Abnormal Relaxation Behavior of Excited Electrons in the Flat Band of Kagome Compound Nb3Cl8

Carrier dynamics is crucial in semiconductors, and it determines their conductivity, response time, and overall functionality. In flat bands (FBs), carriers with high effective masses are predicted to host unconventional transport properties. The FBs usually overlap with other trivial energy bands, however, making it difficult to accurately distinguish their carrier dynamics. In this paper, we have investigated the flat-band carrier dynamics of excited electrons in Nb3Cl8, which hosts ideal nonoverlapping FBs near the Fermi level. The optical transition between Hubbard bands is abnormally weakened, exhibiting weak interband absorption and its related slow photoresponse with a time constant of ∼120 s, which are associated with flat-band Mottness-induced large electron effective mass and parity-forbidden transitions. Besides, the localized states created by chlorine vacancies also act as trapping centers for carriers with a time constant of ∼600 s, which are similar to those of the compact localized states of the FB, making the relaxation behavior even more extraordinary. The presence and impacts of atomic defects are confirmed experimentally and theoretically. This work has revealed the abnormal flat-band carrier dynamics of Nb3Cl8, which is essential for understanding the optical, electrical, and thermal transport properties of flat-band materials.

Ta4SBr11: A Cluster Mott Insulator with a Corrugated, Van der Waals Layered Structure

The compound Ta4SBr11 was prepared by a comproportionation reaction of tantalum bromide with tantalum and elemental sulfur. The crystal structure, as refined by single-crystal X-ray diffraction, is composed of clusters with Ta4S cores, arranged in corrugated van der Waals layers. Individual layers appear to be displaced relative to each other along one direction. Successful crystal growth in a melt of CsBr yielded black platelets of Ta4SBr11, which were used to investigate the electrical properties of the compound. The electronic structure was studied by diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy and by density functional theory (DFT) band structure calculations, revealing this material to be a small-gap semiconductor. DFT results, in combination with magnetic susceptibility measurements, suggest that metallicity originating from the one unpaired Ta d electron per cluster is most likely suppressed by electronic correlations, forming a cluster Mott insulator.

Electronic structure and transport in the potential Luttinger liquids CsNb3Br7S and RbNb3Br7S

The crystal structures of ANb3Br7S (A = Rb and Cs) have been refined by single crystal X-ray diffraction, and are found to form highly anisotropic materials based on chains of the triangular Nb3 cluster core. The Nb3 cluster core contains seven valence electrons, six of them being assigned to Nb-Nb bonds within the Nb3 triangle and one unpaired d electron. The presence of this surplus electron gives rise to the formation of correlated electronic states. The connectivity in the structures is represented by one-dimensional [Nb3Br7S]- chains, containing a sulphur atom capping one face (μ3) of the triangular niobium cluster, which is believed to induce an important electronic feature. Several types of studies are undertaken to obtain deeper insight into the understanding of this unusual material: the crystal structure, morphology and elastic properties are analysed, as well the (photo-)electrical properties and NMR relaxation. Electronic structure (DFT) calculations are performed in order to understand the electronic structure and transport in these compounds, and, based on the experimental and theoretical results, we propose that the electronic interactions along the Nb chains are sufficiently one-dimensional to give rise to Luttinger liquid (rather than Fermi liquid) behaviour of the metallic electrons.

Possible quantum-spin-liquid state in van der Waals cluster magnet Nb3Cl8

The cluster magnet Nb3Cl8consists of Nb3trimmers that form an emergentS= 1/2 two-dimensional triangular layers, which are bonded by weak van der Waals interactions. Recent studies show that its room-temperature electronic state can be well described as a single-band Mott insulator. However, the magnetic ground state is non-magnetic due to a structural transition below about 100 K. Here we show that there exists a thickness threshold below which the structural transition will not happen. For a bulk crystal, a small fraction of the sample maintains the high-temperature structure at low temperatures and such remnant gives rise to linear-temperature dependence of the specific heat at very low temperatures. This is further confirmed by the measurements on ground powder sample orc-axis pressed single crystals, which prohibits the formation of the non-magnetic state. Moreover, the intrinsic magnetic susceptibility also tends to be constant with decreasing temperature. Our results suggest that Nb3Cl8with the high-temperature structure may host a quantum-spin-liquid ground state with spinon Fermi surfaces, which can be achieved by making the thickness of a sample smaller than a certain threshold.

Topological Flat Bands in 2D Breathing-Kagome Lattice Nb3 TeCl7

Flat bands (FBs) can appear in two-dimensional (2D) geometrically frustrated systems caused by quantum destructive interference (QDI). However, the scarcity of pure 2D frustrated crystal structures in natural materials makes FBs hard to be identified, let alone modulate FBs relating to electronic properties. Here, the experimental evidence of the complete electronic QDI induced FB contributed by the 2D breathing-kagome layers of Nb atoms in Nb3 TeCl7 (NTC) is reported. An identical chemical state and 2D localization characteristics of the Nb breathing-kagome layers are experimentally confirmed, based on which NTC is demonstrated to be a superior concrete candidate for the breathing-kagome tight-binding model. Furthermore, it theoretically establishes the tunable roles of the on-site energy over Nb sites on bandwidth, energy position, and topology of FBs in NTC. This work opens an aveanue to manipulate FB characteristics in these 4d transition-metal-based breathing-kagome materials.

Terahertz Spectroscopy and DFT Analysis of Phonon Dynamics of the Layered Van der Waals Semiconductor Nb3 X 8 (X = Cl, I)

We have conducted a terahertz spectroscopic study and a density functional theory analysis of the phonon dynamics of the layered van der Waals semiconductors Nb₃Cl₈ and Nb₃I₈. Several infrared-active phonon modes were observed in the terahertz region, and their frequencies were found to be in excellent agreement with our first-principles lattice dynamics calculations. For Nb₃Cl₈, the observed phonon spectra are consistent with a structural transition at 90 K from the high-temperature P3̅m1 phase to the low-temperature R3̅m phase. Also, our study confirmed that the structural and magnetic transitions were coupled in Nb₃Cl₈. For Nb₃I₈, which is nonmagnetic at and below room temperature, no significant temperature or magnetic field dependence was observed in the phonon spectra. Our study provides an intriguing connection between the structural properties and the paramagnetic-nonmagnetic transitions in Nb₃Cl₈ and Nb₃I₈.

Observation of Topological Flat Bands in the Kagome Semiconductor Nb3Cl8

The destructive interference of wavefunctions in a kagome lattice can give rise to topological flat bands (TFBs) with a highly degenerate state of electrons. Recently, TFBs have been observed in several kagome metals, including Fe₃Sn₂, FeSn, CoSn, and YMn₆Sn₆. Nonetheless, kagome materials that are both exfoliable and semiconducting are lacking, which seriously hinders their device applications. Herein, we show that Nb₃Cl₈, which hosts a breathing kagome lattice, is gapped out because of the absence of inversion symmetry, while the TFBs survive because of the protection of the mirror reflection symmetry. By angle-resolved photoemission spectroscopy measurements and first-principles calculations, we directly observe the TFBs and a moderate band gap in Nb₃Cl₈. By mechanical exfoliation, we successfully obtain monolayer Nb₃Cl₈, which is stable under ambient conditions. In addition, our calculations show that monolayer Nb₃Cl₈ has a magnetic ground state, thus providing opportunities to study the interplay among geometry, topology, and magnetism.

The field-free Josephson diode in a van der Waals heterostructure

The superconducting analogue to the semiconducting diode, the Josephson diode, has long been sought with multiple avenues to realization being proposed by theorists^1-3. Showing magnetic-field-free, single-directional superconductivity with Josephson coupling, it would serve as the building block for next-generation superconducting circuit technology. Here we realized the Josephson diode by fabricating an inversion symmetry breaking van der Waals heterostructure of NbSe₂/Nb₃Br₈/NbSe₂. We demonstrate that even without a magnetic field, the junction can be superconducting with a positive current while being resistive with a negative current. The ΔI_c behaviour (the difference between positive and negative critical currents) with magnetic field is symmetric and Josephson coupling is proved through the Fraunhofer pattern. Also, stable half-wave rectification of a square-wave excitation was achieved with a very low switching current density, high rectification ratio and high robustness. This non-reciprocal behaviour strongly violates the known Josephson relations and opens the door to discover new mechanisms and physical phenomena through integration of quantum materials with Josephson junctions, and provides new avenues for superconducting quantum devices.

Twisting of 2D Kagomé Sheets in Layered Intermetallics

Chemical bonding in 2D layered materials and van der Waals solids is central to understanding and harnessing their unique electronic, magnetic, optical, thermal, and superconducting properties. Here, we report the discovery of spontaneous, bidirectional, bilayer twisting (twist angle ∼4.5°) in the metallic kagomé MgCo₆Ge₆ at T = 100(2) K via X-ray diffraction measurements, enabled by the preparation of single crystals by the Laser Bridgman method. Despite the appearance of static twisting on cooling from T ∼300 to 100 K, no evidence for a phase transition was found in physical property measurements. Combined with the presence of an Einstein phonon mode contribution in the specific heat, this implies that the twisting exists at all temperatures but is thermally fluctuating at room temperature. Crystal Orbital Hamilton Population analysis demonstrates that the cooperative twisting between layers stabilizes the Co-kagomé network when coupled to strongly bonded and rigid (Ge₂) dimers that connect adjacent layers. Further modeling of the displacive disorder in the crystal structure shows the presence of a second, Mg-deficient, stacking sequence. This alternative stacking sequence also exhibits interlayer twisting, but with a different pattern, consistent with the change in electron count due to the removal of Mg. Magnetization, resistivity, and low-temperature specific heat measurements are all consistent with a Pauli paramagnetic, strongly correlated metal. Our results provide crucial insight into how chemical concepts lead to interesting electronic structures and behaviors in layered materials.

Chemistry of Quantum Spin Liquids

Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection of solid-state chemistry, condensed matter physics, and materials science and engineering. In this review, we provide the current status of the crystal chemistry, synthetic techniques, physical properties, and research methods in the field of quantum spin liquids. We highlight a number of specific quantum spin liquid candidate materials and their structure-property relationships, elucidating their fascinating behavior and connecting it to the intricacies of their structures. Furthermore, we share our thoughts on defects and their inevitable presence in materials, of which quantum spin liquids are no exception, which can complicate the interpretation of characterization of these materials, and urge the community to extend their attention to materials preparation and data analysis, cognizant of the impact of defects. This review was written with the intention of providing guidance on improving the materials design and growth of quantum spin liquids, and to paint a picture of the beauty of the underlying chemistry of this exciting class of materials.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

Anomalous thickness-dependent electrical conductivity in van der Waals layered transition metal halide, Nb3Cl8

Understanding the electronic transport properties of layered, van der Waals transition metal halides (TMHs) and chalcogenides is a highly active research topic today. Of particular interest is the evolution of those properties with changing thickness as the 2D limit is approached. Here, we present the electrical conductivity of exfoliated single crystals of the TMH, cluster magnet, Nb₃Cl₈, over a wide range of thicknesses both with and without hexagonal boron nitride (hBN) encapsulation. The conductivity is found to increase by more than three orders of magnitude when the thickness is decreased from 280 µm to 5 nm, at 300 K. At low temperatures and below ∼50 nm, the conductance becomes thickness independent, implying surface conduction is dominating. Temperature dependent conductivity measurements indicate Nb₃Cl₈ is an insulator, however, the effective activation energy decreases from a bulk value of 310 meV to 140 meV by 5 nm. X-ray photoelectron spectroscopy (XPS) shows mild surface oxidation in devices without hBN capping, however, no significant difference in transport is observed when compared to the capped devices, implying the thickness dependent transport behavior is intrinsic to the material. A conduction mechanism comprised of a higher conductivity surface channel in parallel with a lower conductivity interlayer channel is discussed.

Nonpolar-to-Polar Trimerization Transitions in the S = 1 Kagomé Magnet Na2Ti3Cl8

Kagomé lattice magnets have emerged as a versatile platform on which to discover and explore the underlying physics of quantum-spin liquids and related states of matter, although experimental examples of ideal kagomé lattices remain rare. Here we report that Na₂Ti₃Cl₈ is an ideal realization of an insulating S = 1 kagomé magnet. This material undergoes a discrete two-step trimerization upon cooling, transforming from a centrosymmetric, paramagnetic high-temperature (HT) R3m phase to noncentrosymmetric, polar, and trimerized intermediate- (IT) and low-temperature (LT) R3m phases via two successive first-order phase transitions. Symmetry mode decomposition analysis shows that trimerization requires activation of the proper polar order parameter Γ₂^- and that this mode becomes active at the HT → IT phase transition. The magnitude of this order parameter approximately doubles at the IT → LT transition, with possible activation of a second polar mode, corresponding to Na₂ and Ti₃Cl₈ displacing layers toward each other, at the IT → LT transition. Specific heat measurements reveal comparable changes in entropy between the LT → IT transition, 18.6(1.0) J (mol of f.u.)^-1 K^-1, and the IT → LT transition, 16.8(1.0) J (mol of f.u.)^-1 K^-1, demonstrating loss of the magnetic degrees of freedom and constraining possible models for the magnetic and electronic structures of the IT and LT phases. Thus, Na₂Ti₃Cl₈ demonstrates a novel mechanism to obtain polar structures driven by geometrically frustrated lattices and metal-metal bonding and highlights the rich physics arising from kagomé lattice materials.

Tunable Magnetic Transition to a Singlet Ground State in a 2D van der Waals Layered Trimerized Kagomé Magnet

Incorporating magnetism into two-dimensional (2D) van der Waals (vdW) heterostructures is crucial for the development of functional electronic and magnetic devices. Here, we show that Nb₃X₈ (X = Cl, Br) is a family of 2D layered trimerized kagomé magnets that are paramagnetic at high temperatures and undergo a first-order phase transition on cooling to a singlet magnetic state. X-ray diffraction shows that a rearrangement of the vdW stacking accompanies the magnetic transition, with high- and low-temperature phases consistent with scanning transmission electron microscopy images of the end members α-Nb₃Cl₈ and β-Nb₃Br₈. The temperature of this transition is systematically varied across the solid solution Nb₃Cl_8-xBr_x (x = 0-8), with x = 6 having transitions near room temperature. The solid solution also varies the optical properties, which are further modulated by the phase transition. As such, they provide a platform on which to understand and exploit the interplay between dimensionality, magnetism, and optoelectronic behavior in vdW materials.