Direct observation of the spin texture in SmB6 as evidence of the topological Kondo insulator

Chiral Kondo lattice in doped MoTe2/WSe2 bilayers

We theoretically study the interplay between magnetism and a heavy Fermi liquid in the AB-stacked transition metal dichalcogenide bilayer system, MoTe2/WSe2, in the regime in which the Mo layer supports localized magnetic moments coupled by interlayer electron tunneling to a weakly correlated band of itinerant electrons in the W layer. We show that the interlayer electron transfer leads to a chiral Kondo exchange, with consequences including a strong dependence of the Kondo temperature on carrier concentration and anomalous Hall effect due to a topological hybridization gap. The theoretical model exhibits two phases, a small Fermi surface magnet and a large Fermi surface heavy Fermi liquid; at the mean-field level, the transition between them is first order. Our results provide concrete experimental predictions for ongoing experiments on MoTe2/WSe2 bilayer heterostructures and introduces a controlled route to observe a topological selective Mott transition.

Observation of the Superconducting Proximity Effect from Surface States in SmB_{6}/YB_{6} Thin Film Heterostructures via Terahertz Spectroscopy

The ac conduction of epitaxially grown SmB_{6} thin films and superconducting heterostructures of SmB_{6}/YB_{6} are investigated via time-domain terahertz spectroscopy. A two-channel model of thickness-dependent bulk states and thickness-independent surface states accurately describes the measured conductance of bare SmB_{6} thin films, demonstrating the presence of surface states in SmB_{6}. While the observed reductions in the simultaneously measured superconducting gap, transition temperature, and superfluid density of SmB_{6}/YB_{6} heterostructures relative to bare YB_{6} indicate the penetration of proximity-induced superconductivity into the SmB_{6} overlayer; the corresponding SmB_{6}-thickness independence between different heterostructures indicates that the induced superconductivity is predominantly confined to the interface surface state of the SmB_{6}. This study demonstrates the ability of terahertz spectroscopy to probe proximity-induced superconductivity at an interface buried within a heterostructure, and our results show that SmB_{6} behaves as a predominantly insulating bulk surrounded by conducting surface states in both the normal and induced-superconducting states in both terahertz and dc responses, which is consistent with the topological Kondo insulator picture.

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.

Previous work exploring the robustness of topological surface states to perturbations has mostly focused on surfaces with the same atomic structure as the bulk. Here the authors demonstrate the effect of surface reconstruction on the topological surfaces on the (100) surface of SmB6.

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 Fe_1.03Te 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.

Charge-neutral fermions and magnetic field-driven instability in insulating YbIr3Si7

Kondo lattice materials, where localized magnetic moments couple to itinerant electrons, provide a very rich backdrop for strong electron correlations. They are known to realize many exotic phenomena, with a dramatic example being recent observations of quantum oscillations and metallic thermal conduction in insulators, implying the emergence of enigmatic charge-neutral fermions. Here, we show that thermal conductivity and specific heat measurements in insulating YbIr₃Si₇ reveal emergent neutral excitations, whose properties are sensitively changed by a field-driven transition between two antiferromagnetic phases. In the low-field phase, a significant violation of the Wiedemann-Franz law demonstrates that YbIr₃Si₇ is a charge insulator but a thermal metal. In the high-field phase, thermal conductivity exhibits a sharp drop below 300 mK, indicating a transition from a thermal metal into an insulator/semimetal driven by the magnetic transition. These results suggest that spin degrees of freedom directly couple to the neutral fermions, whose emergent Fermi surface undergoes a field-driven instability at low temperatures.

Anisotropic magnetoresistance as evidence of spin-momentum inter-locking in topological Kondo insulator SmB6 nanowires

SmB₆, which opens up an insulating bulk gap due to hybridization between itinerant d-electrons and localized f-electrons below a critical temperature, turns out to be a topological Kondo insulator possessing exotic conducting states on its surface. However, measurement of the surface-states in SmB₆ draws controversial conclusions, depending on the growth methods and experimental techniques used. Herein, we report anisotropic magnetoresistance (AMR) observed in the Kondo energy gap of a single SmB₆ nanowire that is immune to magnetic dopant pollution and features a square cross-section to show high-symmetry crystal facets. The AMR clearly shows a cosine function of included angle θ between magnetic field and measuring current with a period of π. The positive AMR is interpreted by anisotropically lifting the topological protection of spin-momentum inter-locking surface-states by rotating the in-plane magnetic field, which, therefore, provides the transport evidence that supports the topologically nontrivial nature of the SmB₆ surface-states.

On Strong f-Electron Localization Effect in a Topological Kondo Insulator

We study a strong f-electron localization effect on the surface state of a generic topological Kondo insulator (TKI) system by performing a mean-field theoretic (MFT) calculation within the framework of the periodic Anderson model (PAM) using the slave boson technique. The surface metallicity, together with bulk insulation, requires this type of localization. A key distinction between surface states in a conventional insulator and a topological insulator is that, along a course joining two time-reversal invariant momenta (TRIM) in the same BZ, there will be an intersection of these surface states, an even/odd number of times, with the Fermi energy inside the spectral gap. For an even (odd) number of surface state crossings, the surface states are topologically trivial (non-trivial). The symmetry consideration and the pictorial representation of the surface band structure obtained here show an odd number of crossings, leading to the conclusion that, at least within the PAM framework, the generic system is a strong topological insulator.

Omnipresence of Weak Antilocalization (WAL) in Bi2Se3 Thin Films: A Review on Its Origin

Topological insulators are materials with time-reversal symmetric states of matter in which an insulating bulk is surrounded by protected Dirac-like edge or surface states. Among topological insulators, Bi2Se3 has attracted special attention due to its simple surface band structure and its relatively large band gap that should enhance the contribution of its surface to transport, which is usually masked by the appearance of defects. In order to avoid this difficulty, several features characteristic of topological insulators in the quantum regime, such as the weak-antilocalization effect, can be explored through magnetotransport experiments carried out on thin films of this material. Here, we review the existing literature on the magnetotransport properties of Bi2Se3 thin films, paying thorough attention to the weak-antilocalization effect, which is omnipresent no matter the film quality. We carefully follow the different situations found in reported experiments, from the most ideal situations, with a strong surface contribution, towards more realistic cases where the bulk contribution dominates. We have compared the transport data found in literature to shed light on the intrinsic properties of Bi2Se3, finding a clear relationship between the mobility and the phase coherence length of the films that could trigger further experiments on transport in topological systems.

Robust Surface States and Coherence Phenomena in Magnetically Alloyed SmB_{6}

Samarium hexaboride is a candidate for the topological Kondo insulator state, in which Kondo coherence is predicted to give rise to an insulating gap spanned by topological surface states. Here we investigate the surface and bulk electronic properties of magnetically alloyed Sm_{1-x}M_{x}B_{6} (M=Ce, Eu), using angle-resolved photoemission spectroscopy and complementary characterization techniques. Remarkably, topologically nontrivial bulk and surface band structures are found to persist in highly modified samples with up to 30% Sm substitution and with an antiferromagnetic ground state in the case of Eu doping. The results are interpreted in terms of a hierarchy of energy scales, in which surface state emergence is linked to the formation of a direct Kondo gap, while low-temperature transport trends depend on the indirect gap.

A Retrospective of Materials Synthesis at the Paul Scherrer Institut (PSI)

The availability of high-quality and well characterized materials is a key factor for condensed-matter research [...]

Metallic surface states in a correlated d-electron topological Kondo insulator candidate FeSb2

The resistance of a conventional insulator diverges as temperature approaches zero. The peculiar low-temperature resistivity saturation in the 4f Kondo insulator (KI) SmB₆ has spurred proposals of a correlation-driven topological Kondo insulator (TKI) with exotic ground states. However, the scarcity of model TKI material families leaves difficulties in disentangling key ingredients from irrelevant details. Here we use angle-resolved photoemission spectroscopy (ARPES) to study FeSb₂, a correlated d-electron KI candidate that also exhibits a low-temperature resistivity saturation. On the (010) surface, we find a rich assemblage of metallic states with two-dimensional dispersion. Measurements of the bulk band structure reveal band renormalization, a large temperature-dependent band shift, and flat spectral features along certain high-symmetry directions, providing spectroscopic evidence for strong correlations. Our observations suggest that exotic insulating states resembling those in SmB₆ and YbB₁₂ may also exist in systems with d instead of f electrons.

Ground state anomalies in SmB6

SmB6 has drawn much attention in recent times due to the discovery of anomalies in its ground state properties as well as prediction of topologically protected gapless surface states. Varied theories have been proposed to capture the ground state anomalies. Here, we studied the electronic structure of SmB6 employing density functional theory using different exchange correlation potentials, spin-orbit coupling and electron correlation strength. We discover that a suitable choice of interaction parameters such as spin-orbit coupling, electron correlation strength and exchange interaction within the generalized gradient approximation provides a good description of the spectral functions observed in the angle-resolved photoemission spectroscopy (ARPES) studies. The Fermi surface plots exhibit electron pockets around X-point and hole pockets around ΓX line having dominant Sm 4f character. These observations corroborate well with the recent experimental results involving quantum oscillation measurements, ARPES, etc. In addition to primarily Sm 4f contributions observed at the Fermi level, the results exhibit significantly large contribution from B 2p states compared to weak Sm 5d contributions. This suggests important role of B 2p - Sm 4f hybridization in the exotic physics of this system.

Valence transition in topological Kondo insulator

We investigate the valence transition in three-dimensional topological Kondo insulator through slave-boson analysis of periodic Anderson model. By including the effect of intra-atomic Coulomb correlation [Formula: see text] between conduction and local electrons, we find a first-order valence transition from Kondo region to mixed valence state upon ascending of local f- level above a critical [Formula: see text], and this valence transition usually occurs very close to or simultaneously with a topological transition. Near the parameter region of zero-temperature valence transition, rise of temperature can generate a thermal valence transition from mixed valence to Kondo region, accompanied by a first-order topological transition. Remarkably, above a critical [Formula: see text] which is considerably smaller than that generating paramagnetic valence transition, the original continuous antiferromagnetic transition is shifted to first order one, at which a discontinuous valence shift takes place. Upon increasing [Formula: see text], the paramagnetic valence transition approaches then converges with the first-order antiferromagnetic transition, leaving a significant valence shift on the magnetic boundary. The continuous antiferromagnetic transition, first-order antiferromagnetic transition, paramagnetic valence transition and topological transitions are all summarized in a global phase diagram. Our proposed exotic transition processes can help to understand the thermal valence variation as well as the valence shift around the pressure-induced magnetic transition in topological Kondo insulator candidates and in other heavy-fermion systems.

Intrinsic Low-Temperature Magnetism in SmB_{6}

By means of new muon spin relaxation experiments, we disentangle extrinsic and intrinsic sources of low-temperature bulk magnetism in the candidate topological Kondo insulator (TKI) SmB_{6}. Results on Al-flux-grown SmB_{6} single crystals are compared to those on a large floating-zone-grown ^{154}Sm ^{11}B_{6} single crystal in which a 14 meV bulk spin exciton has been detected by inelastic neutron scattering. Below ∼10  K, we detect the gradual development of quasistatic magnetism due to rare-earth impurities and Sm vacancies. Our measurements also reveal two additional forms of intrinsic magnetism: (1) underlying low-energy (∼100  meV) weak magnetic moment (∼10^{-2}  μ_{B}) fluctuations similar to those detected in the related candidate TKI YbB_{12} that persist down to millikelvin temperatures, and (2) magnetic fluctuations consistent with a 2.6 meV bulk magnetic excitation at zero magnetic field that appears to hinder surface conductivity above ∼4.5  K. We discuss potential origins of the magnetism.

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 |LSL_zS_z〉 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.

Non-trivial surface states of samarium hexaboride at the (111) surface

The peculiar metallic electronic states observed in the Kondo insulator, samarium hexaboride (SmB₆), has stimulated considerable attention among those studying non-trivial electronic phenomena. However, experimental studies of these states have led to controversial conclusions mainly due to the difficulty and inhomogeneity of the SmB₆ crystal surface. Here, we show the detailed electronic structure of SmB₆ with angle-resolved photoelectron spectroscopy measurements of the three-fold (111) surface where only two inequivalent time-reversal-invariant momenta (TRIM) exist. We observe the metallic two-dimensional state was dispersed across the bulk Kondo gap. Its helical in-plane spin polarisation around the surface TRIM indicates that SmB₆ is topologically non-trivial, according to the topological classification theory for weakly correlated systems. Based on these results, we propose a simple picture of the controversial topological classification of SmB₆.

Samarium hexaboride has unusual electronic properties that have been suggested to arise from topological effects. Here the authors present spin-resolved ARPES measurements of the (111) surface and observe surface states that may give insight into the bulk topological properties.

Revealing hidden spin-momentum locking in a high-temperature cuprate superconductor

Cuprate superconductors have long been thought of as having strong electronic correlations but negligible spin-orbit coupling. Using spin- and angle-resolved photoemission spectroscopy, we discovered that one of the most studied cuprate superconductors, Bi2212, has a nontrivial spin texture with a spin-momentum locking that circles the Brillouin zone center and a spin-layer locking that allows states of opposite spin to be localized in different parts of the unit cell. Our findings pose challenges for the vast majority of models of cuprates, such as the Hubbard model and its variants, where spin-orbit interaction has been mostly neglected, and open the intriguing question of how the high-temperature superconducting state emerges in the presence of this nontrivial spin texture.

Interacting topological insulators: a review

The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful research areas for both experimentalists and theorists. The physics of topological insulators is typically well described by band theory and systems of non-interacting fermions. In contrast, several of the most fascinating effects in condensed matter physics merely exist due to electron-electron interactions, examples include unconventional superconductivity, the Kondo effect, and the Mott-Hubbard transition. The aim of this review article is to give an overview of the manifold directions which emerge when topological bandstructures and correlation physics interfere and compete. These include the study of the stability of topological bandstructures and correlated topological insulators. Interaction-induced topological phases such as the topological Kondo insulator provide another exciting topic. More exotic states of matter such as topological Mott insulator and fractional Chern insulators only exist due to the interplay of topology and strong interactions and do not have any bandstructure analogue. Eventually the relation between topological bandstructures and frustrated quantum magnetism in certain transition metal oxides is emphasized.

Magnetic and defect probes of the SmB6 surface state

The impact of nonmagnetic and magnetic impurities on topological insulators is a central focus concerning their fundamental physics and possible spintronics and quantum computing applications. Combining scanning tunneling spectroscopy with transport measurements, we investigate, both locally and globally, the effect of nonmagnetic and magnetic substituents in SmB₆, a predicted topological Kondo insulator. Around the so-introduced substitutents and in accord with theoretical predictions, the surface states are locally suppressed with different length scales depending on the substituent's magnetic properties. For sufficiently high substituent concentrations, these states are globally destroyed. Similarly, using a magnetic tip in tunneling spectroscopy also resulted in largely suppressed surface states. Hence, a destruction of the surface states is always observed close to atoms with substantial magnetic moment. This points to the topological nature of the surface states in SmB₆ and illustrates how magnetic impurities destroy the surface states from microscopic to macroscopic length scales.

[Formula: see text] 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 [Formula: see text]-classification formula for these states. By calculating the [Formula: see text] 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.

Single crystal growth and anisotropic physical properties of Sm4Co3Ga16

We have synthesized high quality single crystals of Sm₄Co₃Ga₁₆ with gallium flux and investigated its physical properties with electrical resistivity, magnetization and specific-heat measurements. Antiferromagnetic transition below 6.7 K has been detected. No superconducting transitions have been dectected down to 0.5 K from our single crystals. Based on our experimental result, Sm³⁺ state in Sm₄Co₃Ga₁₆ is likely well localized, in which stable magnetic moment in its doubly degenerated ground state contributes to the magnetic order with little interference of Kondo type of interaction.

Spin Transport and Accumulation in a 2D Weyl Fermion System

In this work, we demonstrate a new route to realizing an experimentally controllable spin-Hall effect (SHE), on the surface of 3D topological insulators, which depends fundamentally on the spin-orbit-coupled (SOC) nature of the 2D Weyl fermions. Spin transport is solely due to the spin-torque current in this system, and the SHE arises from chiral spin-flip scattering off non-SOC scalar impurities, of potential strength V and size a. The resultant spin-Hall angle has a fixed sign, with θ^{SH}∼O{[V^{2}]/[v_{F}^{2}/a^{2}](k_{F}a)^{4}} being a strongly dependent function of the Fermi wave vector (k_{F}) and Fermi velocity (v_{F}). Hence, the SHE can be tuned by adjusting the Fermi energy or impurity size.

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.

Nontrivial Nature and Penetration Depth of Topological Surface States in SmB_{6} Thin Films

The nontrivial feature and penetration depth of the topological surface states (TSS) in SmB_{6} were studied via spin pumping. The experiments used SmB_{6} thin films grown on the bulk magnetic insulator Y_{3}Fe_{5}O_{12} (YIG). Upon the excitation of magnetization precession in the YIG, a spin current is generated in the SmB_{6} that produces, via spin-orbit coupling, a lateral electrical voltage in the film. This spin-pumping voltage signal becomes considerably stronger as the temperature decreases from 150 to 10 K, and such an enhancement most likely originates from the spin-momentum locking of the TSS and may thereby serve as evidence for the nontrivial nature of the TSS. The voltage data also show a unique film thickness dependence that suggests a TSS depth of ∼32  nm. The spin-pumping results are supported by transport measurements and analyses using a tight binding model.

Samarium hexaboride is a trivial surface conductor

SmB₆ is predicted to be the first member of the intersection of topological insulators and Kondo insulators, strongly correlated materials in which the Fermi level lies in the gap of a many-body resonance that forms by hybridization between localized and itinerant states. While robust, surface-only conductivity at low temperature and the observation of surface states at the expected high symmetry points appear to confirm this prediction, we find both surface states at the (100) surface to be topologically trivial. We find the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bar{\varGamma }}$$\end{document}Γ¯ state to appear Rashba split and explain the prominent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar X$$\end{document}X¯ state by a surface shift of the many-body resonance. We propose that the latter mechanism, which applies to several crystal terminations, can explain the unusual surface conductivity. While additional, as yet unobserved topological surface states cannot be excluded, our results show that a firm connection between the two material classes is still outstanding.

Samarium hexahoride is argued to be a topological Kondo insulator, but this claim remains under debate. Here, Hlawenka et al. provide a topologically trivial explanation for the conducting states at the (100) surface of samarium hexaboride; an explanation based on Rashba splitting and a surface shift of the Kondo resonance.

4f Crystal Field Ground State of the Strongly Correlated Topological Insulator SmB_{6}

We investigated the crystal-electric field ground state of the 4f manifold in the strongly correlated topological insulator SmB_{6} using core-level nonresonant inelastic x-ray scattering. The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the Γ_{8} quartet state of the Sm f^{5}  J=5/2 configuration governs the ground-state symmetry and, hence, the topological properties of SmB_{6}. Our findings contradict the results of density functional calculations reported so far.

How to probe the spin contribution to momentum relaxation in topological insulators

Topological insulators exhibit a metallic surface state in which the directions of the carriers' momentum and spin are locked together. This characteristic property, which lies at the heart of proposed applications of topological insulators, protects carriers in the surface state from back-scattering unless the scattering centres are time-reversal symmetry breaking (i.e. magnetic). Here, we introduce a method of probing the effect of magnetic scattering by decorating the surface of topological insulators with molecules, whose magnetic degrees of freedom can be engineered independently of their electrostatic structure. We show that this approach allows us to separate the effects of magnetic and non-magnetic scattering in the perturbative limit. We thereby confirm that the low-temperature conductivity of SmB6 is dominated by a surface state and that the momentum of quasiparticles in this state is particularly sensitive to magnetic scatterers, as expected in a topological insulator.

Thin films of topological Kondo insulator candidate SmB6: Strong spin-orbit torque without exclusive surface conduction

The advent of topological insulators (TIs), a novel class of materials that harbor a metallic spin-chiral surface state coexisting with band-insulating bulk, opens up new possibilities for spintronics. One promising route is current-induced switching of an adjacent magnetic layer via spin-orbit torque (SOT), arising from the large spin-orbit coupling intrinsically possessed by TIs. The Kondo insulator SmB6 has been recently proposed to be a strongly correlated TI, supported by the observation of a metallic surface state in bulk SmB6, as evidenced by the thickness independence of the low-temperature resistance plateau. We report the synthesis of epitaxial (001) SmB6/Si thin films and a systematic thickness-dependent electrical transport study. Although the low-temperature resistance plateau is observed for all films from 50 to 500 nm in thickness, the resistance is distinctively thickness-dependent and does not support the notion of surface conduction and interior insulation. On the other hand, we demonstrate that SmB6 can generate a large SOT to switch an adjacent ferromagnetic layer, even at room temperature. The effective SOT generated from SmB6 is comparable to that from β-W, one of the strongest SOT materials.

Recent trends in spin-resolved photoelectron spectroscopy

Since the discovery of the Rashba effect on crystal surfaces and also the discovery of topological insulators, spin- and angle-resolved photoelectron spectroscopy (SARPES) has become more and more important, as the technique can measure directly the electronic band structure of materials with spin resolution. In the same way that the discovery of high-Tc superconductors promoted the development of high-resolution angle-resolved photoelectron spectroscopy, the discovery of this new class of materials has stimulated the development of new SARPES apparatus with new functions and higher resolution, such as spin vector analysis, ten times higher energy and angular resolution than conventional SARPES, multichannel spin detection, and so on. In addition, the utilization of vacuum ultra violet lasers also opens a pathway to the realization of novel SARPES measurements. In this review, such recent trends in SARPES techniques and measurements will be overviewed.

The fluctuating population of Sm 4f configurations in topological Kondo insulator SmB6 explored with high-resolution X-ray absorption and emission spectra

High-resolution partial-fluorescence-yield X-ray absorption and resonant X-ray emission spectra were used to characterize the temperature dependence of Sm 4f configurations and orbital/charge degree of freedom in SmB₆. The variation of Sm 4f configurations responds well to the formed Kondo gap, below 140 K, and an in-gap state, below 40 K. The topological in-gap state is correlated with the fluctuating population of Sm 4f configurations that arises via carrier transfer between 3d⁹4f⁶ and 3d⁹4f⁵ states; both states are partially delocalized, and the mediating 5d orbital plays the role of a transfer path. Complementary results shown in this work thus manifest the importance of configuration fluctuations and orbital delocalization in the topological surface state of SmB₆.

Skyrme Insulators: Insulators at the Brink of Superconductivity

Current theories of superfluidity are based on the idea of a coherent quantum state with topologically protected quantized circulation. When this topological protection is absent, as in the case of ^{3}He-A, the coherent quantum state no longer supports persistent superflow. Here, we argue that the loss of topological protection in a superconductor gives rise to an insulating ground state. We specifically introduce the concept of a Skyrme insulator to describe the coherent dielectric state that results from the topological failure of superflow carried by a complex-vector order parameter. We apply this idea to the case of SmB_{6}, arguing that the observation of a diamagnetic Fermi surface within an insulating bulk can be understood as a realization of this state. Our theory enables us to understand the linear specific heat of SmB_{6} in terms of a neutral Majorana Fermi sea and leads us to predict that in low fields of order a Gauss, SmB_{6} will develop a Meissner effect.

Additional energy scale in SmB6 at low-temperature

Topological insulators give rise to exquisite electronic properties because of their spin-momentum locked Dirac-cone-like band structure. Recently, it has been suggested that the required opposite parities between valence and conduction band along with strong spin-orbit coupling can be realized in correlated materials. Particularly, SmB6 has been proposed as candidate material for a topological Kondo insulator. Here we observe, by utilizing scanning tunnelling microscopy and spectroscopy down to 0.35 K, several states within the hybridization gap of about ±20 meV on well characterized (001) surfaces of SmB6. The spectroscopic response to impurities and magnetic fields allows to distinguish between dominating bulk and surface contributions to these states. The surface contributions develop particularly strongly below about 7 K, which can be understood in terms of a suppressed Kondo effect at the surface. Our high-resolution data provide insight into the electronic structure of SmB6, which reconciles many current discrepancies on this compound.

Giant Isotropic Nernst Effect in an Anisotropic Kondo Semimetal

The "failed Kondo insulator" CeNiSn has long been suspected to be a nodal metal, with a node in the hybridization matrix elements. Here we carry out a series of Nernst effect experiments to delineate whether the severely anisotropic magnetotransport coefficients do indeed derive from a nodal metal or can simply be explained by a highly anisotropic Fermi surface. Our experiments reveal that despite an almost twentyfold anisotropy in the Hall conductivity, the large Nernst signal is isotropic. Taken in conjunction with the magnetotransport anisotropy, these results provide strong support for an isotropic Fermi surface with a large anisotropy in quasiparticle mass derived from a nodal hybridization.

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.

Spin- and angle-resolved photoemission on the topological Kondo insulator candidate: SmB6

Topological Kondo insulators are a new class of topological insulators in which metallic surface states protected by topological invariants reside in the bulk band gap at low temperatures. Unlike other 3D topological insulators, a truly insulating bulk state, which is critical for potential applications in next-generation electronic devices, is guaranteed by many-body effects in the topological Kondo insulator. Furthermore, the system has strong electron correlations that can serve as a testbed for interacting topological theories. This topical review focuses on recent advances in the study of SmB6, the most promising candidate for a topological Kondo insulator, from the perspective of spin- and angle-resolved photoemission spectroscopy with highlights of some important transport results.

Topological surface states interacting with bulk excitations in the Kondo insulator SmB6 revealed via planar tunneling spectroscopy

Samarium hexaboride (SmB6), a well-known Kondo insulator in which the insulating bulk arises from strong electron correlations, has recently attracted great attention owing to increasing evidence for its topological nature, thereby harboring protected surface states. However, corroborative spectroscopic evidence is still lacking, unlike in the weakly correlated counterparts, including Bi2Se3 Here, we report results from planar tunneling that unveil the detailed spectroscopic properties of SmB6 The tunneling conductance obtained on the (001) and (011) single crystal surfaces reveals linear density of states as expected for two and one Dirac cone(s), respectively. Quite remarkably, it is found that these topological states are not protected completely within the bulk hybridization gap. A phenomenological model of the tunneling process invoking interaction of the surface states with bulk excitations (spin excitons), as predicted by a recent theory, provides a consistent explanation for all of the observed features. Our spectroscopic study supports and explains the proposed picture of the incompletely protected surface states in this topological Kondo insulator SmB6.

Radio Frequency Tunable Oscillator Device Based on a SmB_{6} Microcrystal

Radio frequency tunable oscillators are vital electronic components for signal generation, characterization, and processing. They are often constructed with a resonant circuit and a "negative" resistor, such as a Gunn diode, involving complex structure and large footprints. Here we report that a piece of SmB_{6}, 100  μm in size, works as a current-controlled oscillator in the 30 MHz frequency range. SmB_{6} is a strongly correlated Kondo insulator that was recently found to have a robust surface state likely to be protected by the topology of its electronics structure. We exploit its nonlinear dynamics, and demonstrate large ac voltage outputs with frequencies from 20 Hz to 30 MHz by adjusting a small dc bias current. The behaviors of these oscillators agree well with a theoretical model describing the thermal and electronic dynamics of coupled surface and bulk states. With reduced crystal size we anticipate the device to work at higher frequencies, even in the THz regime. This type of oscillator might be realized in other materials with a metallic surface and a semiconducting bulk.

Chern Kondo Insulator in an Optical Lattice

We propose to realize and observe Chern Kondo insulators in an optical superlattice with laser-assisted s and p orbital hybridization and a synthetic gauge field, which can be engineered based on the recent cold atom experiments. Considering a double-well square optical lattice, the localized s orbitals are decoupled from itinerant p bands and are driven into a Mott insulator due to the strong Hubbard interaction. Raman laser beams are then applied to induce tunnelings between s and p orbitals, and generate a staggered flux simultaneously. Because of the strong Hubbard interaction of s orbital states, we predict the existence of a critical Raman laser-assisted coupling, beyond which the Kondo screening is achieved, and then a fully gapped Chern Kondo phase emerges, with the topology characterized by integer Chern numbers. Being a strongly correlated topological state, the Chern Kondo phase is different from the single-particle quantum anomalous Hall state, and can be identified by measuring the band topology and double occupancy of s orbitals. The experimental realization and detection of the predicted Chern Kondo insulator are also proposed.

Kondo Breakdown and Quantum Oscillations in SmB_{6}

Recent quantum oscillation experiments on SmB_{6} pose a paradox, for while the angular dependence of the oscillation frequencies suggest a 3D bulk Fermi surface, SmB_{6} remains robustly insulating to very high magnetic fields. Moreover, a sudden low temperature upturn in the amplitude of the oscillations raises the possibility of quantum criticality. Here we discuss recently proposed mechanisms for this effect, contrasting bulk and surface scenarios. We argue that topological surface states permit us to reconcile the various data with bulk transport and spectroscopy measurements, interpreting the low temperature upturn in the quantum oscillation amplitudes as a result of surface Kondo breakdown and the high frequency oscillations as large topologically protected orbits around the X point. We discuss various predictions that can be used to test this theory.

CeRu4Sn6: a strongly correlated material with nontrivial topology

Topological insulators form a novel state of matter that provides new opportunities to create unique quantum phenomena. While the materials used so far are based on semiconductors, recent theoretical studies predict that also strongly correlated systems can show non-trivial topological properties, thereby allowing even the emergence of surface phenomena that are not possible with topological band insulators. From a practical point of view, it is also expected that strong correlations will reduce the disturbing impact of defects or impurities, and at the same increase the Fermi velocities of the topological surface states. The challenge is now to discover such correlated materials. Here, using advanced x-ray spectroscopies in combination with band structure calculations, we infer that CeRu₄Sn₆ is a strongly correlated material with non-trivial topology.

Distinct Topological Crystalline Phases in Models for the Strongly Correlated Topological Insulator SmB_{6}

SmB_{6} was recently proposed to be both a strong topological insulator and a topological crystalline insulator. For this and related cubic topological Kondo insulators, we prove the existence of four different topological phases, distinguished by the sign of mirror Chern numbers. We characterize these phases in terms of simple observables, and we provide concrete tight-binding models for each phase. Based on theoretical and experimental results for SmB_{6} we conclude that it realizes the phase with C_{k_{z}=0}^{+}=+2, C_{k_{z}=π}^{+}=+1, C_{k_{x}=k_{y}}^{+}=-1, and we propose a corresponding minimal model.

Surface-State Spin Textures and Mirror Chern Numbers in Topological Kondo Insulators

The recent discovery of topological Kondo insulators has triggered renewed interest in the well-known Kondo insulator samarium hexaboride, which is hypothesized to belong to this family. In this Letter, we study the spin texture of the topologically protected surface states in such a topological Kondo insulator. In particular, we derive close relationships between (i) the form of the hybridization matrix at certain high-symmetry points, (ii) the mirror Chern numbers of the system, and (iii) the observable spin texture of the topological surface states. In this way, a robust classification of topological Kondo insulators and their surface-state spin texture is achieved. We underpin our findings with numerical calculations of several simplified and realistic models for systems like samarium hexaboride.

Kondo breakdown in topological Kondo insulators

Motivated by the observation of light surface states in SmB6, we examine the effects of surface Kondo breakdown in topological Kondo insulators. We present both numerical and analytic results which show that the decoupling of the localized moments at the surface disturbs the compensation between light and heavy electrons and dopes the Dirac cone. Dispersion of these uncompensated surface states is dominated by intersite hopping, which leads to much lighter quasiparticles. These surface states are also highly durable against the effects of surface magnetism and decreasing thickness of the sample.

Concept of a multichannel spin-resolving electron analyzer based on Mott scattering

The concept of a multichannel electron spin detector based on optical imaging principles and Mott scattering (iMott) is presented. A multichannel electron image produced by a standard angle-resolving (photo) electron analyzer or microscope is re-imaged by an electrostatic lens at an accelerating voltage of 40 kV onto the Au target. Quasi-elastic electrons bearing spin asymmetry of the Mott scattering are imaged by magnetic lenses onto position-sensitive electron CCDs whose differential signals yield the multichannel spin asymmetry image. Fundamental advantages of this concept include acceptance of inherently divergent electron sources from the electron analyzer or microscope focal plane as well as small aberrations achieved by virtue of high accelerating voltages, as demonstrated by extensive ray-tracing analysis. The efficiency gain compared with the single-channel Mott detector can be a factor of more than 10(4) which opens new prospects of spin-resolved spectroscopies in application not only to standard bulk and surface systems (Rashba effect, topological insulators, etc.) but also to buried heterostructures. The simultaneous spin detection combined with fast CCD readout enables efficient use of the iMott detectors at X-ray free-electron laser facilities.

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.

Emergent photovoltage on SmB6 surface upon bulk-gap evolution revealed by pump-and-probe photoemission spectroscopy

Recent studies suggest that an exemplary Kondo insulator SmB₆ belongs to a new class of topological insulators (TIs), in which non-trivial spin-polarized metallic states emerge on surface upon the formation of Kondo hybridization gap in the bulk. Remarkably, the bulk resistivity reaches more than 20 Ω cm at 4 K, making SmB₆ a candidate for a so-called bulk-insulating TI. We here investigate optical-pulse responses of SmB₆ by pump-and-probe photoemission spectroscopy. Surface photovoltage effect is observed below ~90 K. This indicates that an optically-active band bending region develops beneath the novel metallic surface upon the bulk-gap evolution. The photovoltaic effect persists for >200 µs, which is long enough to be detected by electronics devices, and could be utilized for optical gating of the novel metallic surface.

Interaction driven subgap spin exciton in the Kondo insulator SmB6

Using inelastic neutron scattering, we map a 14 meV coherent resonant mode in the topological Kondo insulator SmB6 and describe its relation to the low energy insulating band structure. The resonant intensity is confined to the X and R high symmetry points, repeating outside the first Brillouin zone and dispersing less than 2 meV, with a 5d-like magnetic form factor. We present a slave-boson treatment of the Anderson Hamiltonian with a third neighbor dominated hybridized band structure. This approach produces a spin exciton below the charge gap with features that are consistent with the observed neutron scattering. We find that maxima in the wave vector dependence of the inelastic neutron scattering indicate band inversion.