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The natural van der Waals heterostructure 4H$_b$-TaS$_2$ composed of alternating 1T- and 1H-TaS$_2$ layers serves as a platform for investigating the electronic correlations and layer-dependent properties of novel quantum materials. The temperature evolution of the conductivity spectra $\sigma(\omega)$ obtained through infrared spectroscopy elucidates the influence of band modifications associated with the charge-density-wave (CDW) superlattice on the 1T layer, resulting in a room-temperature energy gap, $\Delta_{\rm CDW}\approx$ 0.35 eV. However, there is no gap associated to the 1H layer. Supported by density functional theory calculations, we attribute the behavior of interband transitions to the convergence of the layers, which amplifies the charge transfer from the 1T to the 1H layers, progressing as the temperature decreases. This phenomenon leads to an enhanced low-energy spectral weight and carrier density. The presence of an energy gap and the temperature-tunable charge transfer within the bulk of 4H$_b$-TaS$_2$ driven by layer-dependent CDW states contribute to a more comprehensive understanding of other complex compounds of transition-metal dichalcogenides., Comment: 11 pages including SM

The insulating mixed-valent Ir$^{+3.66}$ compound Ba$_4$NbIr$_3$O$_{12}$ hosts two holes per Ir$_3$O$_{12}$ trimer unit. We address the electronic structure via resonant inelastic x-ray scattering (RIXS) at the Ir $L_3$ edge and exact diagonalization. The holes occupy quasimolecular orbitals that are delocalized over a trimer. This gives rise to a rich intra-$t_{2g}$ excitation spectrum that extends from 0.5 eV to energies larger than 2 eV. Furthermore, it yields a strong modulation of the RIXS intensity as a function of the transferred momentum q. A clear fingerprint of the quasimolecular trimer character is the observation of two modulation periods, $2\pi/d$ and $2\pi/2d$, where d and 2d denote the intratrimer Ir-Ir distances. We discuss how the specific modulation reflects the character of the wavefunction of an excited state. Our quantitative analysis shows that spin-orbit coupling $\lambda$ of about 0.4 eV is decisive for the character of the electronic states, despite a large hopping $t_{a_{1g}}$ of about 0.8 eV. The ground state of a single trimer is described very well by both holes occupying the bonding j=1/2 orbital, forming a vanishing quasimolecular moment with J=0., Comment: 19 pages, 13 figures

Kagome materials manifest rich physical properties due to the emergence of abundant electronic phases. Here, we carry out a high-throughput first-principles study of the kagome 1:6:6 family MT$_6$Z$_6$ materials in space group 191, focusing on their phonon instability and electronic flat bands. Different MT$_6$Z$_6$ kagome candidates reveal a remarkable variety of kagome flat bands ranging from unfilled, partially filled, to fully filled. Notably, the Mn/Fe-166 compounds exhibit partially filled flat bands with a pronounced sharp peak in the density of states near the Fermi level, leading to magnetic orders that polarize the bands and stabilize the otherwise unstable phonon. When the flat bands are located away from the Fermi level, we find a large number of phonon instabilities, which can be classified into three types, based on the phonon dispersion and vibrational modes. Type-I instabilities involve the in-plane distortion of kagome nets, while type-II and type-III present out-of-plane distortion of trigonal M and Z atoms. We take MgNi$_6$Ge$_6$ and HfNi$_6$In$_6$ as examples to illustrate the possible CDW structures derived from the emergent type-I and type-II instabilities. The type-I instability in MgNi$_6$Ge$_6$ suggests a nematic phase transition, governed by the local twisting of kagome nets. The type-II instability in HfNi$_6$In$_6$ may result in a hexagonal-to-orthorhombic transition, offering insight into the formation of MT$_6$Z$_6$ in other space groups. Additionally, the predicted ScNb$_6$Sn$_6$ is analyzed as an example of the type-III instability. Our predictions suggest a vast kagome family with rich properties induced by the flat bands, possible CDW transitions, and their interplay with magnetism., Comment: 14 pages, 7 figures, with 1000 pages of additional supplemental materials

Electronic ordering is prevalent in correlated systems, which commonly exhibit competing interactions. Here, we use x-ray diffraction to show that the charge density wave transition temperature of FeGe increases with pressure and evolves towards a $\sqrt{3}\times\sqrt{3}$ periodic lattice modulation, $\mathbf{q}$$^*$=$\left(\frac{1}{3}\ \frac{1}{3}\ \frac{1}{2}\right)$. In the pressure interval between 4$<$$p$$<$12 GPa both orders coexist and the spatial extent of the $\sqrt{3}\times\sqrt{3}$ order at high pressure becomes nearly long-range, $\sim$30 unit cells, while the correlation length of the 2$\times$2 phase remains shorter-ranged. The $\sqrt{3}\times\sqrt{3}$ phase is the ground state above 15 GPa, consistent with harmonic DFT calculations that predict a dimerization induced $\sqrt{3}\times\sqrt{3}$ order without phonon softening. The pressure dependence of the integrated intensities of $\mathbf{q}$$_\mathrm{CDW}=\left(\frac{1}{2}\ 0\ \frac{1}{2}\right)$ and $\mathbf{q}$$^*$ indicates a competition between the 2$\times$2 and $\sqrt{3}\times\sqrt{3}$ and demonstrates that the ground state of FeGe is characterized by a rich landscape of metastable/fragile phases. We discuss possible scenarios based on an order-disorder transformation and the formation of Friedel oscillations.

The intrinsic frustrated nature of a kagome lattice is amenable to the realization of exotic phases of matter, such as quantum spin liquids or spin ices, and more recently the multiple-$\mathrm{\textbf{q}}$ charge density waves (CDW) in the kagome metals. Despite intense efforts to understand the mechanism driving the electronic modulations, its origin is still unknown and hindered by competing interactions and intertwined orders. Here, we identify a dimerization-driven 2D hexagonal charge-diffuse precursor in the antiferromagnetic kagome metal FeGe and demonstrate that the fraction of dimerized/undimerized states is the relevant order parameter of the multiple-$\mathrm{\textbf{q}}$ CDW of a continuous phase transition. The pretransitional charge fluctuations with propagation vector $\mathrm{\textbf{q}=\textbf{q}_M}$ at T$_{\mathrm{CDW}}$$<$T$<$T$^*$(125 K) are anisotropic, hence holding a quasi-long-range bond-orientational order. The broken translational symmetry emerges from the anisotropic diffuse precursor, akin to the Ising scenario of antiferromagnetic triangular lattices. The temperature and momentum dependence of the critical scattering show parallels to the stacked hexatic $\mathrm{B}$-phases reported in liquid crystals and transient states of CDWs and highlight the key role of the topological defect-mediated melting of the CDW in FeGe.

We analyze the transport properties of curved, three-dimensional graphite samples in strong magnetic fields. Focusing on a millimeter-scale graphite cylinder as a prototypical curved object, we perform longitudinal and Hall voltage measurements while applying quantizing magnetic fields. These measurements are investigated as a function of field strength and angles. Most importantly, we find that angle-dependent Shubnikov-de Hass oscillations are superimposed with angle-independent features. Reproducing the experimental observations, we introduce a network model that accounts for the cylindrical geometry effect by conceptualizing the cylinder as composed of strips of planar graphite in an effectively inhomogeneous magnetic field. Our work highlights how the interplay between geometric curvature and quantizing magnetic fields can be leveraged to engineer tunable spatial current densities within solid-state systems, and paves the way for understanding transport properties of curved and bent three-dimensional samples more generally.

The chiral anomaly, a hallmark of chiral spin-1/2 Weyl fermions, is an imbalance between left- and right-moving particles that underpins both high and low energy phenomena, including particle decay and negative longitudinal magnetoresistance in Weyl semimetals. The discovery that chiral crystals can host higher-spin generalizations of Weyl quasiparticles without high-energy counterparts, known as multifold fermions, raises the fundamental question of whether the chiral anomaly is a more general phenomenon. Answering this question requires materials with chiral quasiparticles within a sizable energy window around the Fermi level, that are unaffected by trivial extrinsic effects such as current jetting. Here we report the chiral anomaly of multifold fermions in CoSi, which features multifold bands within about 0.85 eV around the Fermi level. By excluding current jetting through the squeezing test, we measure an intrinsic, longitudinal negative magnetoresistance. We develop the semiclassical theory of magnetotransport of multifold fermions that shows that the negative magnetoresistance originates in their chiral anomaly, despite a sizable and detrimental orbital magnetic moment contribution, previously unaccounted for. A concomitant nonlinear Hall effect supports the multifold-fermion origin of magnetotransport. Our work confirms the chiral anomaly of higher-spin generalizations of Weyl fermions, currently inaccessible outside the solid-state.

We present a high-resolution single crystal x-ray diffraction study of kagome-superconductor \cvs, exploring its response to variations in pressure and temperature. We discover that at low temperatures, the structural modulations of the electronic superlattice, commonly associated with charge-density-wave order, undergo a transformation around $p \sim$ 0.7 GPa from the familiar $2\times2$ pattern to a long-range-ordered modulation at wavevector $q=(0, 3/8, 1/2)$. Our observations align with inferred changes in the CDW pattern from prior transport and nuclear-magnetic-resonance studies, providing new insights into these transitions. Interestingly, the pressure-induced variations in the electronic superlattice correlate with two peaks in the superconducting transition temperature as pressure changes, hinting that fluctuations within the electronic superlattice could be key to stabilizing superconductivity. However, our findings contrast with the minimal pressure dependency anticipated by ab initio calculations of the electronic structure. They also challenge prevailing scenarios based on a Peierls-like nesting mechanism involving van Hove singularities., Comment: Revised version, to appear in PRL

At ambient pressure, HfTe$_{5}$ is a material at the boundary between a weak and a strong topological phase, which can be tuned by changes in its crystalline structure or by the application of high magnetic fields. It exhibits a Lifshitz transition upon cooling, and three-dimensional (3D) quantum Hall effect (QHE) plateaus can be observed at low temperatures. Here, we have investigated the electrical transport properties of HfTe$_{5}$ under hydrostatic pressure up to 3 GPa. We find a pressure-induced crossover from a semimetallic phase at low pressures to an insulating phase at about 1.5 GPa. Our data suggest the presence of a pressure-induced Lifshitz transition at low temperatures within the insulating phase around 2 GPa. The quasi-3D QHE is confined to the low-pressure region in the semimetallic phase. This reveals the importance of the semimetallic groundstate for the emergence of the QHE in HfTe$_{5}$ and thus favors a scenario based on a low carrier density metal in the quantum limit for the observed signatures of the quasi-quantized 3D QHE.

Oscillations of conductance observed in strong magnetic fields are a striking manifestation of the quantum dynamics of charge carriers in solids. The large charge carrier density in typical metals sets the scale of oscillations in both electrical and thermal conductivity, which characterize the Fermi surface. In semimetals, thermal transport at low-charge carrier density is expected to be phonon dominated, yet several experiments observe giant quantum oscillations in thermal transport. This raises the question of whether there is an overarching mechanism leading to sizable oscillations that survives in phonon-dominated semimetals. In this work, we show that such a mechanism exists. It relies on the peculiar phase-space allowed for phonon scattering by electrons when only a few Landau levels are filled. Our measurements on the Dirac semimetal ZrTe5 support this counter-intuitive mechanism through observation of pronounced thermal quantum oscillations, since they occur in similar magnitude and phase in directions parallel and transverse to the magnetic field. Our phase-space argument applies to all low-density semimetals, topological or not, including graphene and bismuth. Our work illustrates that phonon absorption can be leveraged to reveal degrees of freedom through their imprint on longitudinal thermal transport.

The properties of kagome metals are governed by the interdependence of band topology and electronic correlations resulting in remarkably rich phase diagrams. Here, we study the temperature evolution of the bulk electronic structure of the antiferromagnetic kagome metal FeGe using infrared spectroscopy. We uncover drastic changes in the low-energy interband absorption at the 100 K structural phase transition that has been linked to a charge-density-wave (CDW) instability. We explain this effect by the minuscule Fe displacement in the kagome plane, which results in parallel bands in the vicinity of the Fermi level. In contrast to conventional CDW materials, however, the spectral weight shifts to low energies, ruling out the opening of a CDW gap in FeGe.

The topology of the Fermi surface significantly influences the transport properties of a material. Firstly measured through quantum oscillation experiments, the Fermi surfaces of crystals are now commonly characterized using angle-resolved photoemission spectroscopy (ARPES), given the larger information volume it provides. In the case of Weyl semimetals, ARPES has proven remarkably successful in verifying the existence of the Weyl points and the Fermi arcs, which define a Weyl Fermi surface. However, ARPES is limited in resolution, leading to significant uncertainty when measuring relevant features such as the distance between the Weyl points. While quantum oscillation measurements offer higher resolution, they do not reveal insights into the cross-sectional shape of a Fermi surface. Moreover, both techniques lack critical information about transport, like the carriers mean free path. Here, we report measurements unveiling the distinctive peanut-shaped cross-section of the Fermi surface of Weyl fermions and accurately determine the separation between Weyl points in the Weyl semimetal NbP. To surpass the resolution of ARPES, we combine quantum oscillation measurements with transverse electron focusing (TEF) experiments, conducted on microstructured single-crystals. The TEF spectrum relates to the Fermi surface shape, while the frequency of the quantum oscillations to its area. Together, these techniques offer complementary information, enabling the reconstruction of the distinctive Weyl Fermi surface geometry. Concurrently, we extract the electrical transport properties of the bulk Weyl fermions. Our work showcases the integration of quantum oscillations and transverse electron focusing in a singular experiment, allowing for the measurements of complex Fermi surface geometries in high-mobility quantum materials.

The so-called Transport of Intensity Equation (TIE) phase retrieval technique is widely applied in light, x-ray and electron optics to reconstruct, e.g., refractive indices, electric and magnetic fields in solids. Here, we present a largely improved TIE reconstruction algorithm, which properly considers intensity variations as well as unknown boundary conditions in a finite difference implementation of the Transport of Intensity partial differential equation. That largely removes reconstruction artifacts encountered in state-of-the-art Poisson solvers of the TIE, and hence significantly increases the applicability of the technique.

The magneto-optical properties of (001)-oriented NbAs single crystals have been studied in the spectral range from 5 to 150 meV and in magnetic fields of up to 13 T. A rich spectrum of inter-Landau-level transitions is revealed by these measurements. The transitions follow a square-root-like dependence with magnetic field, but the simple linear-band approximation is unable to accurately reproduce the observed behavior of the transitions in applied fields. We argue that the detected magneto-optical spectra should be related to crossing hyperbolic bands, which form the W1 cones. We propose a model Hamiltonian, which describes coupled hyperbolic bands and reproduces the shape of the relevant bands in NbAs. The magneto-optical spectra computed from this Hamiltonian nicely reproduce our observations. We conclude that the hyperbolic-band approach is a minimal model to adequately describe the magneto-optical response of NbAs and that the chiral (conical) bands do not explicitly manifest themselves in the spectra., Comment: 10 pages, SM included

The family of cubic noncentrosymmetric 3-4-3 compounds has become a fertile ground for the discovery of novel correlated metallic and insulating phases. Here, we report the synthesis of a new heavy fermion compound, Ce$_3$Bi$_4$Ni$_3$. It is an isoelectronic analog of the prototypical Kondo insulator Ce$_3$Bi$_4$Pt$_3$ and of the recently discovered Weyl-Kondo semimetal Ce$_3$Bi$_4$Pd$_3$. In contrast to the volume-preserving Pt-Pd substitution, structural and chemical analyses reveal a positive chemical pressure effect in Ce$_3$Bi$_4$Ni$_3$ relative to its heavier counterparts. Based on the results of electrical resistivity, Hall effect, magnetic susceptibility, and specific heat measurements, we identify an energy gap of 65-70 meV, about eight times larger than that in Ce$_3$Bi$_4$Pt$_3$ and about 45 times larger than that of the Kondo-insulating background hosting the Weyl nodes in Ce$_3$Bi$_4$Pd$_3$. We show that this gap as well as other physical properties do not evolve monotonically with increasing atomic number, i.e., in the sequence Ce$_3$Bi$_4$Ni$_3$-Ce$_3$Bi$_4$Pd$_3$-Ce$_3$Bi$_4$Pt$_3$, but instead with increasing partial electronic density of states of the $d$ orbitals at the Fermi energy. To understand under which condition topological states form in these materials is a topic for future studies., Comment: 28 pages, 11 figures

We measured the magneto-reflectivity spectra (4 - 90 meV, 0 - 16 T) of the triple-point semimetal GdPtBi and found them to demonstrate two unusual broad features emerging in field. The electronic bands of GdPtBi are expected to experience large exchange-mediated shifts, which lends itself to a description via effective Zeeman splittings with a large g factor. Based on this approach, along with an ab initio band structure analysis, we propose a model Hamiltonian that describes our observations well and allows us to estimate the effective g factor, g* = 95. We conclude that we directly observe the exchange-induced $\Gamma_{8}$ band inversion in GdPtBi by means of infrared spectroscopy., Comment: 9 pages, SM included

Appearance of quantum oscillations (QO) in both thermodynamic and transport properties of metals at low temperatures is the most striking experimental consequence of the existence of a Fermi surface (FS). The frequency of these oscillations and the temperature dependence of their amplitude provides essential information about the FS topology and fermionic quasiparticle properties. Here, we report the observation of an anomalous suppression of the QO amplitude seen in resistivity (Shubnikov de-Haas effect) at sub-kelvin temperatures in ZrTe5 samples with a single small FS sheet comprising less than 5% of the first Brillouin zone. By comparing these results with measurements of the magneto-acoustic QO and the recovery of the usual Lifshitz-Kosevich behavior of the Shubnikov de-Haas (SdH) effect in ZrTe$_5$ samples with a multi-sheet FS, we show that the suppression of the SdH effect originates from a decoupling of the electron liquid from the lattice. On crossing the so-called Bloch-Gr\"uneisen temperature, T$_BG$, electron-phonon scattering becomes strongly suppressed and in the absence of Umklapp scattering the electronic liquid regains Galilean invariance. In addition, we show, using a combination of zero-field electrical conductivity and ultrasonic-absorption measurements, that entering this regime leads to an abrupt increase of electronic viscosity.

Half-metallic half-Heusler compounds with strong spin-orbit-coupling and broken inversion symmetry in their crystal structure are promising materials for generating and absorbing spin-currents, thus enabling the electric manipulation of magnetization in energy-efficient spintronic devices. In this work, we report the spin-to-charge conversion in sputtered ultrathin films of the half-Heusler compound MnPtSb with thickness (t) in the range from 1 to 6 nm. A combination of X-ray and transmission electron microscopy measurements evidence the epitaxial nature of these ultrathin non-centrosymmetric MnPtSb films, with a clear (111)-orientation obtained on top of (0001) single-crystal sapphire substrates. The study of the thickness (t)-dependent magnetization dynamics of the MnPtSb(t)/Co(5nm)/Au(5nm) heterostructure revealed that the MnPtSb compound can be used as an efficient spin current generator, even at film thicknesses as low as 1 nm. By making use of spin pumping FMR, we measure a remarkable t-dependent spin-charge conversion in the MnPtSb layers, which clearly demonstrate the interfacial origin of the conversion. When interpreted as arising from the inverse Edelstein effect (IEE), the spin-charge conversion efficiency extracted at room temperature for the thinnest MnPtSb layer reaches {\lambda}IEE~3 nm, representing an extremely high spin-charge conversion efficiency at room temperature. The still never explored ultrathin regime of the MnPtSb films studied in this work and the discover of their outstanding functionality are two ingredients which demonstrate the potentiality of such materials for future applications in spintronics., Comment: main text: 17 pages (with 4 figures), plus additional 8 pages of Supplementary Information

The long range electronic modulations recently discovered in the geometrically frustrated kagome lattice have opened new avenues to explore the effect of correlations in materials with topological electron flat bands. The observation of the lattice response to the emergent new phases of matter, a soft phonon mode, has remained elusive and the microscopic origin of charge density waves (CDWs) is still unknown. Here, we show, for the first time, a complete melting of the ScV$_ 6$Sn$_ 6$ (166) kagome lattice. The low energy phonon with propagation vector $\frac{1}{3} \frac{1}{3} \frac{1}{2}$ collapses at 98 K, without the emergence of long-range charge order, which sets in with a propagation vector $\frac{1}{3} \frac{1}{3} \frac{1}{3}$. The CDW is driven (but locks at a different vector) by the softening of an overdamped phonon flat plane at k$_z$=$\pi$. We observe broad phonon anomalies in momentum space, pointing to (1) the existence of approximately flat phonon bands which gain some dispersion due to electron renormalization, and (2) the effects of the momentum dependent electron-phonon interaction in the CDW formation. Ab initio and analytical calculations corroborate the experimental findings to indicate that the weak leading order phonon instability is located at the wave vector $\frac{1}{3} \frac{1}{3} \frac{1}{2}$ of a rather flat collapsed mode. We analytically compute the phonon frequency renormalization from high temperatures to the soft mode, and relate it to a peak in the orbital-resolved susceptibility, obtaining an excellent match with both ab initio and experimental results, and explaining the origin of the approximately flat phonon dispersion. Our data report the first example of the collapse of a softening of a flat phonon plane and promote the 166 compounds of the kagome family as primary candidates to explore correlated flat phonon-topological flat electron physics., Comment: 10 pages, 4 figures

Multiple intriguing phenomena have recently been discovered in tetragonal Heusler compounds, where $D_{2d}$ symmetry sets a unique interplay between Dzyaloshinskii-Moriya (DM) and magnetic dipolar interactions. In the prototype $D_{2d}$ compound Mn$_{1.4}$PtSn, this has allowed the stabilization of exotic spin textures such as first-reported anti-skyrmions or elliptic Bloch-type skyrmions. While less attention has so far been given to the low-field spiral state, this remains extremely interesting as a simplest phase scenario on which to investigate the complex hierarchy of magnetic interactions in this materials family. Here, via resonant small-angle soft x-ray scattering experiments on high-quality single crystals of Mn$_{1.4}$PtSn at low temperatures, we evidence how the underlying $D_{2d}$ symmetry of the DMI in this material is reflected in its magnetic texture. Our studies reveal the existence of a novel and complex metastable phase, which possibly has a mixed character of both the N\'{e}el-type cycloid and the Bloch-type helix, that forms at low temperature in zero fields upon the in-plane field training. This hybrid spin-spiral structure has a remarkable tunability, allowing to tilt its orientation beyond high-symmetry crystallographic directions and control its spiral period. These results broaden the reachness of Heusler $D_{2d}$ materials exotic magnetic phase diagram and extend its tunability, thus enhancing a relevant playground for further fundamental explorations and potential applications in energy saving technologies.

The quantum limit (QL) of an electron liquid, realised at strong magnetic fields, has long been proposed to host a wealth of strongly correlated states of matter. Electronic states in the QL are, for example, quasi-one dimensional (1D), which implies perfectly nested Fermi surfaces prone to instabilities. Whereas the QL typically requires unreachably strong magnetic fields, the topological semimetal ZrTe$_5$ has been shown to reach the QL at fields of only a few Tesla. Here, we characterize the QL of ZrTe$_5$ at fields up to 64 T by a combination of electrical-transport and ultrasound measurements. We find that the Zeeman effect in ZrTe$_5$ enables an efficient tuning of the 1D Landau band structure with magnetic field. This results in a Lifshitz transition to a 1D Weyl regime in which perfect charge neutrality can be achieved. Since no instability-driven phase transitions destabilise the 1D electron liquid for the investigated field strengths and temperatures, our analysis establishes ZrTe$_5$ as a thoroughly understood platform for potentially inducing more exotic interaction-driven phases at lower temperatures.

The phase diagram of the kagome metal family \ch{AV3Sb5} (A = K, Rb, Cs) features both superconductivity and charge density wave (CDW) instabilities, which have generated tremendous recent attention. Nonetheless, significant questions remain. In particular, the temperature evolution and demise of the CDW state has not been extensively studied, and little is known about the co-existence of the CDW with superconductivity at low temperatures. We report an x-ray scattering study of \ch{CsV3Sb5} over a broad range of temperatures from 300 K to $\sim$ 2 K, below the onset of its superconductivity at $\textit{T}_\text{c}\sim$ 2.9 K. Order parameter measurements of the $2\times2\times2$ CDW structure show an unusual and extended linear temperature dependence onsetting at $T^*$ $\sim$ 160 K, much higher than the susceptibility anomaly associated with CDW order at $\textit{T}_\text{CDW}=94$ K. This implies strong CDW fluctuations exist to $\sim1.7\times\textit{T}_\text{CDW}$. The CDW order parameter is observed to be constant from $T=16$ K to 2 K, implying that the CDW and superconducting order co-exist below $\textit{T}_\text{c}$, and, at ambient pressure, any possible competition between the two order parameters is manifested at temperatures well below $\textit{T}_\text{c}$, if at all. Anomalies in the temperature dependence in the lattice parameters coincide with $\textit{T}_\text{CDW}$ for $\textit{c}(T)$ and with $T^*$ for $a(T)$.

Spintronic terahertz (THz) emitters (STE) based on the inverse spin Hall effect in ferromagnetic/heavy metal (FM/HM) heterostructures have become important sources for THz pulse generation. The design, materials and control of these interfaces at the nanometer level has become vital to engineer their THz emission properties.In this work, we present studies of the optimization of such structures through a multi-pronged approach, taking advantage of material and interface engineering to enhance the THz spintronic emission. This includes: the application of multi-stacks of HM/FM junctions and their application to trilayer structures, the use of spin-sinks to simultaneously enhance the THz emitted fields and reduce the use of thick Pt layers to reduce optical absorption, and the use of semi-metals to increase the spin polarization and thus the THz emission. Through these approaches, significant enhancements of the THz field can be achieved. Importantly, taking into account the optical absorption permits to elucidate novel phenomena such as the relation between the spin diffusion length and the spin-sink using THz spectroscopy, as well as possibly distinguishing between self and interface spin-to-charge conversion in semi-metals., Comment: submitted to Applied Physics Letters (2022)

Weyl nodes can be classified into zero-dimensional (0D) Weyl points (WPs), 1D Weyl nodal lines (WNL) and 2D Weyl nodal surfaces (WNS), which possess finite Chern numbers. Up to date, the largest Chern number of WPs identified in Weyl semimetals is 4, which is thought to be a maximal value for linearly crossing points in solids. On the other hand, whether the Chern numbers of nonzero-dimensional linear crossing Weyl nodal objects have one upper limit is still an open question. In this work, combining angle-resolved photoemission spectroscopy with density functional theory calculations, we show that the chiral crystal AlPt hosts a cube-shaped charged Weyl nodal surface which is formed by the linear crossings of two singly-degenerate bands. Different to conventional Weyl nodes, the cube-shaped nodal surface in AlPt is enforced by nonsymmorphic chiral symmetries and time reversal symmetry rather than accidental band crossings, and it possesses a giant Chern number |C| = 26. Moreover, our results and analysis prove that there is no upper limit for the Chern numbers of such kind 2D Weyl nodal object., Comment: 22 pages, 3 figures

We report a temperature dependent x-ray diffraction study of the electronic ordering instabilities in the kagome material CsV$_3$Sb$_5$. Our measurements between 10 K and 120 K reveal an unexpected reorganization of the three-dimensional electronic order in the bulk of CsV$_3$Sb$_5$: At 10 K, a 2x2x2 superstructure modulation due to electronic order is observed, which upon warming changes to a 2x2x4 superstructure at 60 K. The electronic order-order transition discovered here involves a change in the stacking of electronically ordered V$_3$Sb$_5$-layers and agrees perfectly with anomalies previously observed in magneto-transport measurements. This implies that the temperature dependent three-dimensional electronic order plays a decisive role for transport properties, which are related to the Berry-curvature of the V-bands. Our data also show that the bulk electronic order in CsV$_3$Sb$_5$ breaks the 6-fold rotational symmetry of the underlying $P6/mmm$ lattice structure., Comment: 5 pages, 3 figures

Constrained by the Nielsen-Ninomiya no-go theorem, in all so-far experimentally determined Weyl semimetals (WSMs) the Weyl points (WPs) always appear in pairs in the momentum space with no exception. As a consequence, Fermi arcs occur on surfaces which connect the projections of the WPs with opposite chiral charges. However, this situation can be circumvented in the case of unpaired WP, without relevant surface Fermi arc connecting its surface projection, appearing singularly, while its Berry curvature field is absorbed by nontrivial charged nodal walls. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, we show experimentally that a singular Weyl point emerges in PtGa at the center of the Brillouin zone (BZ), which is surrounded by closed Weyl nodal walls located at the BZ boundaries and there is no Fermi arc connecting its surface projection. Our results reveal that nontrivial band crossings of different dimensionalities can emerge concomitantly in condensed matter, while their coexistence ensures the net topological charge of different dimensional topological objects to be zero. Our observation extends the applicable range of the original Nielsen-Ninomiya no-go theorem which was derived from zero dimensional paired WPs with opposite chirality., Comment: 24 pages, 4 figures

Quasi-particle excitations in solids described by the Weyl equation have attracted significant attention in recent years. Thus far, a wide range of solids that have been experimentally realized as Weyl semimetals (WSMs) lack either mirror or inversion symmetry. For the first time, in the absence of both mirror and inversion symmetry, SrSi2 has been predicted as a robust WSM by recent theoretical works. Herein, supported by first-principles calculations, we present systematic angle-resolved photoemission studies of undoped SrSi2 and Ca-doped SrSi2 single crystals. Our results show no evidence of the predicted Weyl fermions at the kz = 0 plane or the Fermi arcs on the (001) surface. With external pressure, the electronic band structure evolved and induced Weyl fermions in this compound, as revealed by first-principle calculations combined with electrical transport property measurements. Moreover, a superconducting transition was observed at pressures above 20 GPa. Our investigations indicate that the SrSi2 system is a good platform for studying topological transitions and correlations with superconductivity.

Dirac semimetals (DSMs) are classified into different phases based on the types of the Dirac fermions. Tuning the transition among different types of the Dirac fermions in one system remains challenging. Recently, KMgBi was predicted to be located at a critical state that various types of Dirac fermions can be induced owing to the existence of a flat band. Here, we carried out systematic studies on the electronic structure of KMgBi single crystal by combining angle-resolve photoemission spectroscopy (ARPES) and scanning tunneling microscopy/spectroscopy (STM/STS). The flat band was clearly observed near the Fermi level. We also revealed a small bandgap of ~ 20 meV between the flat band and the conduction band. These results demonstrate the critical state of KMgBi that transitions among various types of Dirac fermions can be tuned in one system., Comment: 15 pages, 4 figures

Topological Weyl semimetals (TWSs) are exotic crystals possessing emergent relativistic Weyl fermions connected by unique surface Fermi-arcs (SFAs) in their electronic structures. To realize the TWS state, certain symmetry (such as the inversion or time reversal symmetry) must be broken, leading to a topological phase transition (TPT). Despite the great importance in understanding the formation of TWSs and their unusual properties, direct observation of such a TPT has been challenging. Here, using a recently discovered magnetic TWS Co3Sn2S2, we were able to systematically study its TPT with detailed temperature dependence of the electronic structures by angle-resolved photoemission spectroscopy. The TPT with drastic band structures evolution was clearly observed across the Curie temperature (TC = 177 K), including the disappearance of the characteristic SFAs and the recombination of the spin-split bands that leads to the annihilation of Weyl points with opposite chirality. These results not only reveal important insights on the interplay between the magnetism and band topology in TWSs, but also provide a new method to control their exotic physical properties., Comment: 15 pages, 4 figures

The noncentrosymmetric transition metal monopnictides NbP, TaP, NbAs and TaAs are a family of Weyl semimetals in which pairs of protected linear crossings of spin-resolved bands occur. These so-called Weyl nodes are characterized by integer topological charges of opposite sign associated with singular points of Berry curvature in momentum space. In such a system anomalous magnetoelectric responses are predicted, which should only occur if the crossing points are close to the Fermi level and enclosed by Fermi surface pockets penetrated by an integer flux of Berry curvature, dubbed Weyl pockets. TaAs was shown to possess Weyl pockets whereas TaP and NbP have trivial pockets enclosing zero net flux of Berry curvature. Here, via measurements of the magnetic torque, resistivity and magnetisation, we present a comprehensive quantum oscillation study of NbAs, the last member of this family where the precise shape and nature of the Fermi surface pockets is still unknown. We detect six distinct frequency branches, two of which have not been observed before. A comparison to density functional theory calculations suggests that the two largest pockets are topologically trivial, whereas the low frequencies might stem from tiny Weyl pockets. The enclosed Weyl nodes are within a few meV of the Fermi energy.

Mn1.4PtSn is the first material in which antiskyrmions have been observed in ultra-thin single crystalline specimens. While bulk crystals exhibit fractal patterns of purely ferromagnetic domain ordering at room temperature, ultra-thin Mn1.4PtSn lamellae clearly show antiskyrmion lattices with lattice spacings up to several $\mu$m. In the work presented here, we systematically investigate the thickness region from 400 nm to 10 $\mu$m using 100 $\times$ 100 $\mu$m$^2$ -wide Mn1.4PtSn plates, and identify the critical thickness-to-width aspect ratio $\alpha_0 = 0.044$ for the ferromagnetic fractal domain to the non-collinear texture phase transition. Additionally, we also explore these non-collinear magnetic textures below the critical aspect ratio $\alpha_0$ above and below the spin-reorientation transition temperature $T_{SR}$ while applying variable external magnetic fields. What we find is a strong hysteresis for the occurrence of an antiskyrmion lattice, since the antiskyrmions preferentially nucleate by pinching them off from helical stripes in the transition to the field polarized state.

We present an optical conductivity study of the multifold semimetal PdGa, performed in a broad spectral range (100 - 20000 cm-1; 12 meV - 2.5 eV) down to T = 10 K. The conductivity at frequencies below 4000 cm-1 is dominated by free carriers while at higher frequencies interband transitions provide the major contribution. The spectra do not demonstrate a significant temperature evolution: only the intraband part changes as a function of temperature with the plasma frequency remaining constant. The interband contribution to the conductivity exhibits a broad peak at around 5500 cm-1 and increases basically monotonously at frequencies above 9000 cm-1. The band-structure-based computations reproduce these features of the interband conductivity and predict its linear-in-frequency behavior as frequency diminishes., Comment: 7+ pages, published in PRB

Several early transition metal dipnictides have been found to host topological semimetal states and exhibit large magnetoresistance. In this study, we use angle-resolved photoemission spectroscopy (ARPES) and magneto-transport to study the electronic properties of a new transition metal dipnictide ZrP$_2$. We find that ZrP$_2$ exhibits an extremely large and unsaturated magnetoresistance of up to 40,000 % at 2 K, which originates from an almost perfect electron-hole compensation. Our band structure calculations further show that ZrP$_2$ hosts a topological nodal loop in proximity to the Fermi level. Based on the ARPES measurements, we confirm the results of our calculations and determine the surface band structure. Our study establishes ZrP$_2$ as a new platform to investigate near-perfect electron-hole compensation and its interplay with topological band structures., Comment: Accepted for publication in Physical Review B

The spin-orbit coupling (SOC) lifts the band degeneracy that plays a vital role in the search for different topological states, such as topological insulators (TIs) and topological semimetals (TSMs). In TSMs, the SOC can partially gap a degenerate nodal line, leading to the formation of Dirac/Weyl semimetals (DSMs/WSMs). However, such SOC-induced gap structure along the nodal line in TSMs has not yet been systematically investigated experimentally. Here, we report a direct observation of such gap structure in a magnetic WSM Co3Sn2S2 using high resolution angle-resolved photoemission spectroscopy. Our results not only reveal the existence and importance of the strong SOC effect in the formation of the WSM phase in Co3Sn2S2, but also provide insights for the understanding of its exotic physical properties., Comment: 12 pages, 4 figures

Tungsten ditelluride WTe$_2$ is a type-II Weyl semimetal with electronic properties highly sensitive to external pressure, as demonstrated by the superconductivity emerging under pressure. Here, we study the optical conductivity of the type-II Weyl semimetal WTe$_2$ under external pressure at room temperature. With increasing pressure, a pronounced spectral weight transfer occurs from the high-energy to the low-energy interband transitions, with drastic changes in the profile of the optical conductivity spectrum indicating a high sensitivity of the electronic band structure to external pressure. The detailed analysis of the pressure-dependent optical conductivity furthermore reveals anomalies at the pressures $\sim$2 and $\sim$4.5~GPa, where an electronic and a structural phase transition, respectively, were reported in the literature., Comment: 10 pages, 6 figures

We study single crystals of the magnetic superconductor EuRbFe$_4$As$_4$ by magnetization, electron spin resonance (ESR), angle-resolved photoemission spectroscopy (ARPES) and electrical resistance in pulsed magnetic fields up to 630 kOe. The superconducting state below 36.5 K is almost isotropic and only weakly affected by the development of Eu$^{2+}$ magnetic order at 15 K. On the other hand, for the external magnetic field applied along the c-axis the temperature dependence of the ESR linewidth reveals a Berezinskii-Kosterlitz-Thouless topological transition below 15 K. This indicates that Eu$^{2+}$-planes are a good realization of a two-dimensional XY-magnet, which reflects the decoupling of the Eu$^{2+}$ magnetic moments from superconducting FeAs-layers.

Synthesis of new materials that can host magnetic skyrmions and their thorough experimental and theoretical characterization are essential for future technological applications. The $\beta$-Mn-type compound FePtMo$_3$N is one such novel material that belongs to the chiral space group $P4_132$, where the antisymmetric Dzyaloshinkii-Moriya interaction is allowed due to the absence of inversion symmetry. We report the results of small-angle neutron scattering (SANS) measurements of FePtMo$_3$N and demonstrate that its magnetic ground state is a long-period spin helix with a Curie temperature of 222~K. The magnetic field-induced redistribution of the SANS intensity showed that the helical structure transforms to a lattice of skyrmions at $\sim$13~mT at temperatures just below $T_{\text C}$. Our key observation is that the skyrmion state in FePtMo$_3$N is robust against field cooling down to the lowest temperatures. Moreover, once the metastable state is prepared by field cooling, the skyrmion lattice exists even in zero field. Furthermore, we show that the skyrmion size in FePtMo$_3$N exhibits high sensitivity to the sample temperature and can be continuously tuned between 120 and 210~nm. This offers new prospects in the control of topological properties of chiral magnets., Comment: 6 pages, 4 figures

Nuclear magnetic resonance (NMR) was recently shown to measure the bulk band inversion of Bi$_2$Se$_3$ through changes in the $^{209}$Bi nuclear quadrupole interaction, and the corresponding tensor of the local electric field gradient was found to follow, surprisingly, the direction of the external magnetic field if the sample is rotated. This manifests a hidden property of the charge carriers in the bulk of this topological insulator, which is explored here with another material, Bi$_2$Te$_3$. It is found that two electric field gradients appear to be present at $^{209}$Bi, one rests with the lattice, as usual, while a second follows the external field if it is rotated with respect to the crystal axes. These electronic degrees of freedom correspond to an effective rotation of $j$-electrons, and their level life time is believed to be responsible for a new quadrupolar relaxation that should lead to other special properties including the electronic specific heat., Comment: 4 pages, 3 figures

The tetragonal compound Mn$_{1.4}$PtSn with the $D_{2d}$ symmetry recently attracted attention as the first known material that hosts magnetic antiskyrmions, which differ from the so far known skyrmions by their internal structure. The latter have been found in a number of magnets with the chiral crystal structure. In previous works, the existence of antiskyrmions in Mn$_{1.4}$PtSn was unambiguously demonstrated in real space by means of Lorentz transmission electron microscopy on thin-plate samples ($\sim$100~nm thick). In the present study, we used small-angle neutron scattering and magnetic force microscopy to perform reciprocal- and real-space imaging of the magnetic texture of bulk Mn$_{1.4}$PtSn single-crystals at different temperatures and in applied magnetic field. We found that the magnetic texture in the bulk differs significantly from that of thin-plate samples. Instead of spin helices or an antiskyrmion lattice, we observe an anisotropic fractal magnetic pattern of closure domains in zero field above the spin-reorientation transition temperature, which transforms into a set of bubble domains in high field. Below the spin-reorientation transition temperature the strong in-plane anisotropy as well as the fractal self-affinity in zero field is gradually lost, while the formation of bubble domains in high field remains robust. The results of our study highlight the importance of dipole-dipole interactions in thin-plate samples for the stabilization of antiskyrmions and identify criteria which should guide the search for potential (anti)skyrmion host materials. Moreover, they provide consistent interpretations of the previously reported magnetotransport anomalies of the bulk crystals.

The absence of mirror symmetry, or chirality, is behind striking natural phenomena found in systems as diverse as DNA and crystalline solids. A remarkable example occurs when chiral semimetals with topologically protected band degeneracies are illuminated with circularly polarized light. Under the right conditions, the part of the generated photocurrent that switches sign upon reversal of the light's polarization, known as the circular photogalvanic effect, is predicted to depend only on fundamental constants. The conditions to observe quantization are non-universal, and depend on material parameters and the incident frequency. In this work, we perform terahertz emission spectroscopy with tunable photon energy from 0.2 eV - 1.1 eV in the chiral topological semimetal CoSi. We identify a large longitudinal photocurrent peaked at 0.4 eV reaching $\sim$ 550 $\mu A/V^{2}$, which is much larger than the photocurrent in any chiral crystal reported in the literature. Using first-principles calculations we establish that the peak originates from topological band crossings, reaching 3.3$\pm$0.3 in units of the quantization constant. Our calculations indicate that the quantized CPGE is within reach in CoSi upon doping and increase of the hot-carrier lifetime. The large photo-conductivity suggests that topological semimetals could potentially be used as novel mid-infrared detectors., Comment: Fig.4 color updated

Chiral topological semimetals are materials that break both inversion and mirror symmetries. They host interesting phenomena such as the quantized circular photogalvanic effect (CPGE) and the chiral magnetic effect. In this work, we report a comprehensive theoretical and experimental analysis of the linear and non-linear optical responses of the chiral topological semimetal RhSi, which is known to host multifold fermions. We show that the characteristic features of the optical conductivity, which display two distinct quasi-linear regimes above and below 0.4 eV, can be linked to excitations of different kinds of multifold fermions. The characteristic features of the CPGE, which displays a sign change at 0.4 eV and a large non-quantized response peak of around 160 $\mu \textrm{A V}^{-2}$ at 0.7 eV, are explained by assuming that the chemical potential crosses a flat hole band at the Brillouin zone center. Our theory predicts that, in order to observe a quantized CPGE in RhSi, it is necessary to increase the chemical potential as well as the quasiparticle lifetime. More broadly our methodology, especially the development of the broadband terahertz emission spectroscopy, could be widely applied to study photo-galvanic effects in noncentrosymmetric materials and in topological insulators in a contact-less way and accelerate the technological development of efficient infrared detectors based on topological semimetals., Comment: Accepted in npj Quantum Materials; Abstract updated

We report an angle-resolved photoemission study of a series of hole and electron doped iron-based superconductors, their parent compound BaFe2As2, and their cousins BaCr2As2 and BaCo2As2. We focus on the energy (E) dependent scattering rate Gamma(E) as a function of the 3d count and on the renormalization function Z(E) of the inner hole pocket, which is the hot spot in these compounds. We obtain a non-Fermi-liquid-like linear in energy scattering rate Gamma(E>> kBT), independent of the dopant concentration. The main result is that the slope beta=Gamma(E >> kBT)/E, reaches its maxima near optimal doping and scales with the superconducting transition temperature. This supports the spin fluctuation model for superconductivity for these materials. In the optimally hole-doped compound, the slope of the scattering rate of the inner hole pocket is about three times bigger than the Planckian limit Gamma(E)/E~1. This result together with the energy dependence of the renormalization function Z(E) signals very incoherent charge carriers in the normal state which transform at low temperatures to a coherent unconventional superconducting state., Comment: 5 pages, 2 figures

We report on the pressure evolution of the giant anomalous Hall effect (AHE) in the chiral antiferromagnet Mn$_3$Ge. The AHE originating from the non-vanishing Berry curvature in Mn$_3$Ge can be continuously tuned by application of hydrostatic pressure. At room temperature, the Hall signal changes sign as a function of pressure and vanishes completely at $p=1.53$ GPa. Even though the Hall conductivity changes sign upon increasing pressure, the room-temperature saturation value of 23 ${\rm \Omega^{-1}cm^{-1}}$ at 2.85 GPa is remarkably high and comparable to the saturation value at ambient pressure of about 40 ${\rm \Omega^{-1}cm^{-1}}$. The change in the Hall conductivity can be directly linked to a gradual change of the size of the in-plane components of the Mn moments in the non-collinear triangular magnetic structure. Our findings, therefore, provide a route for tuning of the AHE in the chiral antiferromagnetic Mn$_3$Ge., Comment: 5 pages, 4 figures

We report the optical conductivity in high-quality crystals of the chiral topological semimetal CoSi, which hosts exotic quasiparticles known as multifold fermions. We find that the optical response is separated into several distinct regions as a function of frequency, each dominated by different types of quasiparticles. The low-frequency intraband response is captured by a narrow Drude peak from a high-mobility electron pocket of double Weyl quasi-particles, and the temperature dependence of the spectral weight is consistent with its Fermi velocity. By subtracting the low-frequency sharp Drude and phonon peaks at low temperatures, we reveal two intermediate quasi-linear inter-band contributions separated by a kink at 0.2 eV. Using Wannier tight-binding models based on first-principle calculations, we link the optical conductivity above and below 0.2 eV to interband transitions near the double Weyl fermion and a threefold fermion, respectively. We analyze and determine the chemical potential relative to the energy of the threefold fermion, revealing the importance of transitions between a linearly dispersing band and a flat band. More strikingly, below 0.1 eV our data are best explained if spin-orbit coupling is included, suggesting that at these energies the optical response is governed by transitions between a previously unobserved four-fold spin-3/2 node and a Weyl node. Our comprehensive combined experimental and theoretical study provides a way to resolve different types of multifold fermions in CoSi at different energy. More broadly our results provide the necessary basis to interpret the burgeoning set of optical and transport experiments in chiral topological semimetals.

Ni-Mn-In magnetic shape-memory Heusler alloys exhibit generally a large thermal hysteresis at their first-order martensitic phase transition which hinder a technological application in magnetic refrigeration. By optimizing the Cu content in Ni$_2$Cu$_x$Mn$_{1.4-x}$In$_{0.6}$, we obtained a thermal hysteresis of the martensitic phase transition in Ni$_{2}$Cu$_{0.2}$Mn$_{1.2}$In$_{0.6}$ of only 6 K. We can explain this very small hysteresis by an almost perfect habit plane at the interface of martensite and austenite phases. Application of hydrostatic pressure does not reduce the hysteresis further, but shifts the martensitic transition close to room temperature. The isothermal entropy change does not depend on warming or cooling protocols and is pressure independent. Experiments in pulsed-magnetic fields on Ni$_{2}$Cu$_{0.2}$Mn$_{1.2}$In$_{0.6}$ find a reversible magnetocaloric effect with a maximum adiabatic temperature change of -13 K., Comment: 7 pages, 4 figures

We report an improved reversibility of magnetostriction and inverse magnetocaloric effect (MCE) for the magnetic shape-memory Heusler alloy Ni$_{1.8}$Mn$_{1.8}$In$_{0.4}$. We show that the magnetostriction and MCE crucially depends on the geometrical compatibility of the austenite and martensite phases. Detailed information on the compatibility of both phases has been obtained from the transformation matrix calculated from x-ray diffraction data. The uniqueness of the lattice parameters results in an improved reversibility of the magnetostriction and the MCE. In the thermal hysteresis region of the martensitic transformation, the maximum relative length change is 0.3% and the adiabatic temperature change $\Delta T_{ad}\approx -10$ K in pulsed magnetic fields. Our results reveal that the approach of geometric compatibility will allow one to design materials with reversible magnetostriction and reversible inverse MCE at a first-order magnetostructural phase transition in shape-memory Heusler alloys., Comment: 6 pages, 4 figures

The large magnetocaloric effect (MCE) observed in Ni-Mn based shape-memory Heusler alloys put them forward to use in magnetic refrigeration technology. It is associated with a first-order magnetostructural (martensitic) phase transition. We conducted a comprehensive study of the MCE for the off-stoichiometric Heusler alloy Ni$_{2.2}$Mn$_{0.8}$Ga in the vicinity of its first-order magnetostructural phase transition. We found a reversible MCE under repeated magnetic field cycles. The reversible behavior can be attributed to the small thermal hysteresis of the martensitic phase transition. Based on the analysis of our detailed temperature dependent X-ray diffraction data, we demonstrate the geometric compatibility of the cubic austenite and tetragonal martensite phases. This finding directly relates the reversible MCE behavior to an improved geometric compatibility condition between cubic austenite and tetragonal martensite phases. The approach will help to design shape-memory Heusler alloys with a large reversible MCE taking advantage of the first-order martensitic phase transition., Comment: 6 pages, 4 figures

Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe5, adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit., Comment: 26 pages with 4 figures

Landau-level spectroscopy, the optical analysis of electrons in materials subject to a strong magnetic field, is a versatile probe of the electronic band structure and has been successfully used in the identification of novel states of matter such as Dirac electrons, topological materials or Weyl semimetals. The latter arise from a complex interplay between crystal symmetry, spin-orbit interaction and inverse ordering of electronic bands. Here, we report on unusual Landau-level transitions in the monopnictide TaP that decrease in energy with increasing magnetic field. We show that these transitions arise naturally at intermediate energies in time-reversal-invariant Weyl semimetals where the Weyl nodes are formed by a partially gapped nodal-loop in the band structure. We propose a simple theoretical model for electronic bands in these Weyl materials that captures the collected magneto-optical data to great extent., Comment: 6 pages, 3 figures + supplementary materials, accepted in Phys. Rev. Lett

Recently, a Verwey-type transition in the mixed-valence alkali sesquioxide Cs$_4$O$_6$ was deduced from the charge ordering of molecular peroxide O$_2^{2-}$ and superoxide O$_2^-$ anions accompanied by the structural transformation and a dramatic change in electronic conductivity [Adler et al, Sci. Adv 4, eaap7581 (2018)]. Here, we report that in the sister compound Rb$_4$O$_6$ a similar Verwey-type charge ordering transition is strongly linked to O$_2^-$ orbital and spin dynamics. On cooling, a powder neutron diffraction experiment reveals a charge ordering and a cubic-to-tetragonal transition at $T_{\rm CO}=290$ K, which is followed by a further structural instability at $T_{\rm s}=92$ K that involves an additional reorientation of magnetic O$_2^-$ anions. Magnetic resonance techniques supported by density functional theory computations suggest the emergence of a peculiar type of $\pi^*$-orbital ordering of the magnetically active O$_2^-$ units, which promotes the formation of a quantum spin state composed of weakly coupled spin dimers. These results reveal that similarly as in 3$d$ transition metal compounds, also in in the $\pi^*$ open-shell alkali sesquioxides the interplay between Jahn-Teller-like electron-lattice coupling and Kugel-Khomskii-type superexchange determines the nature of orbital ordering and the magnetic ground state.