arXiv subjects

R. Khasanov

Publications and source records attributed to R. Khasanov.

At least 19 recordsLinked to original sources

arXiv2026

Correlated charge order intertwined with time-reversal symmetry-breaking nodal superconductivity in the dual flat band kagome superconductor CeRu$_{3}$Si$_{2}$

Kagome materials provide a powerful platform for exploring how flat electronic bands promote symmetry-breaking quantum states, yet studies have so far focused mainly on kagome-derived $d$-electron flat bands. In this paper, we introduce CeRu$_{3}$Si$_{2}$, a kagome superconductor in which our first-principles calculations show the coexistence of Ru $d$-orbital kagome flat bands and heavy-fermion flat bands derived from Ce$^{4+}$ $4f$-states. X-ray diffraction reveals a dominant 1/2 charge order with a much weaker 1/3 component persisting up to room temperature. Theoretical calculations further highlight the correlated nature of these charge-order states. Deep within the charge-ordered state, magnetoresistance emerges below 80 K and strengthens further below 30 K. Zero-field muon spin-rotation measurements show no time-reversal symmetry (TRS) breaking in the normal state, in contrast to LaRu$_{3}$Si$_{2}$ and YRu$_{3}$Si$_{2}$. However, an applied magnetic field induces weak magnetism. Across the $A$Ru$_{3}$Si$_{2}$ family ($A$ = La, Y, and Ce), the superconducting transition temperature $T_{\rm c}$ scales linearly with the onset temperature of normal-state TRS breaking $T_{\rm {TRSB}}$ and the magnitude of the field-induced magnetic response, revealing a direct positive correlation between normal-state symmetry breaking and superconductivity. Furthermore, we identify that CeRu$_{3}$Si$_{2}$ is the first 132-type kagome compound to host nodal superconductivity together with spontaneous internal magnetic fields, providing clear evidence for intrinsic TRS breaking in the superconducting state. These results establish CeRu$_{3}$Si$_{2}$ as a unique platform where intertwined kagome $d$- and heavy fermion $f$-electron flat bands generate a rich hierarchy of electronic orders.

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arXiv2026

Unified pressure and field response across distinct charge-order regimes in Ti-doped CsV$_3$Sb$_5$

Understanding the phase diagram of kagome superconductors from a microscopic perspective is crucial for clarifying the interplay between charge order and superconductivity. Ti-doped CsV$_{3}$Sb$_{5}$ exhibits a nonmonotonic temperature-doping phase diagram in which both $T_{\rm c}$ and the charge-order temperature initially decrease with doping, followed by a crossover from long-range to short-range charge order and a subsequent increase in $T_{\rm c}$. Here, we report a muon spin rotation ($\mu$SR) study of Ti-doped CsV$_{3}$Sb$_{5}$ at two representative compositions: underdoped (Ti$_{0.05}$-CVS) and optimally doped (Ti$_{0.22}$-CVS). Using zero-field, high-field, and high-pressure $\mu$SR, we find spontaneous time-reversal-symmetry (TRS) breaking in the normal state of both compositions, strongly enhanced by an applied magnetic field and associated with long-range and short-range charge-order correlations, respectively. In the superconducting state, both samples exhibit anisotropic nodeless pairing with low superfluid density. Hydrostatic pressure substantially enhances both $T_{\rm c}$ and the superfluid density (by $\sim$2.5), revealing a linear correlation between them and pointing to unconventional pairing. Above $\sim$1 GPa, a crossover from anisotropic to isotropic nodeless pairing is observed. Despite the different nature of charge order in the two doping regimes, the superconducting responses are remarkably similar, suggesting that the competition between superconductivity and charge order occurs on a local scale, largely independent of the long-range coherence of the charge-ordered state.

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arXiv2026

The stripe state at 1/8 Ba doping hosts optimal superconductivity in La-214 cuprates under low in-plane stress

The cuprate system La$_{2-x}$Ba$_{x}$CuO$_{4}$ (LBCO) exhibits a pronounced sensitivity to in-plane uniaxial stress, particularly near the 1/8 doping anomaly, where stripe order strongly suppresses bulk superconductivity. While previous studies have focused on compositions close to 0.125, the commensurate $x$=0.125 phase remains largely unexplored under symmetry-selective lattice tuning. Here, we combine muon-spin rotation (${\mu}$SR), AC susceptibility, and electrical resistivity to investigate superconductivity, spin-stripe order, and structural response in LBCO-0.125 under in-plane uniaxial stress applied 45$^\circ$ to the Cu-O bond direction. Complementary resistivity measurements on $x$=0.115 and 0.135 track the evolution across both sides of the anomaly. We observe a giant enhancement of the bulk superconducting transition temperature in LBCO-0.125, increasing from 5 K to 37 K under 0.5 GPa. While the onset temperature of spin-stripe order decreases only modestly, the magnetic volume fraction is reduced by about a factor of two, with local order preserved. Simultaneously, the resistivity peak associated with the LTT phase is fully suppressed across all dopings. These results demonstrate that suppression of the LTT phase and reduction of the static spin-stripe-ordered volume fraction are crucial for the development of optimal three-dimensional superconductivity. Strikingly, the composition $x$=0.125, with the most robust stripe stability and the lowest ambient-pressure $T_{\rm c}$ develops the highest $T_{\rm c}$ under stress, reaching a zero-resistance state at 37 K and an onset of the superconducting transition as high as 46 K. This behavior indicates that stripe-related interactions enhance pairing strength, while static stripe order competes with superconductivity primarily at the level of phase coherence rather than pairing itself.

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arXiv2026

Divergent Pressure Response of Superconductivity in Sc$_{6}$MTe$_{2}$ ($M$ = Fe, Ru and Ir)

Identifying and understanding non-BCS superconductivity remains a central challenge in condensed-matter physics. Here we focus on the Sc$_{6}$MTe$_{2}$ family (M =d-electron metal), which provides a unique platform of isostructural compounds exhibiting superconductivity across 3d, 4d, and 5d systems. Using hydrostatic pressure as an additional tuning parameter, muon-spin rotation (${\mu}$SR) and AC susceptibility measurements uncover strongly contrasting pressure responses of superconductivity across the Sc$_{6}$MTe$_{2}$ series. The superconducting transition temperature, $T_{\rm C}$ decreases under pressure in the 3d Fe-based compound but increases for the 4d Ru- and 5d Ir-based systems, with the Ru compound showing the largest enhancement of nearly 50% within 2 GPa. The superfluid density exhibits similarly distinct pressure dependences, remaining nearly pressure independent for Fe while decreasing with increasing pressure for Ru and Ir. This suggests fundamentally different correlations between $T_{\rm C}$ and the superfluid density. Together, these results indicate that superconductivity emerging from strongly correlated and spin-orbit-dominated regimes in Sc$_{6}$MTe$_{2}$ is likely governed by different microscopic mechanisms and offer a useful experimental basis for future microscopic theoretical studies.

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arXiv2025

Distinct Uniaxial Stress and Pressure Fingerprint of Superconductivity in the 3D Kagome Lattice Compound CeRu2

The exploration of tunable superconductivity in strongly correlated electron systems is a central pursuit in condensed matter physics, with implications for both fundamental understanding and potential applications. The Laves phase CeRu$_{2}$, a pyrochlore compound, exhibits a three-dimensional (3D) Kagome lattice type geometry giving rise to flat bands and degenerate Dirac points, where band structure features intertwine with strong multi-orbital interaction effects deriving from its correlated electronic structure. Here, we combine muon spin rotation ($μ$SR), uniaxial in-plane stress, and hydrostatic pressure to probe the superconducting state of CeRu$_{2}$. Uniaxial stress up to 0.22 GPa induces a dome-shaped evolution of the critical temperature $T_{\rm c}$, with an initial plateau, successively followed by enhancement and suppression without any structural phase transition. Stress is further found to drive a crossover from anisotropic to isotropic $s$-wave pairing. In contrast, hydrostatic pressure up to 2.2 GPa leaves $T_{\rm c}$ largely unchanged but alters the superfluid density from exponential to linear behavior at low temperatures, indicative of nodal superconductivity under hydrostatic pressure. Taken together, these results indicate that CeRu$_{2}$ occupies an ideal position in parameter space, enabling highly responsive and multifold tunability of superconductivity in this three-dimensional correlated electronic system. This warrants further quantitative analysis of the interplay between lattice geometry, electronic correlations, and pairing symmetry.

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arXiv2025

Discovery of High-Temperature Charge Order and Time-Reversal Symmetry-Breaking in the Kagome Superconductor YRu3Si2

The identification of high-temperature unconventional charge order and superconductivity in kagome quantum materials is pivotal for deepening our understanding of geometrically frustrated and correlated electron systems, and for harnessing their exotic properties in future quantum technologies. Here, we report the discovery of a remarkably rich phase diagram in the kagome superconductor YRu$_{3}$Si$_{2}$, uncovered through a unique combination of muon spin rotation ($μ$SR), magnetotransport, X-ray diffraction (XRD), and density functional theory (DFT) calculations. Our study reveals the emergence of a charge-ordered state with a propagation vector of (1/2, 0, 0), setting a record onset temperature of 800 K for such an order in a kagome system and for quantum materials more broadly. In addition, we observe time-reversal symmetry (TRS) breaking below $T_{2}^{*}$ ${\simeq}$ 25 K and field-induced magnetism below $T_{1}^{*}$ ${\simeq}$ 90 K, indicating the presence of a hidden magnetic state. These transitions are mirrored in the magnetoresistance data, which show a clear onset at ${\sim}$ $T_{1}^{*}$ and a pronounced increase below ${\sim}$ $T_{2}^{*}$, ultimately reaching a maximum magnetoresistance of 45${\%}$. Band structure calculations identify two van Hove singularities (VHSs) near the Fermi level, one of which resides within a flat band, suggesting a strong interplay between electronic correlations and emergent orders. At low temperatures, we find bulk superconductivity below $T_{\rm c}$ = 3.4 K, characterized by a pairing symmetry with either two isotropic full gaps or an anisotropic nodeless gap. Together, our findings point to a coexistence of high-temperature charge order, tunable magnetism, and multigap superconductivity in YRu$_{3}$Si$_{2}$, positioning it as a compelling platform for exploring correlated kagome physics.

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arXiv2025

Fluctuating magnetism in Zn-doped averievite with well-separated kagome layers

Kagome lattice decorated with S=1/2 spins is one of the most discussed ways to realize a quantum spin liquid. However, all previous material realizations of this model have suffered from additional complications, ranging from additional interactions to impurity effects. Recently, a new quantum kagome system has been identified in the form of averievite Cu(5-x)ZnxV2O10(CsCl), featuring a unique double-layer spacing between the kagome planes. Using muon spin spectroscopy we show that only a complete substitution (i.e. $x=2$) of interplanar copper ions leads to a quantum-disordered ground state. In contrast, the parent compound ($x=0$) exhibits long-range magnetic order, with a phase transition around 24 K. Experiments performed on the partially substituted material ($x=1$) show that the transformation proceeds through an intermediate disordered, partially frozen ground state, unaffected by pressures up to 23 kbar. Our study provides a microscopic view of the magnetism of the decoupling of the kagome layers and establishes the averievite as a new material platform for the experimental study of the fully-decoupled kagome layers.

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arXiv2025

Anisotropic superconductivity in the quasi-one-dimensional superconductor V$_2$Ga$_5$

The intermetallic quasi-one-dimensional binary superconductor V$_2$Ga$_5$ was recently found to exhibit a topologically nontrivial normal state, making it a natural candidate for a topological superconductor (TSC). By combining dc-magnetization, nuclear magnetic resonance (NMR), and muon-spin rotation ({$μ$SR) measurements on high-quality V$_2$Ga$_5$ single crystals, we investigate the electronic properties of its normal- and superconducting (SC) ground states. NMR measurements in the normal state indicate a strong anisotropy in both the line shifts and the relaxation rates. Such anisotropy persists also in the superconducting state, as shown by the magnetization- and $μ$SR-spectroscopy results. In the latter case, data collected at different temperatures, pressures, and directions of the magnetic field evidence a fully-gapped, strongly anisotropic superconductivity. At the same time, hydrostatic pressure is shown to only lower the $T_c$ value, but not to change the superfluid density nor its temperature dependence. Lastly, we discuss the search for topological signatures in the normal state of V$_2$Ga$_5$, as well as a peak splitting in the FFT of the $μ$SR spectrum, possibly related to an unconventional vortex lattice. Our results suggest that V$_2$Ga$_5$ is a novel system, whose anisotropy plays a key role in determining its unusual electronic properties.

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arXiv2025

Competing Quantum Orders in 6R-TaS$_2$: Unconventional Superconductivity, Charge Order, and an Anomalous Hall Effect phase

The transition metal dichalcogenide 6R-TaS$_{2}$ offers a natural platform for studying the interplay among charge density wave (CDW) order, superconductivity, and transport anomalies. Recent findings reveal that, in the intermediate temperature range between charge order and superconductivity, a hidden order emerges around $T^{*}$ ${\simeq}$ 35 K-as evidenced by strong magnetoresistance and an anomalous Hall effect (AHE). However, the nature of the superconducting pairing, the hidden order, and their relationship with the CDW remain unclear. Using $μ$SR, magnetotransport, susceptibility, and hydrostatic pressure techniques, we identify a nodal superconducting state with low superfluid density at ambient pressure, with no spontaneous magnetic order detected below $T^{*}$. This indicates that the AHE originates from the band structure rather than magnetism. Under pressures up to 2 GPa, the superfluid density rises markedly in correlation with the superconducting transition temperature, the nodal pairing shifts to a nodeless state, and the CDW onset is reduced by half. Notably, AHE is fully suppressed and magnetoresistance drops by 50${\%}$ within just 0.2 GPa, highlighting the fragility of the hidden order. These results reveal an unconventional superconducting pairing in 6R-TaS$_{2}$, competing with both CDW and hidden orders through weakened interlayer coupling and competition for the same electronic states. With a multifaceted approach, we establish a comprehensive phase diagram that reveals the intricate interplay and competition between the intertwined quantum orders in 6R-TaS$_{2}$.

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arXiv2025

Contrasting $c$-axis and in-plane uniaxial stress effects on superconductivity and stripe order in La$_{1.885}$Ba$_{0.115}$CuO$_4$

The cuprate superconductor La$_{2-x}$Ba$_x$CuO$_4$ (LBCO) near $x=0.125$ is a striking example of intertwined electronic orders, where 3D superconductivity is anomalously suppressed, allowing spin and charge stripe order to develop, in a manner consistent with the emergence of a pair-density-wave (PDW) state. Understanding this interplay remains a key challenge in cuprates, highlighting the necessity of external tuning for deeper insight. While in-plane (within the CuO plane) uniaxial stress enhances superconductivity and suppresses stripe order, the effects of $c$-axis compression (perpendicular to the CuO plane) remains largely unexplored. Here, we use muon spin rotation ($μ$SR) and AC susceptibility with an in situ piezoelectric stress device to investigate the spin-stripe order and superconductivity in LBCO-0.115 under $c$-axis compression. The measurements reveal a gradual suppression of the superconducting transition temperature ($T_{\rm c}$) with increasing $c$-axis stress, in stark contrast to the strong enhancement observed under in-plane stress. We further show that while in-plane stress rapidly reduces both the magnetic volume fraction ($V_{\rm m}$) and the spin-stripe ordering temperature ($T_{\rm so}$), $c$-axis compression has no effect, with $V_{\rm m}$ and $T_{\rm so}$ exhibiting an almost unchanged behavior up to the highest applied stress of 0.21 GPa. These findings demonstrate a strong anisotropy in stress response, underscoring the critical role of crystallographic anisotropy in governing competing electronic phases in LBCO.

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arXiv2024

Pressure-Induced Enhancement of Superfluid Density in Transition Metal Dichalcogenides with and without Charge Density Wave

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,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 and magnetotransport experiments investigating the effects of hydrostatic pressure on the superconducting transition temperature ($T_{\rm c}$), the temperature-dependent magnetic penetration depth ($λ_\mathrm{eff}$), 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 maximum applied pressure of 2 GPa, surpassing that of 2H-NbSe$_{2}$. Despite the absence of CDW order, a sizeable 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 $T_{\rm c}$ exhibits an unconventional correlation, indicating a noteworthy similarity with the behavior observed in cuprate, kagome, and iron-based superconductors.

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arXiv2024

Pressure induced transition from chiral charge order to time-reversal symmetry-breaking superconducting state in Nb-doped CsV$_3$Sb$_5$

The experimental realisation of unconventional superconductivity and charge order in kagome systems \textit{A}V$_3$Sb$_5$ is of critical importance. We conducted a highly systematic study of Cs(V$_{1-x}$Nb$_x$)$_3$Sb$_5$ with $x$=0.07 (Nb$_{0.07}$-CVS) by employing a unique combination of tuning parameters such as doping, hydrostatic pressure, magnetic fields, and depth, using muon spin rotation, AC susceptibility, and STM. We uncovered tunable magnetism in the normal state of Nb$_{0.07}$-CVS, which transitions to a time-reversal symmetry (TRS) breaking superconducting state under pressure. Specifically, our findings reveal that the bulk of Nb$_{0.07}$-CVS (at depths greater than 20 nm from the surface) experiences TRS breaking below $T^*=40~$K, lower than the charge order onset temperature, $T_\mathrm{CO}$ = 58 K. However, near the surface (within 20 nm from the surface), the TRS breaking signal doubles and onsets at $T_\mathrm{CO}$, indicating that Nb-doping decouples TRS breaking from charge order in the bulk but synchronises them near the surface. Additionally, Nb-doping raises the superconducting critical temperature $T_\mathrm{C}$ from 2.5 K to 4.4 K. Applying hydrostatic pressure enhances both $T_\mathrm{C}$ and the superfluid density by a factor of two, with a critical pressure $p_\mathrm{cr}$ ${\simeq}$ 0.85 GPa, suggesting competition with charge order. Notably, above $p_\mathrm{cr}$, we observe nodeless electron pairing and weak internal fields below $T_\mathrm{C}$, indicating broken TRS in the superconducting state. Overall, these results demonstrate a highly unconventional normal state with a depth-tunable onset of TRS breaking at ambient pressure, a transition to TRS-breaking superconductivity under low hydrostatic pressure, and an unconventional scaling between $T_\mathrm{C}$ and the superfluid density.

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arXiv2024

Origin of the suppression of magnetic order in MnSi under hydrostatic pressure

We experimentally study the evolution of the magnetic moment $m$ and exchange interaction $J$ as a function of hydrostatic pressure in the zero-field helimagnetic phase of the strongly correlated electron system MnSi. The suppression of magnetic order at $\approx 1.5$~GPa is shown to arise from the $J$ collapse and not from a quantum fluctuations induced reduction of $m$. Our work provides benchmarks for first principles theories that are challenged by the presence of strong correlations and the possible role of Hund's coupling. In addition, our experimental data are consistent with a reorientation of the magnetic propagation wavevector recently evidenced above $\approx 1.2$~GPa. This result calls for a thorough investigation of the crystal structure in this pressure range.

cond-mat.str-el↗

arXiv2024

Hydrostatic and chemical pressure driven crossover from commensurate to the incommensurate state of the Weyl semimetal Mn$_{3+x}$Sn$_{1-x}$

The observation of large intrinsic anomalous Hall conductivity (AHC) in the non-collinear antiferromagnetic (AFM) phase of the Weyl semimetal Mn$_3$Sn generates enormous interest in uncovering the entanglement between the real space magnetic ordering and the momentum space band structure. Previous studies show that changes in the magnetic structure induced by the application of hydrostatic and chemical pressure can significantly affect the AHC of Mn$_{3+x}$Sn$_{1-x}$ system. Here, we employ the muon spin relaxation/rotation ($μ^+$SR) technique to systematically investigate the evolution of different magnetic states in the Mn$_{3+x}$Sn$_{1-x}$ as a function of hydrostatic and chemical pressure. We find two muon sites experimentally, which is also supported by our \textit{ab initio} calculations. Our $μ^+$SR experiments affirm that the $x = 0.05$ compound exhibits a commensurate magnetic state throughout the magnetically ordered phase below the Neel temperature $T_N \approx 420$~K in ambient pressure. In contrast, we observe an incommensurate magnetic state below $T_{IC} \sim 175$~K when a hydrostatic pressure of 1.5~GPa is applied. A similar transition from the commensurate to incommensurate state is also found with chemical pressure for $x = 0.04$ and $x = 0.03$, using $μ^+$SR and elastic neutron scattering experiments. Using band structure calculations, we have shown the emergence of Fermi nesting in Mn$_3$Sn and the subsequent development of incommensurate magnetic ordering under hydrostatic/chemical pressure.

cond-mat.str-el↗

arXiv2024

Evidence chain for time-reversal symmetry-breaking kagome superconductivity

Superconductivity and magnetism are antagonistic quantum matter, while their intertwining has long been considered in frustrated-lattice systems1-3. In this work, we utilize scanning tunneling microscopy and muon spin resonance to discover time-reversal symmetry-breaking superconductivity in kagome metal Cs(V,Ta)3Sb5, where the Cooper pairing exhibits magnetism and is modulated by it. In the magnetic channel, we observe spontaneous internal magnetism in a full-gap superconducting state. Under perturbations of inverse magnetic fields, we detect a time-reversal asymmetrical interference of Bogoliubov quasi-particles at a circular vector. At this vector, the pairing gap spontaneously modulates, which is distinct from pair density waves occurring at a point vector and consistent with the theoretical proposal of unusual interference effect under time-reversal symmetry-breaking. The correlation between internal magnetism, Bogoliubov quasi-particles, and pairing modulation provides a chain of experimental clues for time-reversal symmetry-breaking kagome superconductivity.

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arXiv2024

Microscopic study of the impurity effect in the kagome superconductor La(Ru$_{1-x}$Fe$_{x}$)$_{3}$Si$_{2}$

We report on the effect of magnetic impurities on the microscopic superconducting (SC) properties of the kagome-lattice superconductor La(Ru$_{1-x}$Fe$_{x}$)$_{3}$Si$_{2}$ using muon spin relaxation/rotation. A strong suppression of the superconducting critical temperature $T_{\rm c}$, the SC volume fraction, and the superfluid density was observed. We further find a correlation between the superfluid density and $T_{\rm c}$ 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.

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arXiv2024

Charge orders with distinct magnetic response in a prototypical kagome superconductor LaRu$_{3}$Si$_{2}$

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 $T_{\rm CO,2}$.

cond-mat.supr-con↗

arXiv2024

Depth-dependent study of time-reversal symmetry-breaking in the kagome superconductor $A$V$_{3}$Sb$_{5}$

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.

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