmB6(001)

The topology and spin-orbital polarization of two-dimensional (2D) surface electronic states have been extensively studied in this decade. One major interest in them is their close relationship with the parities of the bulk (3D) electronic states. In this context, the surface is often regarded as a simple truncation of the bulk crystal. Here we show breakdown of the bulk-related in-plane rotation symmetry in the topological surface states (TSSs) of the Kondo insulator SmB6. Angle-resolved photoelectron spectroscopy (ARPES) performed on the vicinal SmB6(001)-p(2 × 2) surface showed that TSSs are anisotropic and that the Fermi contour lacks the fourfold rotation symmetry maintained in the bulk. This result emphasizes the important role of the surface atomic structure even in TSSs. Moreover, it suggests that the engineering of surface atomic structure could provide a new pathway to tailor various properties among TSSs, such as anisotropic surface conductivity, nesting of surface Fermi contours, or the number and position of van Hove singularities in 2D reciprocal space.

Spin-selective tunneling from nanowires of the candidate topological Kondo insulator SmB6.

Incorporating relativistic physics into quantum tunneling can lead to exotic behavior such as perfect transmission through Klein tunneling. Here, we probed the tunneling properties of spin-momentum-locked relativistic fermions by designing and implementing a tunneling geometry that uses nanowires of the topological Kondo insulator candidate samarium hexaboride. The nanowires are attached to the end of scanning tunneling microscope tips and used to image the bicollinear stripe spin order in the antiferromagnet Fe1.03Te with a Neel temperature of about 50 kelvin. The antiferromagnetic stripes become invisible above 10 kelvin concomitant with the suppression of the topological surface states in the tip. We further demonstrate that the direction of spin polarization is tied to the tunneling direction. Our technique establishes samarium hexaboride nanowires as ideal conduits for spin-polarized currents.

Magnetoquantum oscillations in the specific heat of a topological Kondo insulator

Surprisingly, magnetoquantum oscillations (MQOs) characteristic of a metal with a Fermi surface have been observed in measurements of the topological Kondo insulator SmB6. As these MQO have only been observed in measurements of magnetic torque (dHvA) and not in measurements of magnetoresistance (SdH), a debate has arisen as to whether the MQO are an extrinsic effect arising from rare-earth impurities, defects, and/or aluminum inclusions or an intrinsic effect revealing the existence of charge-neutral excitations. We report here the first observation of MQO in the low-temperature specific heat of SmB6. The observed frequencies and their angular dependence for these flux-grown samples are consistent with previous results based on magnetic torque for SmB6 but the inferred effective masses are significantly larger than previously reported. Such oscillations can only be observed if the MQO are of bulk thermodynamic origin; the measured magnetic-field dependent oscillation amplitude and effective mass allow us to rule out suggestions of an extrinsic, aluminum inclusion-based origin for the MQO.

Non-trivial impurity and field effects in topological Kondo insulator SmB6

Topological Kondo Insulator SmB6 is a strongly correlated material where a spin–orbit interaction between the localized odd-parity f-electron and even parity d-electron levels lead to a band inversion and opening of an insulating gap. The non-trivial topology (Z2 = -1) leads to the formation of a topologically protected conducting surface state due to the presence of strong correlation physics. Although the bulk material is known to form a topological Kondo gap, recent magnetic quantum oscillation experiments on SmB6 find an unconventional Fermi surface whose origin remains a matter of intense debate, and the possible role of topological surfacestate and impurity induced in-gap states have been proposed. By utilizing a realistic multi-orbital tight-binding Hamiltonian, this work aims to develop a microscopic model to study the effects of perturbations like external magnetic fields, and impurities on the low energy bulk and topological surface state properties of SmB6. We further examine the role of an external electric field in tuning the non-trivial topological surface state in SmB6 and provide experimentally observable signatures in the local density of state (LDOS) near non-magnetic and magnetic impurities. Additionally, we study the surface Ferromagnetism that arises in SmB6 as observed by magnetoresistance experiments.

Crystal Growth by the Floating Zone Method of Ce-Substituted Crystals of the Topological Kondo Insulator SmB6

SmB6 is a mixed valence topological Kondo insulator. To investigate the effect of substituting Sm with magnetic Ce ions on the physical properties of samarium hexaboride, Ce-substituted SmB6 crystals were grown by the floating zone method for the first time as large, good quality single crystal boules. The crystal growth conditions are reported. Structural, magnetic and transport properties of single crystals of Sm1−xCexB6 (x=0.05, 0.10 and 0.20) were investigated using X-ray diffraction techniques, electrical resistivity and magnetisation measurements. Phase composition analysis of the powder X-ray diffraction data collected on the as-grown boules revealed that the main phase was that of the parent compound, SmB6. Substitution of Sm ions with magnetic Ce ions does not lead to long-range magnetic ordering in the Sm1−xCexB6 crystals. The substitution with 5% Ce and above suppresses the cross-over from bulk conductivity at high temperatures to surface-only conductivity at low temperatures.

Electrical detection of the inverse Edelstein effect on the surface of SmB6

We report the measurement of spin current induced charge accumulation, the inverse Edelstein effect (IEE), on the surface of a candidate topological Kondo insulator SmB6 single crystal. Robust surface conduction channel of SmB6 has been shown to exhibit large degree of spin-momentum locking, and spin polarized current through an external ferromagnetic contact induces the spin dependent charge accumulation on the surface of SmB6. The dependences of the IEE signal on the bias current, an external magnetic field direction and temperature are consistent with the anticlockwise spin texture for the surface band in SmB6 in the momentum space, and the direction and magnitude of the effect compared with the normal Edelstein signal are clearly explained by the Onsager reciprocal relation. Furthermore, we estimate spin-to-charge conversion efficiency, the IEE length, as 4.46 nm that is an order of magnitude larger than the efficiency found in other typical Rashba interfaces, implying that the Rashba contribution to the IEE signal could be small. Building upon existing reports on the surface charge and spin conduction nature on this material, our results provide additional evidence that the surface of SmB6 supports spin polarized conduction channel.

Surface Conductivity of the Ytterbium-Doped Topological Kondo-Insulator SmB6

The temperature dependence of the conductivity of the topological Kondo-insulator (TKI) Sm1 – xYbxB6 is investigated in the temperature range 2 < T < 300 K for compositions with x ≤ 0.024. It is found that the ytterbium impurity most strongly affects the low-temperature (T < 20 K) electrical conductivity: when changing from x = 0 to x = 0.024, the activation energy of bulk conductivity decreases by 1.8 times from 4 to 2.2 meV, and the 2D surface conductivity increases by six times. The separation made for the contributions to the conductivity enables us to establish that the one-parameter scaling model can be used for describing the conductivity of 2D surface states in the Sm1 – xYbxB6 TKI in which both the interaction with phonons and the electron–electron scattering effects are taken into account.

Electron Spin Resonance in Strongly Correlated Metals

Modern technique of electron spin resonance (ESR) measurements and data analysis in strongly correlated metals, which allows finding the full set of spectroscopic parameters including oscillating magnetization, relaxation parameter (line width), and hyromagnetic ratio (g-factor), is described. Application of the considered method is illustrated by such examples as metallic systems CeB6, Mn1−xFexSi, GdB6, HoxLu1−xB12, and metallic surface of topological Kondo insulator SmB6. It is shown that ESR in strongly correlated metals provides a unique tool for studying short-range correlations at the nanoscale of a spin polaron type, electron nematic effects, and spin fluctuation transitions. Application of ESR technique opens new opportunities for observation of quantum critical points, including hidden ones. In many cases, it is just ESR, which either indicates the necessity for clarification or deep revision of the prevailing paradigm, or constitutes the basis for a new concept of magnetic properties of various strongly correlated metals.

Hall-coefficient diagnostics of the surface state in pressurized SmB6

In this study, we report the first results of the high-pressure Hall coefficient (RH) measurements in the putative topological Kondo insulator SmB6 up to 37 GPa. Below 10 GPa, our data reveal that RH(T) exhibits a prominent peak upon cooling below 20 K. Remarkably, the temperature at which surface conduction dominates coincides with the temperature of the peak in RH(T). The temperature dependent resistance and Hall coefficient can be well fitted by a two-channel model with contributions from the metallic surface and the thermally activated bulk states. When the bulk of SmB6 becomes metallic and magnetic at ~ 10 GPa, both the RH(T) peak and the resistance plateau disappear simultaneously. Our results indicate that the RH(T) peak is a fingerprint to diagnose the presence of a metallic surface state in SmB6. The high-pressure magnetic state of SmB6 is robust to 180 GPa, and no evidence of superconductivity is observed in the metallic phase.

Spin Fluctuations at the Surface of Strongly Correlated Topological Insulator SmB6

The low temperature (T < 5 K) electron spin resonance in topological Kondo insulator SmB6 is investigated. It is shown that spin relaxation time of the paramagnetic centers responsible for low temperature electron spin resonance in SmB6 is about ~ 10−8 s, which exceeds by five orders of magnitude the widely accepted spin and charge fluctuation time ~ 10−13 s in the homogeneous mixed valence state of this material. This discrepancy may be attributed to the formation of the specific paramagnetic centers in the sample surface–spin polarons.

Magnetoresistance hysteresis in topological Kondo insulator SmB6 nanowire**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0300802) and the National Natural Science Foundation of China (Grant Nos. 61825401 and 11774004).

SmB6, a topological Kondo insulator, with a gapped bulk state and metallic surface state has aroused great research interest. Here, we report an exotic hysteresis behavior of magnetoresistance in individual SmB6 nanowire in a temperature range in which both surface and bulk states contribute to the total conductance. Under a magnetic field parallel to the SmB6 nanowire, the resistance suddenly increases at the turning point from up-sweep to down-sweep of the magnetic field. The magnetoresistance hysteresis loops are well consistent with the magnetocaloric effect. Our results suggest that the SmB6 nanowires possess potential applications in the magnetic cooling technology.

Breakdown of the strong multiplet description of the Sm2+ ion in the topological Kondo insulator SmB6: specific heat studies

We have theoretically confirmed the existence of in-gap real quantum-mechanical states in SmB6, which have been suggested by experiments. These in-gap states, below the hybridization gap of 20 meV, are related to the Sm2+ ion states and can be revealed by calculations within the spin-orbital |LSLzSz〉 space, with L = 3 and S = 3. Our approach overcomes difficulties related to the singlet J = 0 multiplet ground state. The in-gap states originate from the 49-fold degenerated term 7F (4f 6), which is split by cubic crystal-field (CEF) and spin-orbit (s − o) interactions. There is competition between these interactions: the six-order CEF interactions produce a 7-fold degenerated ground state, whereas the s − o interactions, even the weakest one, produce a singlet (J = 0) ground state. We have found preliminary CEF and s − o parameters that produce the lowest states at 0 K (singlet) and 91 K (triplet) and the next triplet at 221 K, i.e., within the hybridization gap. The derived states well explain the large extra specific heat of SmB6, confirming the consistency and adequateness of our theoretical approach with the breakdown of the strong multiplet description of the Sm2+ ion in SmB6.

Magnetic Properties of the Topological Kondo Insulator SmB6: Localized Magnetic Moments and Pauli Paramagnetism

The magnetic properties of the topological Kondo insulator SmB6 are studied in the temperature range T T*, the magnetization qualitatively corresponds to the model of decay of Kondo singlets and is determined by the Pauli paramagnetism, which includes both the linear and nonlinear contributions. In the range T < T*, the Pauli paramagnetism becomes supplemented in the threshold manner by the contribution of localized magnetic moments. The performed estimate of effective magnetic moments arising at T < T* gives anomalously high values μ* ∼ (7–14) μB ion, far exceeding the values μ* ∼ (3–5) μB expected for a separate magnetic Sm3+ ion. This is a signature of the possible spin-polaron nature of localized magnetic moments in the topological Kondo insulator SmB6.

Anomalous Z2 antiferromagnetic topological phase in pressurized SmB6

Antiferromagnetic materials, whose time-reversal symmetry is broken, can be classified into the Z2 topology if they respect some specific symmetry. Since the theoretical proposal, however, no materials have been found to host the antiferromagnetic topological (AFT) phase to date. Here, for the first time, we demonstrate that the topological Kondo insulator SmB6 can be an AFT system when pressurized to undergo an antiferromagnetic phase transition. In addition to propose the possible candidate for an AFT material, in this work we also illustrate the anomalous topological surface states of the AFT phase which has not been discussed before. Originating from the interplay between the topological properties and the antiferromagnetic surface magnetization, the topological surface states of the AFT phase behave differently as compared with those of a topological insulator. Besides, the AFT insulators are also found promising in the generation of tunable spin currents, which is an important application in spintronics.

Magnetoresistance Anomaly in Topological Kondo Insulator SmB6 Nanowires with Strong Surface Magnetism.

Topological Kondo insulators (TKIs) are a new class of topological materials in which topological surface states dominate the transport properties at low temperatures. They are also an ideal platform for studying the interplay between strong electron correlations and topological order. Here, hysteretic magnetoresistance (MR) is observed in TKI SmB6 thin nanowires at temperatures up to 8 K, revealing the strong magnetism at the surface of SmB6. It is also found that such MR anomaly exhibits an intriguing finite size effect and only appears in nanowires with diameter smaller than 58 nm. These nontrivial phenomena are discussed in terms of the latest Kondo breakdown model, which incorporates the RKKY magnetic interaction mediated by surface states with the strong electron correlation in SmB6. It would provide new insight into the nature of TKI surface states. Additionally, a non‐monotonically temperature dependent positive magnetoresistance is observed at intermediate temperatures, suggesting the possible impurity‐band conduction in SmB6, other than the surface state transport at low temperatures and the bulk‐band transport at high temperatures.

Intrinsic optical conductivity of a symmetric topological insulator

In this work we analytically investigate the longitudinal optical conductivity of the symmetric topological insulator. The conductivity expressions at T = 0 are derived using the Kubo formula and expressed as a function of the ratio of the Dresselhaus and Rashba parameters that characterize the low-energy Hamiltonian. We find that the longitudinal inter-band conductivity vanishes when Dresselhaus and Rashba parameters are equal in strength, also called the persistent spin helix state. The calculations are extended to obtain the frequency-dependent real and imaginary components of the optical conductivity for the topological Kondo insulator SmB6 which exhibits symmetric and anisotropic Dirac cones hosting topological states at point on the surface Brillouin zone.

Topological Kondo insulators: Negative pressure tuning.

Large tensile pressure applied to the putative topological Kondo insulator SmB6 results in an expansion of the lattice in all directions, and a huge increase in the temperature range over which surface-dominated conduction can be observed.

Suppression of magnetic excitations near the surface of the topological Kondo insulator SmB6

We present a detailed investigation of the temperature and depth dependence of the magnetic properties of 3D topological Kondo insulator SmB6 , in particular near its surface. We find that local magnetic field fluctuations detected in the bulk are suppressed rapidly with decreasing depths, disappearing almost completely at the surface. We attribute the magnetic excitations to spin excitons in bulk SmB6 , which produce local magnetic fields of about ~1.8 mT fluctuating on a time scale of ~60 ns. We find that the excitonic fluctuations are suppressed when approaching the surface on a length scale of 40-90 nm, accompanied by a small enhancement in static magnetic fields. We associate this length scale to the size of the excitonic state.

Spin injection and inverse Edelstein effect in the surface states of topological Kondo insulator SmB6

There has been considerable interest in exploiting the spin degrees of freedom of electrons for potential information storage and computing technologies. Topological insulators (TIs), a class of quantum materials, have special gapless edge/surface states, where the spin polarization of the Dirac fermions is locked to the momentum direction. This spin–momentum locking property gives rise to very interesting spin-dependent physical phenomena such as the Edelstein and inverse Edelstein effects. However, the spin injection in pure surface states of TI is very challenging because of the coexistence of the highly conducting bulk states. Here, we experimentally demonstrate the spin injection and observe the inverse Edelstein effect in the surface states of a topological Kondo insulator, SmB6. At low temperatures when only surface carriers are present, a clear spin signal is observed. Furthermore, the magnetic field angle dependence of the spin signal is consistent with spin–momentum locking property of surface states of SmB6.