Kondo Insulator Research Articles

Resistivity saturation in Kondo insulators

Resistivities of heavy-fermion insulators typically saturate below a characteristic temperature T*. For some, metallic surface states, potentially from a non-trivial bulk topology, are a likely source of residual conduction. Here, we establish an alternative mechanism: at low temperature, in addition to the charge gap, the scattering rate turns into a relevant energy scale, invalidating the semi-classical Boltzmann picture. Then, finite lifetimes of intrinsic carriers drive residual conduction, impose the existence of a crossover T*, and control—now on par with the gap—the quantum regime emerging below it. Assisted by realistic many-body simulations, we showcase the mechanism for the Kondo insulator Ce3Bi4Pt3, for which residual conduction is a bulk property, and elucidate how its saturation regime evolves under external pressure and varying disorder. Deriving a phenomenological formula for the quantum regime, we also unriddle the ill-understood bulk conductivity of SmB6—demonstrating a wide applicability of our mechanism in correlated narrow-gap semiconductors.

Spectral properties of strongly correlated multi-impurity models in the Kondo insulator regime: Emergent coherence, metallic surface states, and quantum phase transitions

We investigate the real-space spectral properties of strongly-correlated multi-impurity arrays in the Kondo insulator regime. Employing a recently developed mapping onto an effective correlated cluster problem makes the problem accessible to the numerical renormalization group. The evolution of the spectrum as function of cluster size and cluster site is studied. We applied the extended Lieb-Mattis theorem to predict whether the spectral function must vanish at the Fermi energy developing a true pseudo-gap or whether the spectral function remains finite at $\w=0$. Our numerical renormalization group spectra confirm the predictions of the theorem and shows a metallic behavior at the surface of a cluster prevailing in arbitrary spatial dimensions. We present a conventional minimal extension of a particle-hole symmetric Anderson lattice model at $U=0$ that leads to a gapped bulk band but a surface band with mainly $f$-orbital character for weak and moderate hybridization strength. The change in the site-dependent spectra upon introducing a Kondo hole in the center of the cluster are presented as a function of the hole-orbital energy. In particular the spectral signatures across the Kosterlitz-Thouless type quantum phase transition from a singlet to a local moment fixed point are discussed.

Mapping out the emergence of topological features in the highly alloyed topological Kondo insulators Sm1−xMxB6(M=Eu,Ce)

SmB${}_{6}$ is a strongly correlated material that has been considered as a topological insulator and a Kondo insulator. Here, the authors use angle-resolved photoemission spectroscopy to chart the evolution of topologically linked electronic structure features versus doping in Sm${}_{1\ensuremath{-}x}$${M}_{x}$B${}_{6}$ ($M$=Eu, Ce). Topological band coherence phenomena are observed out to remarkably high alloy compositions (30% Eu and 50% Ce). Combined with numerical modeling, these results suggest that the topological surface-state spectral feature is protected by a hybridization gap much larger than the insulating gap.

Topology of SmB6 determined by dynamical mean field theory

Whether ${\mathrm{SmB}}_{6}$ is a topological insulator remains hotly debated. Our density functional theory plus dynamical mean field theory calculations are in excellent agreement with a large range of experiments, from the $4{f}^{5.5}$ intermediate valency to x-ray and photoemission spectra. We show that ${\mathrm{SmB}}_{6}$ is a strongly correlated topological insulator, albeit not a Kondo insulator, using a symmetry analysis of the ``pole extended'' Hamiltonian, which fully captures the effect of the self-energy arising from the strong electron-electron correlation within the Sm $4f$ orbitals. The topological surface states are analyzed, addressing conflicting interpretations of photoemission data.

Topological surface conduction in Kondo insulator YbB12

Kondo insulators have recently aroused great interest because they are promising materials that host a topological insulator state caused by the strong electron interactions. Moreover, recent observations of the quantum oscillations in the insulating state of Kondo insulators have come as a great surprise. Here, to investigate the surface electronic state of a prototype Kondo insulator YbB12, we measured the transport properties of single crystals and microstructures. In all samples, the temperature dependence of the electrical resistivity is insulating at high temperatures and the resistivity exhibits a plateau at low temperatures. The magnitude of the plateau value decreases with reducing sample thickness, which is quantitatively consistent with the surface electronic conduction in the bulk insulating YbB12. Moreover, the magnetoresistance of the microstructures exhibits a weak-antilocalization effect at low field. These results are consistent with the presence of a topologically protected surface state, suggesting that YbB12 is a candidate material for a topological Kondo insulator. The high field resistivity measurements up to µ 0 H = 50 T of the microstructures provide supporting evidence that the quantum oscillations of the resistivity in YbB12 occurs in the insulating bulk.

Surface excitations relaxation in the Kondo insulator Sm1−xGdxB6

The interplay between non-trivial topological states of matter and strong electronic correlations is one of the most compelling open questions in condensed matter physics. Due to experimental challenges, there is an increasing desire to find more microscopic techniques to complement the results of more traditional experiments. In this work, we locally explore the Kondo insulator Sm$_{1-x}$Gd$_{x}$B$_{6}$ by means of electron spin resonance (ESR) of Gd$^{3+}$ ions at low temperatures. Our analysis reveals that the Gd$^{3+}$ ESR line shape shows an anomalous evolution as a function of temperature, wherein for highly dilute samples (x $\approx$ 0.0002) the Gd$^{3+}$ ESR line shape changes from a localized ESR local moment character to a diffusive-like character. Upon manipulating the sample surface with a focused ion beam we demonstrate, in combination with electrical resistivity measurements, that the localized character of the Gd$^{3+}$ ESR line shape is recovered by increasing the penetration of the microwave in the sample. This provides compelling evidence for the contribution of surface or near-surface excitations to the relaxation mechanism in the Gd$^{3+}$ spin dynamics. Our work brings new insights into the importance of non-trivial surface excitations in ESR, opening new routes to be explored both theoretically and experimentally.

Small to large Fermi surface transition in a single-band model using randomly coupled ancillas

We describe a solvable model of a quantum transition in a single band model involving a change in the size of the electron Fermi surface without any symmetry breaking. In a model with electron density $1-p$, we find a 'large' Fermi surface state with the conventional Luttinger volume $1-p$ of electrons for $p>p_c$, and a first order transition to a 'small' Fermi surface state with a non-Luttinger volume $p$ of holes for $p<p_c$. As required by extended Luttinger theorems, the small Fermi surface state also has fractionalized spinon excitations. The model has electrons with strong local interactions in a single band; after a canonical transformation, the interactions are transferred to a coupling to two layers of ancilla qubits, as proposed by Zhang and Sachdev (Phys. Rev. Research ${\bf 2}$, 023172 (2020)). Solvability is achieved by employing random exchange interactions within the ancilla layers, and taking the large $M$ limit with SU($M$) spin symmetry, as in the Sachdev-Ye-Kitaev models. The local electron spectral function of the small Fermi surface phase displays a particle-hole asymmetric pseudogap, and maps onto the spectral function of a lightly doped Kondo insulator of a Kondo-Heisenberg lattice model. We discuss connections to the physics of the hole-doped cuprates: the asymmetric pseudogap observed in STM, and the sudden change from incoherent to coherent anti-nodal spectra observed recently in photoemission. A holographic analogy to wormhole transitions between multiple black holes is briefly noted.

Ultrafast laser-driven many-body dynamics and Kondo coherence collapse

Ultrafast laser pulse has provided a systematic way to inspect the dynamics of electrons in condensed matter systems. In this paper, by means of time-dependent density matrix renormalization group, we study an ultrafast laser driven Kondo lattice model, in which conduction electrons are strongly coupled with magnetically local moments. The single-particle spectral function due to strong correlation effects and photon emission in the non-equilibrium states under laser driving are calculated. We find laser field excited collective doublon-hole pairs and an associated transient melting of Kondo coherence phase, signifying the collapse of Kondo energy gap. Moreover, we show that the photon emission, induced by a strong laser field, exhibits a different intensity characteristics than in the equilibrium Kondo insulator, which could be explained by the Kondo collapse and related suppression of both intra-band and inter-band contribution in Kondo melting liquid. These theoretical insight is accessible with time- and angle-resolved photoemission spectroscopy and high-harmonic generation spectroscopy, and will stimulate the investigation of nonequilibrium dynamics and nonlinear phenomenon in heavy fermion systems.

High-temperature antiferromagnetism in Yb based heavy fermion systems proximate to a Kondo insulator

Given the parallelism between the physical properties of Ce and Yb based magnets and heavy fermions due to the electron-hole symmetry, it has been rather odd that the transition temperature of the Yb based compounds is normally very small, as low as $\sim$ 1 K or even lower, whereas Ce counterparts may often have the transition temperature well exceeding 10 K. Here, we report our experimental discovery of the transition temperature reaching 20 K for the first time in a Yb based compound at ambient pressure. The Mn substitution at the Al site in an intermediate valence state of $\alpha$-YbAlB$_{4}$ not only induces antiferromagnetic transition at a record high temperature of 20 K but also transforms the heavy fermion liquid state in $\alpha$-YbAlB$_{4}$ into a highly resistive metallic state proximate to a Kondo insulator.

Unified Framework for Charge-Spin Interconversion in Spin-Orbit Materials

Materials with spin-orbit coupling are of great interest for various spintronics applications due to the efficient electrical generation and detection of spin-polarized electrons. Over the past decade, many materials have been studied, including topological insulators, transition metals, Kondo insulators, semimetals, semiconductors, and oxides; however, there is no unifying physical framework for understanding the physics and therefore designing a material system and devices with the desired properties. We present a model that binds together the experimental data observed on the wide variety of materials in a unified manner. We show that in a material with a given spin-momentum locking, the density of states plays a crucial role in determining the charge-spin interconversion efficiency, and a simple inverse relationship can be obtained. Remarkably, experimental data obtained over the last decade on many different materials closely follow such an inverse relationship. We further deduce two figure-of-merits of great current interest: the spin-orbit torque (SOT) efficiency (for the direct effect) and the inverse Rashba-Edelstein effect length (for the inverse effect), which statistically show good agreement with the existing experimental data on wide varieties of materials. Especially, we identify a scaling law for the SOT efficiency with respect to the carrier concentration in the sample, which agrees with existing data. Such an agreement is intriguing since our transport model includes only Fermi surface contributions and fundamentally different from the conventional views of the SOT efficiency that includes contributions from all the occupied states.

Atomistic investigation of surface characteristics and electronic features at high-purity FeSi(110) presenting interfacial metallicity

Iron silicide (FeSi) is a fascinating material that has attracted extensive research efforts for decades, notably revealing unusual temperature-dependent electronic and magnetic characteristics, as well as a close resemblance to the Kondo insulators whereby a coherent picture of intrinsic properties and underlying physics remains to be fully developed. For a better understanding of this narrow-gap semiconductor, we prepared and examined FeSi(110) single-crystal surfaces of high quality. Combined insights from low-temperature scanning tunneling microscopy and density functional theory calculations (DFT) indicate an unreconstructed surface termination presenting rows of Fe-Si pairs. Using high-resolution tunneling spectroscopy (STS), we identify a distinct asymmetric electronic gap in the sub-10 K regime on defect-free terraces. Moreover, the STS data reveal a residual density of states in the gap regime whereby two in-gap states are recognized. The principal origin of these features is rationalized with the help of the DFT-calculated band structure. The computational modeling of a (110)-oriented slab notably evidences the existence of interfacial intragap bands accounting for a markedly increased density of states around the Fermi level. These findings support and provide further insight into the emergence of surface metallicity in the low-temperature regime.

Topological nature of the Kondo insulator SmB6 and its sensitiveness to Sm vacancy

The true topological nature of the Kondo insulator SmB$_6$ remains to be unveiled. Our previous tunneling study not only found evidence for the existence of surface Dirac fermions, but it also uncovered that they inherently interact with the spin excitons, collective excitations in the bulk. We have extended such a spectroscopic investigation into crystals containing a Sm deficiency. The bulk hybridization gap is found to be insensitive to the deficiency up to 1% studied here, but the surface states in Sm-deficient crystals exhibit quite different temperature evolutions from those in stoichiometric ones. We attribute this to the topological surface states remaining incoherent down to the lowest measurement temperature due to their continued interaction with the spin excitons that remain uncondensed. This result shows that the detailed topological nature of SmB$_6$ could vary drastically in the presence of disorder in the lattice. This sensitiveness to disorder is seemingly contradictory to the celebrated topological protection, but it can be understood as being due to the intimate interplay between strong correlations and topological effects.

Unusual high-field metal in a Kondo insulator

Within condensed-matter systems, strong electronic interactions often lead to exotic quantum phases. A recent manifestation of this is the unexpected observation of magnetic quantum oscillations and metallic thermal transport, both properties of systems with Fermi surfaces of itinerant quasiparticles, in the Kondo insulators SmB6 and YbB$_{12}$. To understand these phenomena, it is informative to study their evolution as the energy gap of the Kondo-Insulator state is closed by a large magnetic field. We show here that both the quantum-oscillation frequency and the cyclotron mass display a strong field dependence in the resulting high-field metallic state in $_{12}$. By tracking the Fermi-surface area, we conclude that the same quasiparticle band gives rise to the quantum oscillations in both insulating and metallic states. These data are understood most simply using a two-fluid picture where unusual quasiparticles, contributing little or nothing to charge transport, coexist with conventional fermions. In the metallic state this leads to a heavy-fermion bad metal with negligible magnetoresistance, relatively high resistivity and a very large Kadowaki-Woods ratio, underlining the exotic nature of the fermion ensemble inhabiting $_{12}$.

Self-oxidation-formed boron oxide as a tunnel barrier in SmB6 junctions

Samarium hexaboride (SmB6) belongs to a novel class of quantum matter known as topological Kondo insulators. By utilizing planar tunneling spectroscopy, signatures of spin excitons that interact with the topological surface states have been observed. To uncover additional details about this interaction, the effect on the characteristic features by plasma cleaning and ion beam etching processes, employed to clean the SmB6 crystal surface, are examined. Additionally, the effect of the plasma oxidation process used to form the tunnel barrier is analysed. Comparing the conductance spectra to simulations based on the Blonder-Tinkham-Klapwijk model revealed that the junctions with the highest resistances also had the weakest barrier strengths. Such seemingly contradictory observations may be explained by considering a barrier containing layers of B6O or B3O in addition to B2O3. This suboxide formation appears to be most dominant at higher ion beam energies as well as lower plasma oxidation powers.

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.

Robust hybridization gap in the Kondo insulator YbB12 probed by femtosecond optical spectroscopy

In heavy fermions the relaxation dynamics of photoexcited carriers has been found to be governed by the low energy indirect gap, E$_{g}$, resulting from hybridization between localized moments and conduction band electrons. Here, carrier relaxation dynamics in a prototype Kondo insulator YbB${}_{12}$ is studied over large range of temperatures and over three orders of magnitude. We utilize the intrinsic non-linearity of dynamics to quantitatively determine microscopic parameters, such as electron-hole recombination rate. The extracted value reveals that hybridization is accompanied by a strong charge transfer from localized 4f-levels. The results imply the presence of a hybridization gap up to temperatures of the order of E$_{g}$/k$_{B}\approx200$ K, which is extremely robust against electronic excitation. Finally, below 20 K the data reveal changes in the low energy electronic structure, attributed to short-range antiferromagnetic correlations between the localized levels.

Landau quantization and highly mobile fermions in an insulator.

In strongly correlated materials, quasiparticle excitations can carry fractional quantum numbers. An intriguing possibility is the formation of fractionalized, charge-neutral fermions-for example, spinons1 and fermionic excitons2,3-that result in neutral Fermi surfaces and Landau quantization4,5 in an insulator. Although previous experiments in quantum spin liquids1, topological Kondo insulators6-8 and quantum Hall systems3,9 have hinted at charge-neutral Fermi surfaces, evidence for their existence remains inconclusive. Here we report experimental observation of Landau quantization in a two-dimensional insulator, monolayer tungsten ditelluride (WTe2), a large-gap topological insulator10-13. Using a detection scheme that avoids edge contributions, we find large quantum oscillations in the material's magnetoresistance, with an onset field as small as about 0.5tesla. Despite the huge resistance, the oscillation profile, which exhibits many periods, mimics the Shubnikov-de Haas oscillations in metals. At ultralow temperatures, the observed oscillations evolve into discrete peaks near 1.6tesla, above which the Landau quantized regime is fully developed. Such a low onset field of quantization is comparable to the behaviour of high-mobility conventional two-dimensional electron gases. Our experiments call for further investigation of the unusual ground state of the WTe2 monolayer, including the influence of device components and the possible existence of mobile fermions and charge-neutral Fermi surfaces inside its insulating gap.

Quantum Oscillations and Charge Neutral Fermions in Kondo Insulators

Quantum Oscillations and Charge Neutral Fermions in Kondo Insulators

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.

Temperature-dependent angle-resolved photoemission spectroscopy study of the Ce 4f states in a possible topological Kondo insulator CeRhAs

The electronic structure of a possible topological Kondo insulator of CeRhAs has been investigated by employing temperature $(T)$-dependent angle-resolved photoemission spectroscopy (ARPES). Fermi surfaces (FSs) and band structures are successfully measured for three orthogonal crystallographic planes. The measured Fermi-edge states are found to have a three-dimensional (3D) character, contradictory to the proposed topological surface states of the $2\text{D}$ character. The measured FSs due to the Ce $4f$ electrons agree well with those from the density functional theory band structures unfolded into the reduced Ce-only unit cell. The theoretically predicted hourglass-type bulk bands along $\overline{X}\overline{S}\overline{X}$ are not clearly resolved, in spite of the evident existence of those band features. $T$-dependent ARPES measurements reveal that the coherent Ce $4f$ states, having two pseudogap structures of ${\mathrm{\ensuremath{\Delta}}}_{1}\ensuremath{\sim}80$ meV and ${\mathrm{\ensuremath{\Delta}}}_{2}\ensuremath{\sim}30$ meV, persist to remain above 200 K, in agreement with the high Kondo temperature of CeRhAs.