Heavy fermions. Unconventional Fermi surface in an insulating state

Electronic origin of negative thermal expansion in samarium hexaboride revealed by X-ray diffraction and total scattering

Samarium hexaboride, SmB6, is a negative thermal expansion (NTE) material whose structure is similar to other known NTE materials such as the family of Prussian blues. In the Prussian blues, NTE is due to a phonon mechanism, but we recently showed from DFT calculations that this is unlikely in SmB6 (Li et al., Phys. Chem. Chem. Phys. 2023, 25, 10749). We now report experimental X-ray diffraction and pair distribution function analysis of this material in the temperature range 20-300 K. The interatomic distances shown by both methods are consistent with the NTE instead arising from an electronic effect, by which the samarium atoms lose electrons and thus have a smaller ionic radius as the temperature increases.

Controllable strain-driven topological phase transition and dominant surface-state transport in HfTe5

The fine-tuning of topologically protected states in quantum materials holds great promise for novel electronic devices. However, there are limited methods that allow for the controlled and efficient modulation of the crystal lattice while simultaneously monitoring the changes in the electronic structure within a single sample. Here, we apply significant and controllable strain to high-quality HfTe5 samples and perform electrical transport measurements to reveal the topological phase transition from a weak topological insulator phase to a strong topological insulator phase. After applying high strain to HfTe5 and converting it into a strong topological insulator, we found that the resistivity of the sample increased by 190,500% and that the electronic transport was dominated by the topological surface states at cryogenic temperatures. Our results demonstrate the suitability of HfTe5 as a material for engineering topological properties, with the potential to generalize this approach to study topological phase transitions in van der Waals materials and heterostructures.

Cryogenic spectroscopic imaging scanning tunnelling microscope in a water-cooled magnet down to 1.7 K

Spectroscopic-imaging scanning tunnelling microscope (SI-STM) in a water-cooled magnet (WM) at low temperature has long been desirable in the condensed matter physics area since it is crucial for addressing various scientific problems, such as the behaviour of Cooper electrons crossing Hc2 in a high-temperature superconductor. Here we report on the construction and performance of the first atomically resolved cryogenic SI-STM in a WM. It operates at low temperatures of down to 1.7 K and in magnetic fields of up to 22 T (the WM's upper safety limit). The WM-SI-STM unit features a high-stiffness sapphire-based frame with the lowest eigenfrequency being 16 kHz. A slender piezoelectric scan tube (PST) is coaxially embedded in and glued to the frame. A well-polished zirconia shaft is spring-clamped onto the gold-coated inner wall of the PST to serve both the stepper and the scanner. The microscope unit as a whole is elastically suspended in a tubular sample space inside a 1K-cryostat by a two-stage internal passive vibrational reduction system, achieving a base temperature below 2 K in a static exchange gas. We demonstrate the SI-STM by imaging TaS2 at 50 K and FeSe at 1.7 K. Detecting the well-defined superconducting gap of FeSe, an iron-based superconductor, at variable magnetic fields demonstrates the device's spectroscopic imaging capability. The maximum noise intensity at the typical frequency is 3 pA per square root Hz at 22 T, which is only slightly worse than at 0 T, indicating the insensitivity of the STM to harsh conditions. In addition, our work shows the potential of SI-STMs for use in a WM and hybrid magnet with a 50 mm-bore size where high fields can be generated.

Quantum oscillations of the quasiparticle lifetime in a metal

Following nearly a century of research, it remains a puzzle that the low-lying excitations of metals are remarkably well explained by effective single-particle theories of non-interacting bands1-4. The abundance of interactions in real materials raises the question of direct spectroscopic signatures of phenomena beyond effective single-particle, single-band behaviour. Here we report the identification of quantum oscillations (QOs) in the three-dimensional topological semimetal CoSi, which defy the standard description in two fundamental aspects. First, the oscillation frequency corresponds to the difference of semiclassical quasiparticle (QP) orbits of two bands, which are forbidden as half of the trajectory would oppose the Lorentz force. Second, the oscillations exist up to above 50 K, in strong contrast to all other oscillatory components, which vanish below a few kelvin. Our findings are in excellent agreement with generic model calculations of QOs of the QP lifetime (QPL). Because the only precondition for their existence is a nonlinear coupling of at least two electronic orbits, for example, owing to QP scattering on defects or collective excitations, such QOs of the QPL are generic for any metal featuring Landau quantization with several orbits. They are consistent with certain frequencies in topological semimetals5-9, unconventional superconductors10,11, rare-earth compounds12-14 and Rashba systems15, and permit to identify and gauge correlation phenomena, for example, in two-dimensional materials16,17 and multiband metals18.

Quantum oscillations in field-induced correlated insulators of a moiré superlattice

We report an observation of quantum oscillations (QOs) in the correlated insulators with valley anisotropy of twisted double bilayer graphene (TDBG). The anomalous QOs are best captured in the magneto resistivity oscillations of the insulators at v = -2, with a period of 1/B and an oscillation amplitude as high as 150 kΩ. The QOs can survive up to ∼10 K, and above 12 K, the insulating behaviors are dominant. The QOs of the insulator are strongly D dependent: the carrier density extracted from the 1/B periodicity decreases almost linearly with D from -0.7 to -1.1 V/nm, suggesting a reduced Fermi surface; the effective mass from Lifshitz-Kosevich analysis depends nonlinearly on D, reaching a minimal value of 0.1 me at D = ∼ -1.0 V/nm. Similar observations of QOs are also found at v = 2, as well as in other devices without graphite gate. We interpret the D sensitive QOs of the correlated insulators in the picture of band inversion. By reconstructing an inverted band model with the measured effective mass and Fermi surface, the density of state at the gap, calculated from thermal broadened Landau levels, agrees qualitatively with the observed QOs in the insulators. While more theoretical understandings are needed in the future to fully account for the anomalous QOs in this moiré system, our study suggests that TDBG is an excellent platform to discover exotic phases where correlation and topology are at play.

A Mixed Protonic-Electronic Conductor Base on the Host-Guest Architecture of 2D Metal-Organic Layers and Inorganic Layers

The key to designing and fabricating highly efficient mixed protonic-electronic conductors materials (MPECs) is to integrate the mixed conductive active sites into a single structure, to break through the shortcomings of traditional physical blending. Herein, based on the host-guest interaction, an MPEC is consisted of 2D metal-organic layers and hydrogen-bonded inorganic layers by the assembly methods of layered intercalation. Noticeably, the 2D intercalated materials (≈1.3 nm) exhibit the proton conductivity and electron conductivity, which are 2.02 × 10^-5 and 3.84 × 10^-4 S cm^-1 at 100 °C and 99% relative humidity, much higher than these of pure 2D metal-organic layers (>>1.0 × 10^-10 and 2.01×10^-8 S cm^-1 ), respectively. Furthermore, combining accurate structural information and theoretical calculations reveals that the inserted hydrogen-bonded inorganic layers provide the proton source and a networks of hydrogen-bonds leading to efficient proton transport, meanwhile reducing the bandgap of hybrid architecture and increasing the band electron delocalization of the metal-organic layer to greatly elevate the electron transport of intrinsic 2D metal-organic frameworks.

Spin-Liquid Insulators Can Be Landau's Fermi Liquids

The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.

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.

Solvable 3D Kondo Lattice Exhibiting Pair Density Wave, Odd-Frequency Pairing, and Order Fractionalization

The Kondo lattice model plays a key role in our understanding of quantum materials, but a lack of small parameters has posed a long-standing problem. We present a three-dimensional S=1/2 Kondo lattice model describing a spin liquid within an electron sea. Strong correlations in the spin liquid are treated exactly, enabling a controlled analytical approach. Like a Peierls or BCS phase, a logarithmically divergent susceptibility leads to an instability into a new phase at arbitrarily small Kondo coupling. Our solution captures a plethora of emergent phenomena, including odd-frequency pairing, pair density wave formation and order fractionalization. The ground-state state is a pair density wave with a fractionalized charge e, S=1/2 order parameter, formed between electrons and Majorana fermions.

Quantum oscillations in the magnetization and density of states of insulators

The observation of [Formula: see text]-periodic behavior in Kondo insulators and semiconductor quantum wells challenges the conventional wisdom that quantum oscillations (QOs) necessarily arise from Fermi surfaces in metals. We revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast to metals where all observables exhibit oscillations at the same frequency. The magnetization oscillations arising from occupied Landau levels occur at the same frequency that would exist in the unhybridized case. The LE-DOS oscillations in a disorder-free system are dominated by gap-edge states and exhibit a beat pattern between two distinct frequencies at low temperature. Disorder-induced in-gap states lead to an additional contribution to the DOS at the unhybridized frequency. The temperature dependence of the amplitude and phase of the magnetization and DOS oscillations are also qualitatively different and show marked deviations from the Lifshitz-Kosevich form well known in metals. We also compute transport to ensure that we are probing a regime with insulating upturns in the direct current (DC) resistivity.

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.

Magnetoquantum oscillations in the specific heat of a topological Kondo insulator

Surprisingly, magnetoquantum oscillations (MQOs) characteristic of a metal with a Fermi surface have been observed in measurements of the topological Kondo insulator SmB₆. As these MQO have only been observed in measurements of magnetic torque (dHvA) and not in measurements of magnetoresistance (SdH), a debate has arisen as to whether the MQO are an extrinsic effect arising from rare-earth impurities, defects, and/or aluminum inclusions or an intrinsic effect revealing the existence of charge-neutral excitations. We report here the first observation of MQO in the low-temperature specific heat of SmB₆. The observed frequencies and their angular dependence for these flux-grown samples are consistent with previous results based on magnetic torque for SmB₆but the inferred effective masses are significantly larger than previously reported. Such oscillations can only be observed if the MQO are of bulk thermodynamic origin; the measured magnetic-field dependent oscillation amplitude and effective mass allow us to rule out suggestions of an extrinsic, aluminum inclusion-based origin for the MQO.

Band theoretical approaches to topological physics in strongly-correlatedf-electron Kondo systems

First-principles band structure theory on the basis of the density functional theory (DFT) plays an essential role in the investigation of topological properties of weakly-correlated systems. DFT band structures show clear bulk band crossings for Weyl and Dirac semimetals, and surface band crossings for topological insulators and topological-crystalline insulators. In contrast, for strongly-correlatedf-electron systems, their topological properties are relatively less explored because the simple DFT does not work properly in describing the electronic structures of strongly-correlatedfelectrons. In this perspective, we examine the band theoretical approaches to topological properties of strongly-correlatedf-electron Kondo systems. We recapitulate current status of understanding of electronic structures and topological properties of strongly-correlated 4f-electron systems, such as Ce, SmB₆, and g-SmS, and also a 5f-electron system PuB₄, the electronic structures of which were investigated by the DFT combined with the dynamical mean-field theory (DFT + DMFT). Finally, we provide future directions and perspectives of improving theoretical band approaches to search for new topologicalf-electron systems, as an outlook.

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.

Emergent quasiparticles at Luttinger surfaces

In periodic systems of interacting electrons, Fermi and Luttinger surfaces refer to the locations within the Brillouin zone of poles and zeros, respectively, of the single-particle Green’s function at zero energy and temperature. Such difference in analytic properties underlies the emergence of well-defined quasiparticles close to a Fermi surface, in contrast to their supposed non-existence close to a Luttinger surface, where the single-particle density-of-states vanishes at zero energy. We here show that, contrary to such common belief, dispersive ‘quasiparticles’ with infinite lifetime do exist also close to a pseudo-gapped Luttinger surface. Thermodynamic and dynamic properties of such ‘quasiparticles’ are just those of conventional ones. For instance, they yield well-defined quantum oscillations in Luttinger surface and linear-in-temperature specific heat, which is striking given the vanishing density of states of physical electrons, but actually not uncommon in strongly correlated materials.

The analytic properties of Fermi surfaces give rise to quasiparticles. Now, it is shown that similarly, quasiparticles can be associated with Luttinger surfaces - the locations in the Brillouin zone of zeros of the single-particle Green’s function at zero energy and temperature.

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.

Quantum Oscillations in Two-Dimensional Insulators Induced by Graphite Gates

We demonstrate a mechanism for magnetoresistance oscillations in insulating states of two-dimensional (2D) materials arising from the interaction of the 2D layer and proximal graphite gates. We study a series of devices based on different 2D systems, including mono- and bilayer T_{d}-WTe_{2}, MoTe_{2}/WSe_{2} moiré heterobilayers, and Bernal-stacked bilayer graphene, which all share a similar graphite-gated geometry. We find that the 2D systems, when tuned near an insulating state, generically exhibit magnetoresistance oscillations corresponding to a high-density Fermi surface, in contravention of naïve band theory. Simultaneous measurement of the resistivity of the graphite gates shows that the oscillations of the sample layer are precisely correlated with those of the graphite gates. Further supporting this connection, the oscillations are quenched when the graphite gate is replaced by a low-mobility metal, TaSe_{2}. The observed phenomenon arises from the oscillatory behavior of graphite density of states, which modulates the device capacitance and, as a consequence, the carrier density in the sample layer even when a constant electrochemical potential is maintained between the sample and the gate electrode. Oscillations are most pronounced near insulating states where the resistivity is strongly density dependent. Our study suggests a unified mechanism for quantum oscillations in graphite-gated 2D insulators based on electrostatic sample-gate coupling.

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.

Incoherent transport across the strange-metal regime of overdoped cuprates

Strange metals possess highly unconventional electrical properties, such as a linear-in-temperature resistivity^1-6, an inverse Hall angle that varies as temperature squared^7-9 and a linear-in-field magnetoresistance^10-13. Identifying the origin of these collective anomalies has proved fundamentally challenging, even in materials such as the hole-doped cuprates that possess a simple bandstructure. The prevailing consensus is that strange metallicity in the cuprates is tied to a quantum critical point at a doping p* inside the superconducting dome^14,15. Here we study the high-field in-plane magnetoresistance of two superconducting cuprate families at doping levels beyond p*. At all dopings, the magnetoresistance exhibits quadrature scaling and becomes linear at high values of the ratio of the field and the temperature, indicating that the strange-metal regime extends well beyond p*. Moreover, the magnitude of the magnetoresistance is found to be much larger than predicted by conventional theory and is insensitive to both impurity scattering and magnetic field orientation. These observations, coupled with analysis of the zero-field and Hall resistivities, suggest that despite having a single band, the cuprate strange-metal region hosts two charge sectors, one containing coherent quasiparticles, the other scale-invariant 'Planckian' dissipators.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid

The quasi-two-dimensional Mott insulator α-RuCl_{3} is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of α-RuCl_{3} on graphene, the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such α-RuCl_{3} and graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures, a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridizing with the graphene Dirac band. Using ab initio calculations to determine the parameters of our low-energy model, we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.

DMFT Reveals the Non-Hermitian Topology and Fermi Arcs in Heavy-Fermion Systems

When a strongly correlated system supports well-defined quasiparticles, it allows for an elegant one-body effective description within the non-Hermitian topological theory. While the microscopic many-body Hamiltonian of a closed system remains Hermitian, the one-body quasiparticle Hamiltonian is non-Hermitian due to the finite quasiparticle lifetime. We use such a non-Hermitian description in the heavy-fermion two-dimensional systems with the momentum-dependent hybridization to reveal a fascinating phenomenon which can be directly probed by the spectroscopic measurements, the bulk "Fermi arcs." Starting from a simple two-band model, we first combine the phenomenological approach with the perturbation theory to show the existence of the Fermi arcs and reveal their connection to the topological exceptional points, special points in the Brillouin zone where the Hamiltonian is nondiagonalizable. The appearance of such points necessarily requires that the electrons belonging to different orbitals have different lifetimes. This requirement is naturally satisfied in the heavy-fermion systems, where the itinerant c electrons experience much weaker interaction than the localized f electrons. We then utilize the dynamical mean field theory to numerically calculate the spectral function and confirm our findings. We show that the concept of the exceptional points in the non-Hermitian quasiparticle Hamiltonians is a powerful tool for predicting new phenomena in strongly correlated electron systems.

Intrinsic Bulk Quantum Oscillations in a Bulk Unconventional Insulator SmB6

The finding of bulk quantum oscillations in the Kondo insulator SmB₆ proved a considerable surprise. Subsequent measurements of bulk quantum oscillations in other correlated insulators including YbB₁₂ lent support to our discovery of a class of bulk unconventional insulators that host bulk quantum oscillations. Here we perform a series of experiments to examine evidence for the intrinsic character of bulk quantum oscillations in floating zone-grown single crystals of SmB₆ that have been the subject of our quantum oscillation studies. We present results of thermodynamic, transport, and composition analysis experiments on pristine floating zone-grown single crystals of SmB₆ and compare quantum oscillations with metallic LaB₆ and elemental aluminum. These results establish the intrinsic origin of quantum oscillations from the insulating bulk of floating zone-grown SmB₆. The similarity of the Fermi surface in insulating SmB₆ with the conduction-electron Fermi surface in metallic hexaborides is at the heart of a theoretical mystery.

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No metallic inclusion contribution to quantum oscillations in ultrapure insulating SmB₆

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Unconventional low energy excitations responsible for bulk quantum oscillations in SmB₆

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Insulating SmB₆ Fermi surface resembles conduction-e^- Fermi surface of metallic LaB₆

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

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

Universal signatures of Majorana-like quasiparticles in strongly correlated Landau-Fermi liquids

Motivated by recent experiments in the Kitaev honeycomb lattice, Kondo insulators, and the 'Luttinger's theorem-violating' Fermi liquid phase of the underdoped cuprates, we extend the theoretical machinery of Landau-Fermi liquid theory to a system of itinerant, interacting Majorana-like particles. Building upon a previously introduced model of 'nearly self-conjugate' fermionic polarons, a Landau-Majorana kinetic equation is introduced to describe the collective modes and Fermi surface instabilities in a fluid of particles whose fermionic degrees of freedom obey the Majorana reality condition. At large screening, we show that the Landau-Majorana liquid harbors a Lifshitz transition for specific values of the driving frequency. Moreover, we find the dispersion of the zero sound collective mode in such a system, showing that there exists a specific limit where the Landau-Majorana liquid harbors a stability against Pomeranchuk deformations unseen in the conventional Landau-Fermi liquid. With these results, our work paves the way for possible extensions of the Landau quasiparticle paradigm to nontrivial metallic phases of matter.

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.

30 T scanning tunnelling microscope in a hybrid magnet with essentially non-metallic design

We report on the construction and performance of the first hybrid resistive-superconducting magnet (HM) based scanning tunnelling microscope (STM) above 30 T. This custom-design HM-STM features a novel design of the STM head unit, whose tip-sample approach is implemented using a slender piezoelectric tube (PZT). The scanner shares part of PZT by fixing a sapphire frame onto the front quarter of PZT to construct a compact tip-sample loop, realising an outer diameter of 8.8 mm, which makes it compatible with a narrow sample space. Its main components are made of non-metallic materials of sapphire, which allows it to be immune from eddy currents and to operate under the condition of strong magnetic field fluctuation from a hybrid magnet, as well as cryogen-free cryocooler magnet systems. To analyse the stiffness of the STM head unit, the eigenfrequencies with 11 kHz and 12 kHz in bending modes, 25 kHz in a torsional mode, and 67 kHz in a longitudinal mode were simulated by finite element analysis; also, the drifting rates of the STM in ambient conditions in the X-Y plane and Z direction were measured at 25.5 and 38.2 pm/min, respectively. We present the first atomic images in magnetic fields up to 30.1 T in an HM. The raw data show the stable and distinguished performance while ramping up to maximum fields, indicating the new device's potential capability of operating in the future 45T-hybrid magnet and hundred-field pulsed magnet. Meanwhile, our compact and concentric cylindrical STM insert can operate in the low-temperature tubular sample space housed by the HM bore to develop low-temperature and extreme high-magnetic field STM.

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.

Anomalous Conductance Oscillations in the Hybridization Gap of InAs/GaSb Quantum Wells

We observe the magnetic oscillation of electric conductance in the two-dimensional InAs/GaSb quantum spin Hall insulator. Its insulating bulk origin is unambiguously demonstrated by the antiphase oscillations of the conductance and the resistance. Characteristically, the in-gap oscillation frequency is higher than the Shubnikov-de Haas oscillation close to the conduction band edge in the metallic regime. The temperature dependence shows both thermal activation and smearing effects, which cannot be described by the Lifshitz-Kosevich theory. A two-band Bernevig-Hughes-Zhang model with a large quasiparticle self-energy in the insulating regime is proposed to capture the main properties of the in-gap oscillations.

Transport gap in SmB6 protected against disorder

The inverted resistance method was used in this study to extend the bulk resistivity of [Formula: see text] to a regime where the surface conduction overwhelms the bulk. Remarkably, regardless of the large off-stoichiometric growth conditions (inducing disorder by samarium vacancies, boron interstitials, etc.), the bulk resistivity shows an intrinsic thermally activated behavior that changes ∼7-10 orders of magnitude, suggesting that [Formula: see text] is an ideal insulator that is immune to disorder.

Extremely high conductivity observed in the triple point topological metal MoP

Weyl and Dirac fermions have created much attention in condensed matter physics and materials science. Recently, several additional distinct types of fermions have been predicted. Here, we report ultra-high electrical conductivity in MoP at low temperature, which has recently been established as a triple point fermion material. We show that the electrical resistivity is 6 nΩ cm at 2 K with a large mean free path of 11 microns. de Haas-van Alphen oscillations reveal spin splitting of the Fermi surfaces. In contrast to noble metals with similar conductivity and number of carriers, the magnetoresistance in MoP does not saturate up to 9 T at 2 K. Interestingly, the momentum relaxing time of the electrons is found to be more than 15 times larger than the quantum coherence time. This difference between the scattering scales shows that momentum conserving scattering dominates in MoP at low temperatures.

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.

Anomalous Quantum Oscillations of Interacting Electron-Hole Gases in Inverted Type-II InAs/GaSb Quantum Wells

We report magnetotransport studies of InAs/GaSb bilayer quantum wells in a regime where the interlayer tunneling between the electron and hole gases is suppressed. When the chemical potential is tuned close to the charge neutrality point, we observe anomalous quantum oscillations that are inversely periodic in magnetic field and that have an extremely high frequency despite the highly insulating regime where they are observed. The seemingly contradictory coexistence of a high sheet resistance and high frequency quantum oscillations in the charge neutrality regime cannot be understood within the single-particle picture. We propose an interpretation that attributes our experimental observation to the Coulomb drag between the electron and hole gases, thus providing strong evidence of the significance of Coulomb interaction in this topological insulator.

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.

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.

Nonequilibrium Magnetic Oscillation with Cylindrical Vector Beams

Magnetic oscillation is a generic property of electronic conductors under magnetic fields and widely appreciated as a useful probe of their electronic band structure, i.e. the Fermi surface geometry. However, the usage of the strong static magnetic field makes the measurement insensitive to the magnetic order of the target material. That is, the magnetic order is anyhow turned into a forced ferrromagnetic one. Here we theoretically propose an experimental method of measuring the magnetic oscillation in a magnetic-order-resolved way by using the azimuthal cylindrical vector (CV) beam, an example of topological lightwaves. The azimuthal CV beam is unique in that, when focused tightly, it develops a pure longitudinal magnetic field. We argue that this characteristic focusing property and the discrepancy in the relaxation timescale between conduction electrons and localized magnetic moments allow us to develop the nonequilibrium analogue of the magnetic oscillation measurement. Our optical method would be also applicable to metals under the ultra-high pressure of diamond anvil cells.

Quantum oscillations in an insulator

Even without a Fermi surface, a Kondo insulator exhibits magnetoresistance oscillations

Quantum oscillations of electrical resistivity in an insulator

In metals, orbital motions of conduction electrons on the Fermi surface are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators. Here, we report a notable exception in an insulator-ytterbium dodecaboride (YbB₁₂). The resistivity of YbB₁₂, which is of a much larger magnitude than the resistivity in metals, exhibits distinct quantum oscillations. These unconventional oscillations arise from the insulating bulk, even though the temperature dependence of the oscillation amplitude follows the conventional Fermi liquid theory of metals with a large effective mass. Quantum oscillations in the magnetic torque are also observed, albeit with a lighter effective mass.

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.

Highly Asymmetric Nodal Semimetal in Bulk SmB_{6}

We show that novel low temperature properties of bulk SmB_{6}, including the sudden growth of the de Haas-van Alphen (dHvA) amplitude (and heat capacity) at millikelvin temperatures and a previously unreported linear-in-temperature bulk electrical conductivity at liquid helium temperatures, signal the presence of a highly asymmetric nodal semimetal. We show that a highly asymmetric nodal semimetal is also a predicted property of the Kondo lattice model (with dispersionless f-electron levels) in the presence of Sm vacancies or other defects. We show it can result from a topological transformation of the type recently considered by Shen and Fu and eliminates the necessity of a neutral Fermi surface for explaining bulk dHvA oscillations in SmB_{6}.

Quantum Oscillation from In-Gap States and a Non-Hermitian Landau Level Problem

Motivated by recent experiments on Kondo insulators, we theoretically study quantum oscillations from disorder-induced in-gap states in small-gap insulators. By solving a non-Hermitian Landau level problem that incorporates the imaginary part of electron's self-energy, we show that the oscillation period is determined by the Fermi surface area in the absence of the hybridization gap, and we derive an analytical formula for the oscillation amplitude as a function of the indirect band gap, scattering rates, and temperature. Over a wide parameter range, we find that the effective mass is controlled by scattering rates, while the Dingle factor is controlled by the indirect band gap. We also show the important effect of scattering rates in reshaping the quasiparticle dispersion in connection with angle-resolved photoemission measurements on heavy fermion materials.

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.

Magnetic-Field-Induced Kondo Metal Realized in YbB_{12}

The specific heat of the Kondo insulator YbB_{12} has been measured up to 60 T. The Sommerfeld coefficient γ significantly increases at around 50 T, where the insulator metal transition occurs with a steep increase of the magnetization. γ reaches 67  mJ/(mol K^{2}) at high fields, which directly indicates that the quasiparticles gain a heavy thermodynamic effective mass and transform into a Kondo metal under magnetic fields. The field-induced Kondo metal has a rather high Kondo temperature around 200 K. The strong Kondo coupling proves that the energy gap collapse does not correspond to the breakdown of the Kondo bound state. The steep increase of the magnetization at the transition manifests the sharp density of states at the Fermi energy formed via the Kondo resonance.