Skyrme Insulators: Insulators at the Brink of Superconductivity

High-temperature surface state in Kondo insulator U3Bi4Ni3

The resurgence of interest in Kondo insulators has been driven by two major mysteries: the presence of metallic surface states and the observation of quantum oscillations. To further explore these mysteries, it is crucial to investigate another similar system beyond the two existing ones, SmB6 and YbB12. Here, we address this by reporting on a Kondo insulator, U3Bi4Ni3. Our transport measurements reveal that a surface state emerges below 250 kelvin and dominates transport properties below 150 kelvin, which is well above the temperature scale of SmB6 and YbB12. At low temperatures, the surface conductivity is about one order of magnitude higher than the bulk. The robustness of the surface state indicates that it is inherently protected. The similarities and differences between U3Bi4Ni3 and the other two Kondo insulators will provide valuable insights into the nature of metallic surface states in Kondo insulators and their interplay with strong electron correlations.

Charge-neutral electronic excitations in quantum insulators

Experiments on quantum materials have uncovered many interesting quantum phases ranging from superconductivity to a variety of topological quantum matter including the recently observed fractional quantum anomalous Hall insulators. The findings have come in parallel with the development of approaches to probe the rich excitations inherent in such systems. In contrast to observing electrically charged excitations, the detection of charge-neutral electronic excitations in condensed matter remains difficult, although they are essential to understanding a large class of strongly correlated phases. Low-energy neutral excitations are especially important in characterizing unconventional phases featuring electron fractionalization, such as quantum spin liquids, spin ices and insulators with neutral Fermi surfaces. In this Perspective, we discuss searches for neutral fermionic, bosonic or anyonic excitations in unconventional insulators, highlighting theoretical and experimental progress in probing excitonic insulators, new quantum spin liquid candidates and emergent correlated insulators based on two-dimensional layered crystals and moiré materials. We outline the promises and challenges in probing and using quantum insulators, and discuss exciting new opportunities for future advancements offered by ideas rooted in next-generation quantum materials, devices and experimental schemes.

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.

Effective Model and Magnetic Properties of the Resistive Electron Quadrupling State

Recent experiments [Grinenko et al. Nat. Phys. 17, 1254 (2021)NPAHAX1745-247310.1038/s41567-021-01350-9] reported the observation of a condensate of four-fermion composites. This is a resistive state that spontaneously breaks the time-reversal symmetry, leading to unconventional magnetic properties, detected in muon spin rotation experiments and by the appearance of a spontaneous Nernst effect. In this Letter, we derive an effective model for the four-fermion order parameter that describes the observed spontaneous magnetic fields in this state. We show that this model, which is alike to the Faddeev-Skyrme model can host skyrmions: magnetic-flux-carrying topological excitations.

Topologically Enabled Superconductivity

Majorana zero modes are a much sought-after consequence of one-dimensional topological superconductivity. Here, we show that, in turn, zero modes accompanying dynamical instanton events strongly enhance-in some cases even enable-superconductivity. We find that the dynamics of a one-dimensional topological triplet superconductor is governed by a θ term in the action. For isotropic triplets, this term enables algebraic charge-2e superconductivity, which is destroyed by fluctuations in nontopological superconductors. For anisotropic triplets, zero modes suppress quantum phase slips and stabilize superconductivity over a large region of the phase diagram. We present predictions of correlation functions and thermodynamics for states of topologically enhanced superconductivity.

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.

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.

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.

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

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.

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.

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.

Spin, Orbital, Weyl and Other Glasses in Topological Superfluids

One of the most spectacular discoveries made in superfluid3 He confined in a nanostructured material like aerogel or nafen was the observation of the destruction of the long-range orientational order by a weak random anisotropy. The quenched random anisotropy provided by the confining material strands produces several different glass states resolved in NMR experiments in the chiral superfluid3 He-A and in the time-reversal-invariant polar phase. The smooth textures of spin and orbital order parameters in these glasses can be characterized in terms of the randomly distributed topological charges, which describe skyrmions, spin vortices and hopfions. In addition, in these skyrmion glasses the momentum-space topological invariants are randomly distributed in space. The Chern mosaic, Weyl glass, torsion glass and other exotic topological states are examples of close connections between the real-space and momentum-space topologies in superfluid3 He phases in aerogel.

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 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.

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.

Mixed-valence insulators with neutral Fermi surfaces

Samarium hexaboride is a classic three-dimensional mixed valence system with a high-temperature metallic phase that evolves into a paramagnetic charge insulator below 40 K. A number of recent experiments have suggested the possibility that the low-temperature insulating bulk hosts electrically neutral gapless fermionic excitations. Here we show that a possible ground state of strongly correlated mixed valence insulators—a composite exciton Fermi liquid—hosts a three dimensional Fermi surface of a neutral fermion, that we name the “composite exciton.” We describe the mechanism responsible for the formation of such excitons, discuss the phenomenology of the composite exciton Fermi liquids and make comparison to experiments in SmB₆.

Samarium hexaboride is a candidate topological insulator but recent experiments have found behaviour indicative of a metallic Fermi liquid phase. Here the authors show that the conflicting observations can be accommodated by a model where strong interactions drive the formation of exotic neutral quasiparticles.

Fermi surfaces in Kondo insulators

We report magnetic quantum oscillations measured using torque magnetisation in the Kondo insulator YbB₁₂ and discuss the potential origin of the underlying Fermi surface. Observed quantum oscillations as well as complementary quantities such as a finite linear specific heat capacity in YbB₁₂ exhibit similarities with the Kondo insulator SmB₆, yet also crucial differences. Small heavy Fermi sections are observed in YbB₁₂ with similarities to the neighbouring heavy fermion semimetallic Fermi surface, in contrast to large light Fermi surface sections in SmB₆ which are more similar to the conduction electron Fermi surface. A rich spectrum of theoretical models is suggested to explain the origin across different Kondo insulating families of a bulk Fermi surface potentially from novel itinerant quasiparticles that couple to magnetic fields, yet do not couple to weak DC electric fields.