Gaining a deeper understanding of the interplay between charge density wave (CDW) order and superconductivity in transition metal dichalcogenides (TMDs), particularly within the (4H/2H)-NbX_{2} (X=Se and S) family, remains an open and intriguing challenge. A systematic microscopic study across various compounds in this family is therefore required to unravel this complex interplay. Here, we report on muon spin rotation (µSR) and magnetotransport experiments investigating the effects of hydrostatic pressure on the superconducting transition temperature (T_{c}), the temperature-dependent magnetic penetration depth (λ_{eff}), and the charge density wave order (CDW) in two layered chalcogenide superconductors: 4H-NbSe_{2}, which exhibits CDW order, and 2H-NbS_{2}, which lacks such order. Our observations reveal a substantial 75% enhancement of the superfluid density (n_{s}/m^{*}) in 4H-NbSe_{2} upon the maximum applied pressure of ∼2 GPa, surpassing that of 2H-NbSe_{2}. Despite the absence of CDW order, a sizable 20% growth in superfluid density is also observed for 2H-NbS_{2} under an applied pressure of 1.8 GPa. Notably, the evaluated superconducting gaps in all these TMDs remain largely unaffected by changes in applied pressure, irrespective of pressure-induced partial suppression of CDW order in (4H/2H)-NbSe_{2} or its general absence in 2H-NbS_{2}. These results underscore the complex nature of pressure-induced behaviors in these TMDs, challenging a simplistic view of competition solely between CDW order and superconductivity. Remarkably, the relationship between n_{s}/m^{*} and T_{c} exhibits an unconventional correlation, indicating a noteworthy similarity with the behavior observed in cuprate, kagome, and iron-based superconductors.

The pursuit of a unifying theory for non-BCS superconductivity has faced significant challenges. One approach to overcome such challenges is to perform systematic investigations into superconductors containing d-electron metals in order to elucidate their underlying mechanisms. Recently, the Sc6MTe2 (M = d-electron metal) family has emerged as a unique series of isostructural compounds exhibiting superconductivity across a range of 3d, 4d, and 5d electron systems. In this study, muon spin rotation, neutron diffraction, and magnetization techniques are employed to probe the normal and superconducting states at a microscopic level. These findings reveal extremely dilute superfluid densities that correlate with the critical temperature (Tc). Additionally, high-temperature normal-state transitions that are inversely correlated with Tc are identified. Notably, in Sc6FeTe2, the superconducting pairing symmetry is most likely characterized by two nodeless gaps, one of which closes as electron correlations diminish in the Ru and Ir Sc6MTe2 compounds. These results classify the Sc6MTe2 compounds (M = Fe, Ru, Ir) as unconventional bulk superconductors, where the normal-state transitions and superconducting properties are governed by the interplay between electron correlations and spin-orbit coupling of the d-electron metal.

Understanding how time-reversal symmetry (TRS) breaks in quantum materials is key to uncovering new states of matter and advancing quantum technologies. However, unraveling the interplay between TRS breaking, charge order, and superconductivity in kagome metals continues to be a compelling challenge. Here, we investigate the kagome metal Cs(V1−xNbx)3Sb5 with x = 0.07 using muon spin rotation (μSR), alternating current (AC) magnetic susceptibility, and scanning tunneling microscopy (STM), under combined tuning by chemical doping, hydrostatic pressure, magnetic field, and depth from the surface. We find that TRS breaking in the bulk emerges below 40 K—lower than the charge order onset at 58 K—while near the surface, TRS breaking onsets at 58 K and is twice as strong. Niobium doping raises the superconducting critical temperature from 2.5 K to 4.4 K. Under pressure, both the critical temperature and superfluid density double, with TRS-breaking superconductivity appearing above 0.85 GPa. These findings reveal a depth-tunable TRS-breaking state and unconventional superconducting behavior in kagome systems. Kagome systems are a rich playground to explore the interplay between superconductivity and charge order. Here, the authors present a comprehensive muon spin rotation analysis, coupled with scanning tunnelling microscopy, under various tuning parameters including chemical doping, depth and hydrostatic pressure to investigate time-reversal symmetry-breaking in Nb-doped CsV3Sb5.

Vacancies in solid-state physics are underexplored in materials with strong electron-electron correlations. Recent research on the Ir-Sb binary system revealed an extended buckled-honeycomb vacancy (BHV) order. Superconductivity arises by suppressing BHV ordering through high-pressure growth with excess Ir atoms or Rh substitution, yet the superconducting pairing nature remains unknown. To explore this, we conducted muon spin rotation experiments on Ir1-δ Sb (synthesized at 5.5 GPa, T c = 4.2 K) and ambient pressure synthesized optimally Rh-doped Ir1-x Rh x Sb (x=0.3, T c = 2.7 K). The exponential temperature dependence of the superfluid density suggests a fully gapped superconducting state exists in both samples. The ratio of T c to the superfluid density resembles that of unconventional superconductors. A significant increase in the superfluid density in the high-pressure synthesized sample correlates with T c, indicating that unconventional superconductivity is intrinsic to the Ir-Sb binary system. These findings, along with the dome-shaped phase diagram, highlight IrSb as the first unconventional superconducting parent phase with ordered vacancies, requiring further theoretical investigations.

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.

The two-dimensional kagome lattice is an experimental playground for novel physical phenomena, from frustrated magnetism and topological matter to chiral charge order and unconventional superconductivity. A newly identified kagome superconductor, Ta2V3.1Si0.9 has recently gained attention for possessing a record high critical temperature, T C = 7.5 K for kagome metals at ambient pressure. In this study we conducted a series of muon spin rotation measurements to delve deeper into understanding the superconducting and normal state properties of Ta2V3.1Si0.9. We demonstrate that Ta2V3.1Si0.9 is a bulk superconductor with either a s+s-wave or anisotropic s-wave gap symmetry, and has an unusual paramagnetic shift in response to external magnetic fields in the superconducting state. Additionally, we observe an exceptionally low superfluid density - a distinctive characteristic of unconventional superconductivity - which remarkably is comparable to the superfluid density found in hole-doped cuprates. In its normal state, Ta2V3.1Si0.9 exhibits a significant increase in the zero-field muon spin depolarisation rate, starting at approximately 150 K, which has been observed in other kagome-lattice superconductors, and therefore hints at possible hidden magnetism. These findings characterise Ta2V3.1Si0.9 as an unconventional superconductor and a noteworthy new member of the vanadium-based kagome material family.

The interplay between superconductivity and charge order is a central focus in condensed matter research, with kagome lattice systems offering unique insights. The kagome superconductor LaRu_3Si_2 (T_ c ≃ 6.5 K) exhibits a hierarchy of charge order transitions: primary (T_ co,I ≃ 400 K), secondary (T_ co,II ≃ 80 K), and an additional transition at (T^* ≃ 35 K). The transitions at T_ co,II and T^* are linked to electronic and magnetic responses as revealed by muon-spin rotation and magnetotransport experiments. However, the connection between superconductivity, charge order, and electronic responses has remained elusive. By employing magnetotransport and X-ray diffraction techniques under pressures of up to 40 GPa, we observe that T_ c rises to 9 K at 2 GPa, remains nearly constant up to 12 GPa, and then decreases to 2 K at 40 GPa, resulting in a dome-shaped phase diagram. The resistivity anomaly at T^* and magnetoresistance also exhibit a similar dome-shaped pressure dependence. Furthermore, we find that charge order transitions from long-range to short-range above 12 GPa, correlating with the suppression of T_ c, suggesting superconductivity is closely tied to the charge-ordered state. Specifically, T_ c peaks when charge order and the normal-state electronic responses are optimized. In contrast to systems like the cuprates, transition metal dichalcogenides, and other kagome materials, where superconductivity typically competes with charge order, LaRu_3Si_2 displays a pronounced interdependence between these two phenomena. This distinctive behavior sheds new light on the connection between superconductivity and charge order, offering avenues for theoretical advancements in understanding superconductivity.

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.