The physical properties and their pressure dependence of recently synthesized Ti2AlX (X = B, C, and N) MAX phases are investigated for the very first-time applying density functional theory (DFT). The optimized lattice parameters are in good agreement with the existing literature. The metallic character of the phases is supported by the Fermi level overlap of the conduction band and valence band. Structural parameters of competing phases, elastic constants, and phonon calculations revealed that all three compounds are structurally, mechanically, and dynamically stable under pressure. The materials are brittle in nature at 0 GPa and start exhibiting ductility at around 8 GPa, confirmed by both Pugh's and Poisson's ratios. All three compounds possess good level of hardness. The compounds have moderate machinability. The Debye temperature, phonon thermal conductivity, and melting temperature are moderate; with the highest value observed for Ti2AlN. The lattice thermal conductivity decreases with increasing pressure (up to 10 GPa) and temperature (up to 1500 K). Directional anisotropies in mechanical, optical, and thermal features are at moderate level for all three MAX phases. All the compounds under study exhibit potential as promising TBC (thermal barrier coating) materials. They are also suitable for optical applications.

AbstractThe kagome lattice is an intriguing and rich platform for discovering, tuning and understanding the diverse phases of quantum matter, crucial for advancing modern and future electronics. Despite considerable efforts, accessing correlated phases at room temperature has been challenging. Using single-crystal X-ray diffraction, we discovered charge order above room temperature in La(Ru1−xFex)3Si2(x= 0, 0.01, 0.05), where charge order related to out-of-plane Ru atom displacements appears belowTCO,I ≃ 400 K. The secondary charge ordered phase emerges belowTCO,II ≃ 80–170 K. Furthermore, first principles calculations reveal both the kagome flat band and the van Hove point near the Fermi energy in LaRu3Si2, driven by Ru-dz2orbitals. Our results identify LaRu3Si2as the kagome superconductor with the highest known charge ordering temperature, offering a promising avenue for researching room temperature quantum phases and developing related technologies.

The breaking of time-reversal symmetry (TRS) in the normal state of kagome superconductors $A$V$_{3}$Sb$_{5}$ stands out as a significant feature. Yet the extent to which this effect can be tuned remains uncertain, a crucial aspect to grasp in light of the varying details of TRS breaking observed through different techniques. Here, we employ the unique low-energy muon spin rotation technique combined with local field numerical analysis to study the TRS breaking response as a function of depth from the surface in single crystals of RbV$_{3}$Sb$_{5}$ with charge order and Cs(V$_{0.86}$Ta$_{0.14}$)$_{3}$Sb$_{5}$ without charge order. In the bulk (i.e., > 33 nm from the surface) of RbV$_{3}$Sb$_{5}$, we have detected a notable increase in the internal magnetic field width experienced by the muon ensemble. This increase occurs only within the charge ordered state. Intriguingly, the muon spin relaxation rate is significantly enhanced near the surface (i.e., < 33 nm from the surface) of RbV$_{3}$Sb$_{5}$, and this effect commences at temperatures significantly higher than the onset of charge order. Conversely, in Cs(V$_{0.86}$Ta$_{0.14}$)$_{3}$Sb$_{5}$, we do not observe a similar enhancement in the internal field width, neither in the bulk nor near the surface. These observations indicate a strong connection between charge order and TRS breaking on one hand, and on the other hand, suggest that TRS breaking can occur prior to long-range charge order. This research offers compelling evidence for depth-dependent magnetism in $A$V$_{3}$Sb$_{5}$ superconductors in the presence of charge order. Such findings are likely to elucidate the intricate microscopic mechanisms that underpin the TRS breaking phenomena in these materials.

The kagome lattice has emerged as a promising platform for hosting unconventional chiral charge order at high temperatures. Notably, in LaRu$_{3}$Si$_{2}$, a room-temperature charge-ordered state with a propagation vector of ($\frac{1}{4}$,~0,~0) has been recently identified. However, understanding the interplay between this charge order and superconductivity, particularly with respect to time-reversal-symmetry breaking, remains elusive. In this study, we employ single crystal X-ray diffraction, magnetotransport, and muon-spin rotation experiments to investigate the charge order and its electronic and magnetic responses in LaRu$_{3}$Si$_{2}$ across a wide temperature range down to the superconducting state. Our findings reveal the emergence of a charge order with a propagation vector of ($\frac{1}{6}$,~0,~0) below $T_{\rm CO,2}$ ${\simeq}$ 80 K, coexisting with the previously identified room-temperature primary charge order ($\frac{1}{4}$,~0,~0). The primary charge-ordered state exhibits zero magnetoresistance. In contrast, the appearance of the secondary charge order at $T_{\rm CO,2}$ is accompanied by a notable magnetoresistance response and a pronounced temperature-dependent Hall effect, which experiences a sign reversal, switching from positive to negative below $T^{*}$ ${\simeq}$ 35 K. Intriguingly, we observe an enhancement in the internal field width sensed by the muon ensemble below $T^{*}$ ${\simeq}$ 35 K. Moreover, the muon spin relaxation rate exhibits a substantial increase upon the application of an external magnetic field below $T_{\rm CO,2}$ ${\simeq}$ 80 K. Our results highlight the coexistence of two distinct types of charge order in LaRu$_{3}$Si$_{2}$ within the correlated kagome lattice, namely a non-magnetic charge order ($\frac{1}{4}$,~0,~0) below $T_{\rm co,1}$ ${\simeq}$ 400 K and a time-reversal-symmetry-breaking charge order below $T_{\rm CO,2}$.

We report on the effect of magnetic impurities on the microscopic superconducting (SC) properties of the kagome-lattice superconductor La(Ru1-xFex)3Si2 using muon spin relaxation/rotation. A strong suppression of the superconducting critical temperature Tc, the SC volume fraction, and the superfluid density was observed. We further find a correlation between the superfluid density and Tc which is considered a hallmark feature of unconventional superconductivity. Most remarkably, measurements of the temperature-dependent magnetic penetration depth lambda reveal a change in the low-temperature behavior from exponential saturation to a linear increase, which indicates that Fe doping introduces nodes in the superconducting gap structure at concentrations as low as x = 0.015. Our results point to a rare example of unconventional superconductivity in the correlated kagome lattice and accessible tunability of the superconducting gap structure, offering new insights into the microscopic mechanisms involved in superconducting order.

Non-centrosymmetric germanide-based superconductors have recently attracted particular attention because of their unconventional physical properties. In the present study, we comprehensively investigated the structural and hitherto unexplored electronic, optical, mechanical, thermal, and superconducting state properties of germanide-based superconductors, MGe2 (M = V, Nb, and Ta), using the density functional theory. The obtained lattice parameters and accordingly the volume of the unit cells agree very well with the earlier reported values, indicating the high reliability of the physical properties studied. All the compounds studied herein are dynamically and mechanically stable. The compounds are brittle (ranked: NbGe2 < VGe2 < TaGe2) and elastically anisotropic in nature.The estimated hardness values of MGe2 (M = V, Nb and Ta) are found to be 16.95, 14.96 and 19.6 GPa, respectively. Different optical functions (dielectric functions, reflectivity, absorption coefficient, photoconductivity, refractive index and loss function) and thermal properties (thermal conductivity, thermal expansion coefficient, Debye temperature, specific heat and melting point) are investigated.The reflectance spectra in the visible and near UV region were found to be >50% for all these compounds, demonstrating their potential for application as coating material to reduce heating from incident electromagnetic radiation. Based on the results obtained for thermal properties and comparison with benchmark system, Y4Al12O9 and some other predicted compounds, the titled compounds could also be used as thermal barrier coating materials. Some important parameters for the understanding of the superconducting behavior, such as the Coulomb pseudopotential, London penetration depth, coherence depth, Debye temperature, electron-phonon coupling constant, and Ginzburg-Landau parameter, are also estimated, and the results obtained support that the NbGe(2)and TaGe2 compounds should be categorized as a type-2 superconductors.

Charge ordered kagome lattices have been demonstrated to be intriguing platforms for studying the intertwining of topology, correlation, and magnetism. The recently discovered charge ordered kagome material ScV 6 Sn 6 does not feature a magnetic groundstate or excitations, thus it is often regarded as a conventional paramagnet. Here, using advanced muon-spin rotation spectroscopy, we uncover an unexpected hidden magnetism of the charge order. We observe an enhancement of the internal field width sensed by the muon ensemble, which takes place within the charge ordered state. More importantly, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. Taken together with the hidden magnetism found in A V 3 Sb 5 ( A = K, Rb, Cs) and FeGe kagome systems, our results suggest ubiqitous time-reversal symmetry-breaking in charge ordered kagome lattices.

Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals A V 3 Sb 5 , key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned and ultra-low temperature muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV 3 Sb 5 and KV 3 Sb 5 . At ambient pressure, we observed time-reversal symmetry breaking charge order below T_1^*≃ 110 K in RbV 3 Sb 5 with an additional transition at T_2^*≃ 50 K. Remarkably, the superconducting state displays a nodal energy gap and a reduced superfluid density, which can be attributed to the competition with the charge order. Upon applying pressure, the charge-order transitions are suppressed, the superfluid density increases, and the superconducting state progressively evolves from nodal to nodeless. Once optimal superconductivity is achieved, we find a superconducting pairing state that is not only fully gapped, but also spontaneously breaks time-reversal symmetry. Our results point to unprecedented tunable nodal kagome superconductivity competing with time-reversal symmetry-breaking charge order and offer unique insights into the nature of the pairing state.

We report on the effect of magnetic impurities on the microscopic superconducting (SC) properties of the kagome-lattice superconductor La(Ru_1-xFe_x)_3Si_2 using muon spin relaxation/rotation. A strong suppression of the superconducting critical temperature T_ c, the SC volume fraction, and the superfluid density was observed. We further find a correlation between the superfluid density and T_ c which is considered a hallmark feature of unconventional superconductivity. Most remarkably, measurements of the temperature-dependent magnetic penetration depth λ reveal a change in the low-temperature behavior from exponential saturation to a linear increase, which indicates that Fe doping introduces nodes in the superconducting gap structure at concentrations as low as x= 0.015. Our results point to a rare example of unconventional superconductivity in the correlated kagome lattice and accessible tunability of the superconducting gap structure, offering new insights into the microscopic mechanisms involved in superconducting order.

The kagome lattice is an intriguing and rich platform for discovering, tuning and understanding the diverse phases of quantum matter, which is a necessary premise for utilizing quantum materials in all areas of modern and future electronics in a controlled and optimal way. The system LaRu$_{3}$Si$_{2}$ was shown to exhibit typical kagome band structure features near the Fermi energy formed by the Ru-$dz^{2}$ orbitals and the highest superconducting transition temperature $T_{\rm c}$ ${\simeq}$ 7K among the kagome-lattice materials. However, the effect of electronic correlations on the normal state properties remains elusive. Here, we report the discovery of charge order in La(Ru$_{1-x}$Fe$_{x}$)$_{3}$Si$_{2}$ ($x$ = 0, 0.01, 0.05) beyond room-temperature. Namely, single crystal X-ray diffraction reveals charge order with a propagation vector of ($\frac{1}{4}$,0,0) below $T_{\rm CO-I}$ ${\simeq}$ 400K in all three compounds. At lower temperatures, we see the appearance of a second set of charge order peaks with a propagation vector of ($\frac{1}{6}$,0,0). The introduction of Fe, which is known to quickly suppress superconductivity, does not drastically alter the onset temperature for charge order. Instead, it broadens the scattered intensity such that diffuse scattering appears at the same onset temperature, however does not coalesce into sharp Bragg diffraction peaks until much lower in temperature. Our results present the first example of a charge ordered state at or above room temperature in the correlated kagome lattice with bulk superconductivity.

Local spectroscopic evidence for a nodeless magnetic kagome superconductor CeRu2 C. Mielke III†,1, 2, ∗ H. Liu, 4, † D. Das, J.-X. Yin, L.Z. Deng, R. Gupta, M. Medarde, C.-W. Chu, 8 R. Khasanov, Z.M. Hasan, 9, 10, 11 Y. Shi, 4 H. Luetkens, and Z. Guguchia ‡ Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Physik-Institut, Universitat Zürich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. University of Chinese Academy of Sciences, Beijing 100049, China. Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University, Princeton, New Jersey 08544, USA Department of Physics and Texas Center for Superconductivity, University of Houston, Houston, TX Laboratory for Multiscale Materials Experiments, Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08540, USA Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA Quantum Science Center, Oak Ridge, Tennessee 37831, USA

We report muon spin rotation (µSR) experiments on the microscopic properties of superconductivity and magnetism in the kagome superconductor CeRu2withTc≃5 K. From the measurements of the temperature-dependent magnetic penetration depthλ, the superconducting order parameter exhibits nodeless pairing, which fits best to an anisotropics-wave gap symmetry. We further show that theTc/λ-2ratio is comparable to that of unconventional superconductors. Furthermore, the powerful combination of zero-field (ZF)-µSR and high-fieldµSR has been used to uncover magnetic responses across three characteristic temperatures, identified asT1∗≃110 K,T2∗≃65 K, andT3∗≃40 K. Our experiments classify CeRu2as an exceedingly rare nodeless magnetic kagome superconductor.

Magnetic topological phases of quantum matter are an emerging frontier in physics and materials science, of which kagome magnets appear as a highly promising platform. Here, we explore magnetic correlations in the recently identified topological kagome system TbMn 6 Sn 6 using muon spin rotation, combined with local field analysis and neutron diffraction. Our studies identify an out-of-plane ferrimagnetic structure with slow magnetic fluctuations which exhibit a critical slowing down below T_C1^* ≃ 120 K and finally freeze into static patches with ideal out-of-plane order below T C1 ≃ 20 K. We further show that hydrostatic pressure of 2.1 GPa stabilises the static out-of-plane topological ferrimagnetic ground state in the whole volume of the sample. Therefore the exciting perspective arises of a magnetically-induced topological system whose magnetism can be controlled through external parameters. The present results will stimulate theoretical investigations to obtain a microscopic understanding of the relation between the low-temperature volume-wise magnetic evolution of the static c -axis ferrimagnetic patches and the topological electronic properties in TbMn 6 Sn 6 .

The kagome lattice, the most prominent structural motif in quantum physics, benefits from inherent nontrivial geometry to host diverse quantum phases, ranging from spin-liquid phases, topological matter to intertwined orders, and most rarely unconventional superconductivity. Recently, charge sensitive probes have suggested that the kagome superconductors AV_3Sb_5 (A = K, Rb, Cs) (A = K, Rb, Cs) exhibit unconventional chiral charge order, which is analogous to the long-sought-after quantum order in the Haldane model or Varma model. However, direct evidence for the time-reversal symmetry-breaking of the charge order remains elusive. Here we utilize muon spin relaxation to probe the kagome charge order and superconductivity in KV_3Sb_5. We observe a striking enhancement of the internal field width sensed by the muon ensemble, which takes place just below the charge ordering temperature and persists into the superconducting state. Remarkably, the muon spin relaxation rate below the charge ordering temperature is substantially enhanced by applying an external magnetic field. We further show the multigap nature of superconductivity in KV_3Sb_5 and that the T_c/lambda_{ab}^{-2} ratio is comparable to those of unconventional high-temperature superconductors. Our results point to time-reversal symmetry breaking charge order intertwining with unconventional superconductivity in the correlated kagome lattice.

Unconventional superconductors often feature competing orders, small superfluid density, and nodal electronic pairing. While unusual superconductivity has been proposed in the kagome metals AV3Sb5, key spectroscopic evidence has remained elusive. Here we utilize pressure-tuned (up to 1.85 GPa) and ultra-low temperature (down to 18 mK) muon spin spectroscopy to uncover the unconventional nature of superconductivity in RbV3Sb5. At ambient pressure, we detect an enhancement of the width of the internal magnetic field distribution sensed by the muon ensemble, indicative of time-reversal symmetry breaking charge order. Remarkably, the superconducting state displays nodal energy gap and a reduced superfluid density, which can be attributed to the competition with the novel charge order. Upon applying pressure, the charge-order transitions are suppressed, the superfluid density increases, and the superconducting state progressively evolves from nodal to nodeless. Once charge order is eliminated, we find a superconducting pairing state that is not only fully gapped, but also spontaneously breaks time-reversal symmetry. Our results point to unprecedented tunable nodal kagome superconductivity competing with time-reversal symmetry-breaking charge order and offer unique insights into the nature of the pairing state.

Recent experiments report a charge density wave (CDW) in the antiferromagnet FeGe, but the nature of charge ordering, and the associated structural distortion remains elusive. Here, we unravel the structural and electronic properties of FeGe through in-depth first-principles calculations. Our proposed 2 × 2 × 1 CDW, which is driven by the nesting of the hexagonal features of the Fermi surface, accurately captures atomic topographies observed via scanning tunneling microscopy as well as the enhancement of the kagome-Fe magnetic moment upon transition into the CDW phase. In contrast to earlier studies, we show that FeGe exhibits a generalized Kekul´e distortion in the Ge honeycomb atomic layers. Our results set the stage for further exploration of the topological nature of the ground state of magnetic kagome-honeycomb lattices and their implications for novel transport, magnetic, and optical responses.

The electronic instabilities in CsV3Sb5 are believed to originate from the V 3d-electrons on the kagome plane, however the role of Sb 5p-electrons for 3-dimensional orders is largely unexplored. Here, using resonant tender X-ray scattering and high-pressure X-ray scattering, we report a rare realization of conjoined charge density waves (CDWs) in CsV3Sb5, where a 2 × 2 × 1 CDW in the kagome sublattice and a Sb 5p-electron assisted 2 × 2 × 2 CDW coexist. At ambient pressure, we discover a resonant enhancement on Sb L1-edge (2s→5p) at the 2 × 2 × 2 CDW wavevectors. The resonance, however, is absent at the 2 × 2 × 1 CDW wavevectors. Applying hydrostatic pressure, CDW transition temperatures are separated, where the 2 × 2 × 2 CDW emerges 4 K above the 2 × 2 × 1 CDW at 1 GPa. These observations demonstrate that symmetry-breaking phases in CsV3Sb5 go beyond the minimal framework of kagome electronic bands near van Hove filling.

G. Li, W. Z. Hu, J. Dong, D. Qian, D. Hsieh, M. Z. Hasan, E. Morosan, R. J. Cava, and N. L. Wang ∗ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100080, P. R. China Department of Physics, Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08544, USA Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

Putative helimagnetic phase in the kagome metal Co3Sn2−xInxS2 Z. Guguchia, ∗ H. Zhou, 3 C.N. Wang, J.-X. Yin, C. Mielke III, 5 S.S. Tsirkin, I. Belopolski, S.-S. Zhang, T.A. Cochran, T. Neupert, R. Khasanov, A. Amato, S. Jia, 3 M.Z. Hasan, 6 and H. Luetkens Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland International Center for Quantum Materials and School of Physics, Peking University, Beijing, China. CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Science, Beijing, China. Laboratory for Topological Quantum Matter and Advanced Spectroscopy, Department of Physics, Princeton University, Princeton, New Jersey 08544, USA Department of Physics, University of Zürich, Winterthurerstrasse 190, Zürich, Switzerland Lawrence Berkeley National Laboratory, Berkeley, CA, USA