Observation of possible topological in-gap surface states in the Kondo insulator SmB6 by photoemission

Visualizing the atomic-scale origin of metallic behavior in Kondo insulators

A Kondo lattice is often electrically insulating at low temperatures. However, several recent experiments have detected signatures of bulk metallicity within this Kondo insulating phase. In this study, we visualized the real-space charge landscape within a Kondo lattice with atomic resolution using a scanning tunneling microscope. We discovered nanometer-scale puddles of metallic conduction electrons centered around uranium-site substitutions in the heavy-fermion compound uranium ruthenium silicide (URu₂Si₂) and around samarium-site defects in the topological Kondo insulator samarium hexaboride (SmB₆). These defects disturbed the Kondo screening cloud, leaving behind a fingerprint of the metallic parent state. Our results suggest that the three-dimensional quantum oscillations measured in SmB₆ arise from Kondo-lattice defects, although we cannot exclude other explanations. Our imaging technique could enable the development of atomic-scale charge sensors using heavy-fermion probes.

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.

Study the mixed valence problem in asymmetric Anderson model: Fano-Kondo resonance around Fermi level

We numerically calculate the local density of states (LDOS) in asymmetric Anderson model in mixed valence regime using hierarchical equations of motion approach. Based on the idea that the asymmetric line shape of LDOS around Fermi level stems from the interference between the single particle resonance and the Kondo resonance, we perform a fitting. From the fitting results, we obtain the Kondo temperatures and the Fano factors with changing the single particle energy. The tendency of Kondo temperature agrees with the previous analytic expressions and the Fano factors are in an expected variation of Fano resonance. Our study shows that the Fano-Kondo resonance can reasonably explain the asymmetric line shape of the LDOS around the Fermi level.

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.

Distinct Kondo Screening Behaviors in Heavy Fermion Filled Skutterudites with 4f^{1} and 4f^{2} Configurations

CeOs_{4}Sb_{12} (COS) and PrOs_{4}Sb_{12} (POS) are two representative compounds that provide the ideal vantage point to systematically study the physics of multi-f-electron systems. COS with Ce 4f^{1}, and POS with Pr 4f^{2} configurations show distinct properties of Kondo insulating and heavy fermion superconductivity, respectively. We unveiled the underlying microscopic origin by angle-resolved photoemission spectroscopy studies. Their eV-scale band structure matches well, representing the common characters of conduction electrons in ROs_{4}Sb_{12} systems (R=rare earth). However, f electrons interact differently with conduction electrons in COS and POS. Strong hybridization between conduction electrons and f electrons is observed in COS with band dependent hybridization gaps, and the development of a Kondo insulating state is directly revealed. Although the ground state of POS is a singlet, finite but incoherent hybridization exists, which can be explained by the Kondo scattering with the thermally excited triplet crystalline electric field state. Our results help us to understand the intriguing properties in COS and POS, and provide a clean demonstration of the microscopic differences in heavy fermion systems with 4f^{1} and 4f^{2} configurations.

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.

Tunable Kondo Resonance at a Pristine Two-Dimensional Dirac Semimetal on a Kondo Insulator

The proximity of two different materials leads to an intricate coupling of quasiparticles so that an unprecedented electronic state is often realized at the interface. Here, we demonstrate a resonance-type many-body ground state in graphene, a nonmagnetic two-dimensional Dirac semimetal, when grown on SmB₆, a Kondo insulator, via thermal decomposition of fullerene molecules. This ground state is typically observed in three-dimensional magnetic materials with correlated electrons. Above the characteristic Kondo temperature of the substrate, the electron band structure of pristine graphene remains almost intact. As temperature decreases, however, the Dirac Fermions of graphene become hybridized with the Sm 4f states. Remarkable enhancement of the hybridization and Kondo resonance is observed with further cooling and increasing charge-carrier density of graphene, evidencing the Kondo screening of the Sm 4f local magnetic moment by the conduction electrons of graphene at the interface. These findings manifest the realization of the Kondo effect in graphene by the proximity of SmB₆ that is tuned by the temperature and charge-carrier density of graphene.

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.

Dynamical Bonding Driving Mixed Valency in a Metal Boride

Samarium hexaboride is an anomaly, having many exotic and seemingly mutually incompatible properties. It was proposed to be a mixed-valent semiconductor, and later a topological Kondo insulator, and yet has a Fermi surface despite being an insulator. We propose a new and unified understanding of SmB₆ centered on the hitherto unrecognized dynamical bonding effect: the coexistence of two Sm-B bonding modes within SmB₆ , corresponding to different oxidation states of the Sm. The mixed valency arises in SmB₆ from thermal population of these distinct minima enabled by motion of B. Our model simultaneously explains the thermal valence fluctuations, appearance of magnetic Fermi surface, excess entropy at low temperatures, pressure-induced phase transitions, and related features in Raman spectra and their unexpected dependence on temperature and boron isotope.

Contrast Reversal in Scanning Tunneling Microscopy and Its Implications for the Topological Classification of SmB6

SmB₆ has recently attracted considerable interest as a candidate for the first strongly correlated topological insulator. Such materials promise entirely new properties such as correlation-enhanced bulk bandgaps or a Fermi surface from spin excitations. Whether SmB₆ and its surface states are topological or trivial is still heavily disputed however, and a solution is hindered by major disagreement between angle-resolved photoemission (ARPES) and scanning tunneling microscopy (STM) results. Here, a combined ARPES and STM experiment is conducted. It is discovered that the STM contrast strongly depends on the bias voltage and reverses its sign beyond 1 V. It is shown that the understanding of this contrast reversal is the clue to resolving the discrepancy between ARPES and STM results. In particular, the scanning tunneling spectra reflect a low-energy electronic structure at the surface, which supports a trivial origin of the surface states and the surface metallicity of SmB₆ .

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.

Magnetic field-tuned Fermi liquid in a Kondo insulator

Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the electron spin, yet the required strength of the magnetic field-typically of order 100 T-means that very little is known about this insulator-metal transition. Here we show that Ce[Formula: see text]Bi[Formula: see text]Pd[Formula: see text], owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A metallic Fermi liquid state is established above a critical magnetic field of only [Formula: see text] 11 T. A peak in the strength of electronic correlations near [Formula: see text], which is evident in transport and susceptibility measurements, suggests that Ce[Formula: see text]Bi[Formula: see text]Pd[Formula: see text] may exhibit quantum criticality analogous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed.

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.

Quantum Oscillations in Flux-Grown SmB_{6} with Embedded Aluminum

SmB_{6} is a candidate topological Kondo insulator that displays surface conduction at low temperatures. Here, we perform torque magnetization measurements as a means to detect de Haas-van Alphen (dHvA) oscillations in SmB_{6} crystals grown by aluminum flux. We find that dHvA oscillations occur in single crystals containing embedded aluminum, originating from the flux used to synthesize SmB_{6}. Measurements on a sample with multiple, unconnected aluminum inclusions show that aluminum crystallizes in a preferred orientation within the SmB_{6} cubic lattice. The presence of aluminum is confirmed through bulk susceptibility measurements, but does not show a signature in transport measurements. We discuss the ramifications of our results.

Inorganic Boron-Based Nanostructures: Synthesis, Optoelectronic Properties, and Prospective Applications

Inorganic boron-based nanostructures have great potential for field emission (FE), flexible displays, superconductors, and energy storage because of their high melting point, low density, extreme hardness, and good chemical stability. Until now, most researchers have been focused on one-dimensional (1D) boron-based nanostructures (rare-earth boride (REB₆) nanowires, boron nanowires, and nanotubes). Currently, two-dimensional (2D) borophene attracts most of the attention, due to its unique physical and chemical properties, which make it quite different from its corresponding bulk counterpart. Here, we offer a comprehensive review on the synthesis methods and optoelectronics properties of inorganic boron-based nanostructures, which are mainly concentrated on 1D rare-earth boride nanowires, boron monoelement nanowires, and nanotubes, as well as 2D borophene and borophane. This review paper is organized as follows. In Section I, the synthesis methods of inorganic boron-based nanostructures are systematically introduced. In Section II, we classify their optical and electrical transport properties (field emission, optical absorption, and photoconductive properties). In the last section, we evaluate the optoelectronic behaviors of the known inorganic boron-based nanostructures and propose their future applications.

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.

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.

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.

Towards the manipulation of topological states of matter: a perspective from electron transport

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications.

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.

Quantum phase transition and destruction of Kondo effect in pressurized SmB6

SmB₆ has been a well-known Kondo insulator for decades, but recently attracts extensive new attention as a candidate topological system. Studying SmB₆ under pressure provides an opportunity to acquire the much-needed understanding about the effect of electron correlations on both the metallic surface state and bulk insulating state. Here we do so by studying the evolution of two transport gaps (low temperature gap E_l and high temperature gap E_h) associated with the Kondo effect by measuring the electrical resistivity under high pressure and low temperature (0.3 K) conditions. We associate the gaps with the bulk Kondo hybridization, and from their evolution with pressure we demonstrate an insulator-to-metal transition at ∼4 GPa. At the transition pressure, a large change in the Hall number and a divergence tendency of the electron-electron scattering coefficient provide evidence for a destruction of the Kondo entanglement in the ground state. Our results raise the new prospect for studying topological electronic states in quantum critical materials settings.

Evidence for in-gap surface states on the single phase SmB6(001) surface

Structural and electronic properties of the SmB₆(001) single-crystal surface prepared by Ar⁺ ion sputtering and controlled annealing are investigated by scanning tunneling microscopy. In contrast to the cases of cleaved surfaces, we observe a single phase surface with a non-reconstructed p(1 × 1) lattice on the entire surface at an optimized annealing temperature. The surface is identified as Sm-terminated on the basis of spectroscopic measurements. On a structurally uniform surface, the emergence of the in-gap state, a robust surface state against structural variation, is further confirmed inside a Kondo hybridization gap at 4.4 K by temperature and atomically-resolved spatial dependences of the differential conductance spectrum near the Fermi energy.

Matching DMFT calculations with photoemission spectra of heavy fermion insulators: universal properties of the near-gap spectra of SmB6

Paramagnetic heavy fermion insulators consist of fully occupied quasiparticle bands inherent to Fermi liquid theory. The gap emergence below a characteristic temperature is the ultimate sign of coherence for a many-body system, which in addition can induce a non-trivial band topology. Here, we demonstrate a simple and efficient method to compare a model study and an experimental result for heavy fermion insulators. The temperature dependence of the gap formation in both local moment and mixed valence regimes is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). Using the topological coherence temperature as the scaling factor and choosing the input parameter set within the mixed valence regime, we can unambiguously link the theoretical energy scales to the experimental ones. As a particularly important result, we find improved consistency between the scaled DMFT density of states and the photoemission near-gap spectra of samarium hexaboride (SmB₆).

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.

Emergence of Supersymmetric Quantum Electrodynamics

Supersymmetric (SUSY) gauge theories such as the minimal supersymmetric standard model play a fundamental role in modern particle physics, but have not been verified so far in nature. Here, we show that a SUSY gauge theory with dynamical gauge bosons and fermionic gauginos emerges naturally at the pair-density-wave (PDW) quantum phase transition on the surface of a correlated topological insulator hosting three Dirac cones, such as the topological Kondo insulator SmB_{6}. At the quantum tricritical point between the surface Dirac semimetal and nematic PDW phases, three massless bosonic Cooper pair fields emerge as the superpartners of three massless surface Dirac fermions. The resulting low-energy effective theory is the supersymmetric XYZ model, which is dual by mirror symmetry to N=2 supersymmetric quantum electrodynamics in 2+1 dimensions, providing a first example of emergent supersymmetric gauge theory in condensed matter systems. Supersymmetry allows us to determine certain critical exponents and the optical conductivity of the surface states at the strongly coupled tricritical point exactly, which may be measured in future experiments.

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.

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.

Surface Kondo effect and non-trivial metallic state of the Kondo insulator YbB12

A synergistic effect between strong electron correlation and spin–orbit interaction has been theoretically predicted to realize new topological states of quantum matter on Kondo insulators (KIs), so-called topological Kondo insulators (TKIs). One TKI candidate has been experimentally observed on the KI SmB₆(001), and the origin of the surface states (SS) and the topological order of SmB₆ has been actively discussed. Here, we show a metallic SS on the clean surface of another TKI candidate YbB₁₂(001) using angle-resolved photoelectron spectroscopy. The SS shows temperature-dependent reconstruction corresponding to the Kondo effect observed for bulk states. Despite the low-temperature insulating bulk, the reconstructed SS with c–f hybridization is metallic, forming a closed Fermi contour surrounding on the surface Brillouin zone and agreeing with the theoretically expected behaviour for SS on TKIs. These results demonstrate the temperature-dependent holistic reconstruction of two-dimensional states localized on KIs surface driven by the Kondo effect.

Topological state in Kondo insulators has been provoked in SmB₆, but the origin of surface states and topological order remain elusive. Here, Hagiwara et al. report temperature dependent reconstruction of a metallic surface state on the (001) surface of YbB₁₂ driven by Kondo effect and discuss its origin from topology.

Pressure-induced exotic states in rare earth hexaborides

Finding the exotic phenomena in strongly correlated electron systems (SCESs) and understanding the corresponding microphysics have long been the research frontiers of condensed matter physics. The remarkable examples for the intriguing phenomena discovered in past years include unconventional superconductivity, heavy Fermion behaviors, giant magneto-resistance and so on. A fascinating type of rare earth hexaboride RB6 (R  =  Sm, Yb, Eu and Ce) belongs to a strongly correlated electron system (SCES), but shows unusual ambient-pressure and high-pressure behaviors beyond the phenomena mentioned above. Particularly, the recent discovery of the coexistence of an unusual metallic surface state and an insulating bulk state in SmB6, known to be a Kondo insulator decades ago, by theoretical calculations and many experimental measurements creates new interest for the investigation of the RB6. This significant progress encourages people to revisit the RB6 with an attempt to establish a new physics that links the SCES and the unusual metallic surface state which is a common feature of a topological insulator (TI). It is well known that pressure has the capability of tuning the electronic structure and modifying the ground state of solids, or even inducing a quantum phase transition which is one of the kernel issues in studies of SCESs. In this brief review, we will describe the progress in high pressure studies on the RB6 based on our knowledge and research interests, mainly focusing on the pressure-induced phenomena in YbB6 and SmB6, especially on the quantum phase transitions and their connections with the valence state of the rare earth ions. Moreover, some related high-pressure results obtained from CeB6 and EuB6 are also included. Finally, a summary is given in the conclusions and perspectives section.

Bulk Fermi Surface of Charge-Neutral Excitations in SmB_{6} or Not: A Heat-Transport Study

Recently, there have been increasingly hot debates on whether a bulk Fermi surface of charge-neutral excitations exists in the topological Kondo insulator SmB_{6}. To unambiguously resolve this issue, we perform the low-temperature thermal conductivity measurements of a high-quality SmB_{6} single crystal down to 0.1 K and up to 14.5 T. Our experiments show that the residual linear term of thermal conductivity at the zero field is zero, within the experimental accuracy. Furthermore, the thermal conductivity is insensitive to the magnetic field up to 14.5 T. These results demonstrate the absence of fermionic charge-neutral excitations in bulk SmB_{6}, such as scalar Majorana fermions or spinons and, thus, exclude the existence of a bulk Fermi surface suggested by a recent quantum oscillation study of SmB_{6}. This puts a strong constraint on the explanation of the quantum oscillations observed in SmB_{6}.

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.

Pressure-Resistant Intermediate Valence in the Kondo Insulator SmB_{6}

Resonant x-ray emission spectroscopy was used to determine the pressure dependence of the f-electron occupancy in the Kondo insulator SmB_{6}. Applied pressure reduces the f occupancy, but surprisingly, the material maintains a significant divalent character up to a pressure of at least 35 GPa. Thus, the closure of the resistive activation energy gap and onset of magnetic order are not driven by stabilization of an integer valent state. Over the entire pressure range, the material maintains a remarkably stable intermediate valence that can in principle support a nontrivial band structure.

Uncovering the behavior of Hf2Te2P and the candidate Dirac metal Zr2Te2P

Results are reported for single crystal specimens of Hf2Te2P and compared to its structural analogue Zr2Te2P, which was recently proposed to be a potential reservoir for Dirac physics [1]. Both materials are produced using the iodine vapor phase transport method and the resulting crystals are exfoliable. The bulk electrical transport and thermodynamic properties indicate Fermi liquid behavior at low temperature for both compounds. Quantum oscillations are observed in magnetization measurements for fields applied parallel but not perpendicular to the c-axis, suggesting that the Fermi surfaces are quasi-two dimensional. Frequencies are determined from quantum oscillations for several parts of the Fermi surfaces. Lifshitz-Kosevich fits to the temperature dependent amplitudes of the oscillations reveal small effective masses, with a particularly small value [Formula: see text] for the α branch of Zr2Te2P. Electronic structure calculations are in good agreement with quantum oscillation results and illustrate the effect of a stronger spin-orbit interaction going from Zr to Hf. These results suggest that by using appropriate tuning parameters this class of materials may deepen the pool of novel Dirac phenomena.

Unusual diffusive effects on the ESR of Nd³⁺ ions in the tunable topologically nontrivial semimetal YBiPt

Electron spin resonance (ESR) of diluted Nd(3+) ions in the topologically nontrivial semimetallic (TNSM) YBiPt compound is reported. The cubic YBiPt compound is a non-centrosymmetric half Heusler material which crystallizes in the F43m space group. The low temperature Nd(3+) ESR spectra showed a g-value of 2.66(4) corresponding to a Γ6 cubic crystal field Kramers' doublet ground state. Remarkably, the observed metallic and diffusive (Dysonian) Nd(3+) lineshape presented an unusual dependence with grain size, microwave power, Nd(3+) concentration and temperature. Moreover, the spin dynamic of the localized Nd(3+) ions in YBiPt was found to be characteristic of a phonon-bottleneck regime. It is claimed that, in this regime for YBiPt, phonons are responsible for mediating the diffusion of the microwave energy absorbed at resonance by the Nd(3+) ions to the thermal bath throughout the skin depth (δ ≃ μm). We argue that this is only possible because of the existence of highly mobile conduction electrons inside the skin depth of YBiPt that are strongly coupled to the phonons by spin-orbit coupling. Therefore, our unexpected ESR results point to a coexistence of metallic and insulating behaviors within the skin depth of YBiPt. This scenario is discussed in the light of the TNSM properties of this compound.

On the Chemistry and Physical Properties of Flux and Floating Zone Grown SmB6 Single Crystals

Recent theoretical and experimental findings suggest the long-known but not well understood low temperature resistance plateau of SmB₆ may originate from protected surface states arising from a topologically non-trivial bulk band structure having strong Kondo hybridization. Yet others have ascribed this feature to impurities, vacancies, and surface reconstructions. Given the typical methods used to prepare SmB₆ single crystals, flux and floating-zone procedures, such ascriptions should not be taken lightly. We demonstrate how compositional variations and/or observable amounts of impurities in SmB₆ crystals grown using both procedures affect the physical properties. From X-ray diffraction, neutron diffraction, and X-ray computed tomography experiments we observe that natural isotope containing (SmB₆) and doubly isotope enriched (¹⁵⁴Sm¹¹B₆) crystals prepared using aluminum flux contain co-crystallized, epitaxial aluminum. Further, a large, nearly stoichiometric crystal of SmB₆ was successfully grown using the float-zone technique; upon continuing the zone melting, samarium vacancies were introduced. These samarium vacancies drastically alter the resistance and plateauing magnitude of the low temperature resistance compared to stoichiometric SmB₆. These results highlight that impurities and compositional variations, even at low concentrations, must be considered when collecting/analyzing physical property data of SmB₆. Finally, a more accurate samarium-154 coherent neutron scattering length, 8.9(1) fm, is reported.

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.