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Imperfections in measurements, e.g., deviations and broadening, are not devoid of information; rather, they can reveal valuable physical properties and processes. Scanning tunneling microscopy leverages a negative feedback loop to regulate the tunneling current. Practically, current fluctuates around its set point, and such deviations are considered insignificant and ignored. Here, we investigate the information embedded in these deviations. In the constant-current mode with an active feedback loop, we observe an unexpected persistent DC current offset from its set point when the tunneling junction is periodically perturbed. We demonstrate both experimentally and theoretically that such error signals encode local tunneling barrier heights and the square of local differential conductance as a consequence of the interplay between rectification and active feedback compensation. We provide evidence on the generalizability of this phenomenology to other negative feedback systems. This new approach has the potential to broadly impact physical sciences by allowing rapid measurements without lock-in amplifiers.

Broken time-reversal symmetry in the absence of spin order indicates the presence of unusual phases such as orbital magnetism and loop currents1–4. The recently discovered kagome superconductors AV3Sb5(where A is K, Rb or Cs)5,6display an exotic charge-density-wave (CDW) state and have emerged as a strong candidate for materials hosting a loop current phase. The idea that the CDW breaks time-reversal symmetry7–14is, however, being intensely debated due to conflicting experimental data15–17. Here we use laser-coupled scanning tunnelling microscopy to study RbV3Sb5. By applying linearly polarized light along high-symmetry directions, we show that the relative intensities of the CDW peaks can be reversibly switched, implying a substantial electro-striction response, indicative of strong nonlinear electron–phonon coupling. A similar CDW intensity switching is observed with perpendicular magnetic fields, which implies an unusual piezo-magnetic response that, in turn, requires time-reversal symmetry breaking. We show that the simplest CDW that satisfies these constraints is an out-of-phase combination of bond charge order and loop currents that we dub a congruent CDW flux phase. Our laser scanning tunnelling microscopy data open the door to the possibility of dynamic optical control of complex quantum phenomenon in correlated materials.

Layered crystalline materials that consist of transition metal atoms on a kagome network have emerged as a versatile platform for the study of unusual electronic phenomena. For example, in the vanadium-based kagome superconductors AV3Sb5(where Acan stand for K, Cs or Rb), there is a parent charge density wave phase that appears to simultaneously break both the translational and rotational symmetries of the lattice. Here we show a contrasting situation, where electronic nematic order—the breaking of rotational symmetry without the breaking of translational symmetry—can occur without a corresponding charge density wave. We use spectroscopic-imaging scanning tunnelling microscopy to study the kagome metal CsTi3Bi5that is isostructural to AV3Sb5but with a titanium atom kagome network. CsTi3Bi5does not exhibit any detectable charge density wave state, but a comparison to density functional theory calculations reveals substantial electronic correlation effects at low energies. In comparing the amplitudes of scattering wave vectors along different directions, we discover an electronic anisotropy that breaks the sixfold symmetry of the lattice, arising from both in-plane and out-of-plane titanium-derived dorbitals. Our work uncovers the role of electronic orbitals in CsTi3Bi5, suggestive of a hexagonal analogue of the nematic bond order in Fe-based superconductors.

Controlling properties within a given functional inorganic material structure type is often accomplished through tuning the electronic occupation, which is in turn dictated by the elemental composition determined at the time of material preparation. We employ electrochemical control of the lithium content, with associated electronic occupancy control, to vary the magnetic properties of a material where a kagome-derived network of Mo3triangles carry the spin. In this case, Li is electrochemically inserted into LiScMo3O8, a layered compound containing a breathing Mo kagome network. Up to two additional Li can be inserted into LiScMo3O8, transforming it into Li3ScMo3O8. Li2ScMo3O8prepared by electrochemical lithiation is compared to the quantum spin liquid candidate compound Li2ScMo3O8prepared through high-temperature solid-state methods, which has a slightly different structural stacking sequence but a similar kagome-derived network. Magnetic measurements are supported by first-principles calculations, showing that electrons remain localized on the Mo clusters throughout the doping series. As xis varied in LixScMo3O8, the measurements and calculations reveal the evolution from a diamagnetic band insulator at x= 1 to a geometrically frustrated magnet at x= 2, back to a diamagnetic insulator at x= 3. These results indicate a likelihood of strong coupling between the degree of Li disorder and charge/magnetic ordering over the Mo3clusters.

It has long been hoped that spin liquid states might be observed in materials that realize the triangular-lattice Hubbard model. However, weak spin–orbit coupling and other small perturbations often induce conventional spin freezing or magnetic ordering. Sufficiently strong spin–orbit coupling, however, can renormalize the electronic wavefunction and induce anisotropic exchange interactions that promote magnetic frustration. Here we show that the cooperative interplay of spin–orbit coupling and correlation effects in the triangular-lattice magnet NaRuO2produces an inherently fluctuating magnetic ground state. Despite the presence of a charge gap, we find that low-temperature spin excitations generate a metal-like term in the specific heat and a continuum of excitations in neutron scattering, reminiscent of spin liquid states previously found in triangular-lattice organic magnets. Further cooling produces a crossover into a different, highly disordered spin state whose dynamic spin autocorrelation function reflects persistent fluctuations. These findings establish NaRuO2as a cousin to organic, Heisenberg spin liquid compounds with a low-temperature crossover in quantum disorder.

Kagome metals AV3Sb51(where the Acan stand for K, Cs or Rb) display a rich phase diagram of correlated electron states, including superconductivity2–4and density waves5–7. Within this landscape, recent experiments have revealed signs of a transition below approximately 35 K attributed to an electronic nematic phase that spontaneously breaks the rotational symmetry of the lattice8. Here we show that the rotational symmetry breaking initiates universally at a high temperature in these materials, towards the 2 × 2 charge density wave transition temperature. We do this via spectroscopic-imaging scanning tunnelling microscopy and study the atomic-scale signatures of the electronic symmetry breaking across several materials in the AV3Sb5family: CsV3Sb5, KV3Sb5and Sn-doped CsV3Sb5. Below a substantially lower temperature of about 30 K, we measure the quantum interference of quasiparticles, a key signature for the formation of a coherent electronic state. These quasiparticles display a pronounced unidirectional feature in reciprocal space that strengthens as the superconducting state is approached. Our experiments reveal that high-temperature rotation symmetry breaking and the charge ordering states are separated from the superconducting ground state by an intermediate-temperature regime with coherent unidirectional quasiparticles. This picture is phenomenologically different compared to that in high-temperature superconductors, shedding light on the complex nature of rotation symmetry breaking in AV3Sb5kagome superconductors.

In the kagome metals AV3Sb5(A = K, Rb, Cs), three-dimensional charge order is the primary instability that sets the stage for other collective orders to emerge, including unidirectional stripe order, orbital flux order, electronic nematicity and superconductivity. Here, we use high-resolution angle-resolved photoemission spectroscopy to determine the microscopic structure of three-dimensional charge order in AV3Sb5and its interplay with superconductivity. Our approach is based on identifying an unusual splitting of kagome bands induced by three-dimensional charge order, which provides a sensitive way to refine the spatial charge patterns in neighbouring kagome planes. We found a marked dependence of the three-dimensional charge order structure on composition and doping. The observed difference between CsV3Sb5and the other compounds potentially underpins the double-dome superconductivity in CsV3(Sb,Sn)5and the suppression of Tcin KV3Sb5and RbV3Sb5. Our results provide fresh insights into the rich phase diagram of AV3Sb5.

The kagomé metals RbTi3Bi5and CsTi3Bi5were synthesized both as polycrystalline powders by heating the elements in an argon atmosphere and as single crystals grown using a self-flux method. The compounds crystallize in the hexagonal crystal system isotypically to KV3Sb5(P6/mmm, Z= 1, CsTi3Bi5: a= 5.7873(1), c= 9.2062(1) Å; RbTi3Bi5: a= 5.773(1), c= 9.065(1) Å). The titanium atoms form a kagomé net with bismuth atoms in the hexagons as well as above and below the triangles. The alkali metal atoms are coordinated by 12 bismuth atoms and form AlB2-like slabs between the kagomé layers. Magnetic susceptibility measurements with CsTi3Bi5and RbTi3Bi5single crystals reveal Pauli-paramagnetism and traces of superconductivity caused by CsBi2/RbBi2impurities. Magnetotransport measurements reveal conventional Fermi liquid behavior and quantum oscillations indicative of a single dominant orbit at low temperature. DFT calculations show the characteristic metallic kagomé band structure similar to that of CsV3Sb5with reduced band filling. A symmetry analysis of the band structure does not reveal an obvious and unique signature of a nontrivial topology.

Recently discovered superconductors AV3Sb5(A= K, Rb, Cs)1,2provide a fresh opportunity to study correlation-driven electronic phenomena on a kagome lattice. The observation of an unusual charge density wave (CDW) in the normal state of all the members of the AV3Sb5family2–10has prompted a large effort to identify any ‘hidden’ broken symmetries associated with it. We use spectroscopic-imaging scanning tunnelling microscopy to reveal pronounced intensity anisotropy between the different directions of hexagonal CDW in KV3Sb5. In particular, we find that one of the CDW directions is distinctly different compared with the other two. This observation points to an intrinsic rotation-symmetry-broken electronic ground state where the symmetry is reduced from sixfold to twofold. Furthermore, in contrast to previous reports3, we find that the CDW phase is insensitive to the magnetic-field direction, regardless of the presence or absence of atomic defects. Our experiments, combined with earlier observations of stripe charge ordering in CsV3Sb5, establish correlation-driven rotation symmetry breaking as a unifying feature of AV3Sb5kagome superconductors.

The layered vanadium antimonides AV3Sb5(A = K, Rb, Cs) are a recently discovered family of topological kagome metals that exhibit a range of strongly correlated electronic phases including charge order and superconductivity. However, it is not yet understood how the distinctive electronic structure of the kagome lattice is linked to the observed many-body phenomena. Here we combine angle-resolved photoemission spectroscopy and density functional theory to reveal multiple kagome-derived van Hove singularities (vHS) coexisting near the Fermi level of CsV3Sb5and analyse their contribution to electronic symmetry breaking. The vHS are characterized by two distinct sublattice flavours (p-type and m-type), which originate, respectively, from their pure and mixed sublattice characters. These twofold vHS flavours of the kagome lattice critically determine the pairing symmetry and unconventional ground states emerging in the AV3Sb5series. We establish that, among the multiple vHS in CsV3Sb5, the m-type vHS of the dxz/dyzkagome band and the p-type vHS of the dxy/dx2–y2kagome band are located very close to the Fermi level, setting the stage for electronic symmetry breaking. The former band is characterized by pronounced Fermi surface nesting, while the latter exhibits a higher-order vHS. Our work reveals the essential role of kagome-derived vHS for the collective phenomena realized in the AV3Sb5family.

The kagome lattice provides a fascinating playground to study geometrical frustration, topology and strong correlations. The newly discovered kagome metals AV3Sb5(where A can refer to K, Rb or Cs) exhibit phenomena including topological band structure, symmetry-breaking charge-density waves and superconductivity. Nevertheless, the nature of the symmetry breaking in the charge-density wave phase is not yet clear, despite the fact that it is crucial in order to understand whether the superconductivity is unconventional. In this work, we perform scanning birefringence microscopy on all three members of this family and find that six-fold rotation symmetry is broken at the onset of the charge-density wave transition in all these compounds. We show that the three nematic domains are oriented at 120° to each other and propose that staggered charge-density wave orders with a relative π phase shift between layers is a possibility that can explain these observations. We also perform magneto-optical Kerr effect and circular dichroism measurements. The onset of both signals is at the transition temperature, indicating broken time-reversal symmetry and the existence of the long-sought loop currents in that phase.

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1–18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc~ 2.5 K, a tri-directional charge order with a 2a0period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tcsuperconductors and twisted bilayer graphene.

Intertwining quantum order and non-trivial topology is at the frontier of condensed matter physics1–4. A charge-density-wave-like order with orbital currents has been proposed for achieving the quantum anomalous Hall effect5,6in topological materials and for the hidden phase in cuprate high-temperature superconductors7,8. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy to discover an unconventional chiral charge order in a kagome material, KV3Sb5, with both a topological band structure and a superconducting ground state. Through both topography and spectroscopic imaging, we observe a robust 2 × 2 superlattice. Spectroscopically, an energy gap opens at the Fermi level, across which the 2 × 2 charge modulation exhibits an intensity reversal in real space, signalling charge ordering. At the impurity-pinning-free region, the strength of intrinsic charge modulations further exhibits chiral anisotropy with unusual magnetic field response. Theoretical analysis of our experiments suggests a tantalizing unconventional chiral charge density wave in the frustrated kagome lattice, which can not only lead to a large anomalous Hall effect with orbital magnetism, but also be a precursor of unconventional superconductivity.

Cleavable metallic antiferromagnets may be of use for low-dissipation spintronic devices; however, few are currently known. Here we present orthorhombic MnRhBi3as one such compound and present a thorough study of its physical properties. Exfoliation is demonstrated experimentally, and the cleavage energy and electronic structure are examined by density functional theory calculations. It is concluded that MnRhBi3is a van der Waals-layered material that cleaves easily between neighboring Bi layers and that the Bi atoms have lone pairs extending into the van der Waals gaps. A series of four phase transitions are observed below room temperature, and neutron diffraction shows that at least two of the transitions involve the formation of antiferromagnetic order. Anomalous thermal expansion points to a crystallographic phase transition and/or strong magnetoelastic coupling. This work reveals a complex phase evolution in MnRhBi3and establishes this cleavable antiferromagnetic metal as an interesting material for studying the interplay of structure, magnetism, and transport in the bulk and ultrathin limits, as well as the role of lone pair electrons in interface chemistry and proximity effects in van der Waals heterostructures.

Here we present the discovery and characterization of the kagome metal TbTi3Bi4in tandem with a new series of compounds, the Ln2–xTi6+xBi9(Ln: Tb–Lu) shurikagome metals. We previously reported on the growth of the LnTi3Bi4(Ln: La–Gd3+, Eu2+, Yb2+) family, a chemically diverse and exfoliable series of kagome metals with complex and highly anisotropic magnetism. However, unlike the La–Gd analogs, TbTi3Bi4cannot be synthesized by our previous methodology due to phase competition with crystals of Ln2–xTi6+xBi9(x∼ 1.7–1.2). Here we discuss the phase competition between the LnTi3Bi4and Ln2–xTi6+xBi9families, helping to frame the difficulty in synthesizing LnTi3Bi4compounds with small Ln species and providing a strategy to circumvent the formation of Ln2–xTi6+xBi9. Detailed characterization of the magnetic and electronic transport properties on single crystals of TbTi3Bi4reveals a highly complex landscape of magnetic phases arising from an antiferromagnetic ground state. A series of metamagnetic transitions creates at least 5 unique magnetic phase pockets, including a 1/3 and 2/3 magnetization plateau. Further, the system exhibits an intimate connection between the magnetism and magnetotransport, exhibiting sharp switching from positive (+40%) to negative magnetoresistance (−50%). Like the LnTi3Bi4kagome metals, the Ln2–xTi6+xBi9family exhibits quasi-2D networks of titanium and chains of rare earth. We present the structures and some basic magnetic properties of the Ln2–xTi6+xBi9family alongside our characterization of the newly discovered TbTi3Bi4.

Emerging photovoltaic materials need to prove their viability by demonstrating excellent electronic properties. In ternary and multinary semiconductors, disorder and off-stoichiometry often cause defects that limit the potential for high-efficiency solar cells. Here we report on Zn-rich ZnSnN2(Zn/(Zn + Sn) = 0.67) photoluminescence, high-resolution X-ray diffraction, and electronic structure calculations based on Monte-Carlo structural models. The mutual compensation of Zn excess and O incorporation affords a desirable reduction of the otherwise degenerate n-type doping, but also leads to a strongly off-stoichiometric and disordered atomic structure. It is therefore remarkable that we observe only near-edge photoluminescence from well-resolved excitons and shallow donors and acceptors. Based on first principles calculations, this result is explained by the mutual passivation of ZnSnand ONdefects that renders both electronically benign. The calculated bandgaps range between 1.4 and 1.8 eV, depending on the degree of non-equilibrium disorder. The experimentally determined value of 1.5 eV in post-deposition annealed samples falls within this interval, indicating that further bandgap engineering by disorder control should be feasible viaappropriate annealing protocols.

Recent discoveries of materials with ultralow thermal conductivity open a pathway to significant developments in the field of thermoelectricity. Here, we conduct a comparative study of three chemically similar antimonides to establish the root causes of their extraordinarily low thermal conductivity (0.4–0.6 W m–1K–1at 525 K). The materials of interest are the unconventional type-XI clathrate K58Zn122Sb207, the tunnel compound K6.9Zn21Sb16, and the type-I clathrate K8Zn15.5Cu2.5Sb28discovered herein. Calculations of the phonon dispersions show that the type-XI compound exhibits localized (i.e., rattling) phonon modes with unusually low frequencies that span the entire acoustic regime. In contrast, rattling in type I clathrate is observed only at higher frequencies, and no rattling modes are present in the tunnel structure. Modeling reveals that low-frequency rattling modes profoundly limit the acoustic scattering time; the scattering time of the type-XI clathrate is half that of the type-I clathrate and a quarter of that of the tunnel compound. For all three materials, the thermal conductivities are additionally suppressed by soft framework bonding that lowers the acoustic group velocities and structural complexity that leads to diffusonic character of the optical modes. Understanding the details of thermal transport in structurally complex materials will be crucial for developing the next generation of thermoelectrics.

Here, we present a family of titanium-based kagome metals of the form LnTi3Bi4(Ln: La···Gd3+, Eu2+, Yb2+). Four previously unreported compounds are presented: YbTi3Bi4, GdTi3Bi4, NdTi3Bi4, and PrTi3Bi4. Single-crystal growth methods are provided alongside detailed magnetic and thermodynamic measurements across the entire series. The LnTi3Bi4family of compounds are orthorhombic (Fmmm), layered compounds that exhibit slightly distorted titanium-based kagome nets interwoven with zigzag lanthanide-based (Ln) chains. Crystals are easily exfoliated parallel to the kagome sheets, and angular resolved photoemission (ARPES) measurements highlight the intricacy of the electronic structure in these compounds. Density functional theory (DFT) and ARPES studies find Dirac points near the Fermi level, consistent with the kagome-derived band structure. The magnetic properties and the associated anisotropy emerge from the quasi-1D zigzag chains of Ln and impart a wide array of magnetic ground states ranging from anisotropic ferromagnetism to complex antiferromagnetism with a cascade of metamagnetic transitions. The combination of the kagome-based electronic structure and highly anisotropic Ln-based magnetism on an exfoliatable platform cements the LnTi3Bi4family as an interesting addition to the ever-expanding suite of kagome metals.

A major technological challenge in photovoltaics is the implementation of a lattice matched optically efficient material to be used in conjunction with silicon for tandem photovoltaics. Detailed balance calculations predict an increase in efficiency of up to 12 percentage points for a tandem cell compared with single junction silicon. Given that the III-V materials currently hold world record efficiencies, both for single and multijunction cells, it would be transformative to develop a material that has similar properties to the III-V's which is also lattice matched to silicon. The II-IV-V2 chalcopyrites are a promising class of materials that could satisfy these criteria. ZnSiP2 in particular is known to have a bandgap of ~2 eV, a lattice mismatch with silicon of 0.5%, and is earth abundant. Its direct bandgap is symmetry-forbidden. We have grown single crystals of ZnSiP2 by a flux growth technique. Structure and phase purity have been confirmed by X-ray diffraction and transmission electron microscopy. Optical measurements, along with a calculation of the absorption spectrum, confirm the ~2 eV bandgap. Because of its structural similarity to both crystalline silicon and the III-V's, ZnSiP2 is expected to have good optoelectronic performance.

The recently discovered kagome metal series AV3Sb5(A=K, Rb, Cs) exhibits topologically nontrivial band structures, chiral charge order and superconductivity, presenting a unique platform for realizing exotic electronic states. The nature of the superconducting state and the corresponding pairing symmetry are key questions that demand experimental clarification. Here, using a technique based on the tunneling diode oscillator, the magnetic penetration depth Δλ(T) of CsV3Sb5was measured down to 0.07 K. A clear exponential behavior in Δλ(T) with marked deviations from a Tor T2temperature dependence was observed at low temperatures, indicating an absence of nodal quasiparticles. Temperature dependence of the superfluid density and electronic specific heat can be described by two-gap s-wave superconductivity, consistent with the presence of multiple Fermi surfaces in CsV3Sb5. These results evidence nodeless superconductivity in CsV3Sb5under ambient pressure, and constrain the allowed pairing symmetry.