arXiv subjects

Rustem Khasanov

Publications and source records attributed to Rustem Khasanov.

At least 19 recordsLinked to original sources

arXiv2026

Anomalous field evolution of the mixed-state linewidth in the second superconducting dome of LaFeAsO$_{1-x}M_x$ ($M={\rm F,H}$)

We report a transverse-field muon-spin rotation/relaxation ($\mu$SR) study of the internal-field distribution in the mixed state of LaFeAsO$_{0.89}$F$_{0.11}$ and LaFeAsO$_{0.75}$H$_{0.25}$, representative of the first (SC1) and second (SC2) superconducting domes of the LaFeAsO$_{1-x}M_x$ ($M={\rm F,H}$) family, respectively. Below the superconducting transition temperature $T_{\rm c}$, the linewidth of the internal-field distribution increases in both samples, indicating the formation of a vortex lattice. Above $T_{\rm c}$, the linewidth remains field dependent and increases approximately linearly with field, consistent with broadening of the powder spectrum caused by an anisotropic Knight shift. After subtraction of this normal-state contribution, the superconducting linewidth $\sigma_{\rm sc}$ exhibits qualitatively different field dependences in the two samples. At 4K, the SC1 ($x_{\rm F}=0.11$) sample shows the expected monotonic decrease with increasing field, whereas the SC2 ($x_{\rm H}=0.25$) sample develops a pronounced local maximum near 3T. A contour representation of $\sigma_{\rm sc}(T,H)$ further reveals a ridge of local maxima whose field position, $H_{\sigma,\max}(T)$, shifts to lower fields upon warming and disappears near $T_{\rm c}$. The anomalous field evolution observed in the SC2 sample is consistent with an additional field-induced contribution associated with enhanced Pauli-paramagnetic effects, highlighting the distinct electronic character of the two superconducting domes.

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arXiv2026

Density waves in low-pressure bilayer nickelates

The low-pressure phase diagram of La$_3$Ni$_2$O$_7$ provides an important reference for understanding its pressure-induced high-temperature superconductivity. While the spin-density-wave transition at $T_{\text{SDW}}\approx150$ K is increasingly well established, the origin of the second density-wave transition at $T_{\text{DW}}\approx130$ K has remained unresolved. Here, we perform unrestricted Hartree-Fock calculations to investigate the potential origin of the second transition. {Within the orthorhombic phase, the degeneracy between possible ordering wavevectors at $\boldsymbol{Q}_{Y}=(0,\pi)$ and at $\boldsymbol{Q}_{X}=(\pi,0)$ is lifted and the electronic system} develops a double-stripe spin-density wave with ordering vector $\boldsymbol{Q}_{Y}=(0,\pi)$. We identify that the pure double stripe spin state is unstable in La$_3$Ni$_2$O$_7$ towards a commensurate charge-density wave instability, which favors a spin-modulated double stripe order with intertwined charge and spin instabilities and establish the hierarchy of ordered states in La$_3$Ni$_2$O$_7$. We further discuss our results in the context of available experimental literature and propose further experimental tests to elucidate the origin of the SDW/DW states in this system.

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arXiv2026

$\mu$SR study of time-reversal symmetry constraints and bulk superfluid response in Li$_{0.95}$FeAs

We report zero-field (ZF) and transverse-field (TF) muon-spin rotation/relaxation ($\mu$SR) measurements on superconducting Li$_{0.95}$FeAs ($T_{\rm c}\simeq16.0$ K) grown by a high-pressure self-flux method. The ZF-$\mu$SR data show no detectable change of the electronic relaxation rate on cooling through $T_{\rm c}$, providing no evidence for time-reversal-symmetry breaking in the superconducting state. TF-$\mu$SR measurements reveal a well-developed vortex response with strong flux pinning and a negligible nonsuperconducting contribution, confirming that superconductivity is a bulk property of the sample. From the second moment of the internal field distribution we determine a low-temperature in-plane magnetic penetration depth $\lambda_{ab}= 245(15)$ nm. The temperature dependence of the normalized superfluid density is well described by an effective two-gap model with $\Delta_1 = 2.0(2)$ meV and $\Delta_2 = 0.7(2)$ meV. A quantitative comparison with ARPES-based band weights shows that the $\mu$SR response is dominated by the Fermi-surface sheets carrying the intermediate and small superconducting gaps, whereas the band hosting the largest gap contributes only about 3\% to the total superfluid density and is therefore not resolved in the present analysis. Taken together, these results establish Li$_{0.95}$FeAs as a bulk multigap superconductor without detectable time-reversal symmetry breaking and show how $\mu$SR reconciles the gap scales reported by bulk and surface-sensitive probes in this multiband system.

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arXiv2026

Type-II superconductivity in the Dirac semimetal PdTe2

We report on the microscopic superconducting properties of the Dirac semimetal PdTe2. In this study, we have focused on mosaic crystals of PdTe2, and used detailed zero field and transverse field muon spin relaxation/rotation ($\mu$SR), ac-magnetic susceptibility, and resistivity measurements to investigate their superconducting properties. The magnetic susceptibility measurements reveal two superconducting transition temperatures at 1.8 and 1.6~K, respectively, in agreement with earlier reports. In contrary to these reports, we find that these mosaic PdTe2 crystals, are not type-I, but rather type-II superconductors. In fact, we observe the clear manifestation of a flux line lattice through a clear diamagnetic shift and Gaussian broadening of the Fourier spectra in the superconducting state. This behavior is likely caused by the disorder in the mosaic crystals of PdTe2 studied here. Our analysis of the superconducting order parameter by the means of temperature dependent magnetic penetration depth $\lambda(T)$ reveals a fully gapped superconducting state that can be well-fitted using an s-wave symmetric gap. We find that PdTe2 is a promising model system for the investigation and interplay of non-trivial topology, surface superconductivity, and type-II bulk superconductivity in a van-der-Waals material. Moreover, our results indicate that the superconductivity in this material can be easily modified from type-I to type-II by disorder in the system.

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arXiv2026

Thermodynamic evidence for a pressure-driven crossover from strong- to weak-coupling superconductivity in Pb

The thermodynamic critical field $B_{\rm c}$ provides direct access to the superconducting condensation energy, yet its pressure dependence has been studied much less extensively than that of the transition temperature. Here, muon-spin-rotation/relaxation measurements of the thermodynamic critical field $B_{\rm c}$ of elemental Pb under hydrostatic pressure up to $\simeq2.3$ GPa are reported. From the magnetic-field distribution in the intermediate state, $B_{\rm c}(T)$ is determined and $B_{\rm c}(0)$ is extracted at different pressures. In combination with previously reported high-pressure data for $B_{\rm c}$ and $T_{\rm c}$, it is shown that the pressure dependence of $B_{\rm c}(0)$ follows that of the superconducting gap $\Delta(0)$ more closely than that of the transition temperature $T_{\rm c}$. At higher pressures, the logarithmic pressure derivatives of $B_{\rm c}(0)$ and $T_{\rm c}$ are found to converge, indicating that the coupling strengths ratio $\alpha=\Delta(0)/k_{\rm B}T_{\rm c}$ becomes nearly pressure independent. This behavior is interpreted as thermodynamic evidence for a pressure-driven crossover from strong- to weak-coupling superconductivity in Pb.

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arXiv2026

Pressure-Invariant Isotope Effect as Evidence for Electronically Driven Intertwined Order in Pr$_4$Ni$_3$O$_{10}$

We report muon-spin rotation measurements of the pressure dependence of the oxygen-isotope ($^{16}$O/$^{18}$O) effect on the spin-density wave (SDW) transition in the trilayer Ruddlesden-Popper nickelate Pr$_4$Ni$_3$O$_{10}$. At ambient pressure, the SDW transition shows a finite isotope shift, with $^{16}T_{\rm SDW}=158.04(5)$ K and $^{18}T_{\rm SDW}=159.81(6)$ K. Under hydrostatic pressure, $T_{\rm SDW}$ decreases linearly at nearly identical rates for the two isotope compositions, ${\rm d}\,^{16}T_{\rm SDW}/{\rm d}p=-4.93(5)$ K/GPa and ${\rm d}\,^{18}T_{\rm SDW}/{\rm d}p=-4.90(7)$ K/GPa, such that the isotope shift remains essentially unchanged under compression. The absence of pressure enhancement of the isotope effect points to a predominantly electronic origin of the SDW transition and is consistent with recent inelastic x-ray scattering results, suggesting a new regime of intertwined order in trilayer RP nickelates, which is stabilized by strong spin interactions.

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arXiv2026

Multiple Magnetic Transitions in the Trilayer Nickelate Pr$_4$Ni$_3$O$_{10}$ Revealed by Muon-Spin Rotation

A muon-spin rotation/relaxation ($\mu$SR) study of the trilayer Ruddlesden--Popper nickelate Pr$_4$Ni$_3$O$_{10}$ was performed at ambient pressure and under hydrostatic pressure up to 2.2 GPa. Three magnetic transitions were identified at ambient pressure: the onset of spin-density-wave (SDW) order at $T_{\rm SDW} \simeq 158$ K, an intermediate-temperature transition at $T^{\ast} \simeq 90$--100 K, and a low-temperature transition at $T_{\rm SDW}^{\rm Pr} \simeq 25$--27 K. While the intermediate transition at $T^{\ast}$ induces only minor changes in the internal-field distribution, the transition at $T_{\rm SDW}^{\rm Pr}$ is accompanied by a pronounced reconstruction of the magnetic structure, consistent with previous reports attributing enhanced interlayer coherence to the ordering of the Pr sublattice. The high-temperature transition at $T_{\rm SDW}$ is characterized by the sharp development of static internal magnetic fields with a narrow transition width of $0.65(4)$ K. Weak-transverse-field measurements reveal a finite thermal hysteresis of $0.27(6)$ K, with $T_{\rm SDW}^{\rm warming} > T_{\rm SDW}^{\rm cooling}$, indicating weakly first-order-like behavior. Hydrostatic pressure suppresses $T_{\rm SDW}$ linearly and reduces the ordered Ni magnetic moment $M$, with corresponding rates of ${\rm d}T_{\rm SDW}/{\rm d}p = -4.9(1)$ K/GPa and ${\rm d}\ln M/{\rm d}p = -2.0(5)\times10^{-2}$ GPa$^{-1}$, respectively, thereby demonstrating a gradual weakening of the spin-density-wave instability under compression.

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arXiv2025

Origins of spontaneous magnetic fields in Sr$_2$RuO$_4$

The nature of the broken time reversal symmetry (BTRS) state in Sr$_2$RuO$_4$ remains elusive, and its relation to superconductivity remains controversial. There are various universal predictions for the BTRS state when it is associated with a multicomponent superconducting order parameter. In particular, in the BTRS superconducting state, spontaneous fields appear around crystalline defects, impurities, superconducting domain walls and sample surfaces. However, this phenomenon has not yet been experimentally demonstrated for any BTRS superconductor. Here, we aimed to verify these predictions for Sr$_2$RuO$_4$ by performing muon spin relaxation ($\mu$SR) measurements on Sr$_{2-y}$La$_{y}$RuO$_4$ single crystals at ambient pressure and stoichiometric Sr$_2$RuO$_4$ under hydrostatic pressure. The study allowed us to conclude that spontaneous fields in the BTRS superconducting state of Sr$_2$RuO$_4$ appear around non-magnetic inhomogeneities and, at the same time, decrease with the suppression of $T_{\rm c}$. The observed behaviour is consistent with the prediction for multicomponent BTRS superconductivity in Sr$_2$RuO$_4$. The results of the work are relevant to understanding BTRS superconductivity in general, as they demonstrate, for the first time, the relationship among the superconducting order parameter, the BTRS transition, and crystal-structure inhomogeneities.

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arXiv2025

Magnetism of the alternating monolayer-trilayer phase of La$_3$Ni$_2$O$_7$

Understanding the magnetic ground state of Ruddlesden-Popper nickelates is crucial, as these materials exhibit superconductivity under high pressure and host competing electronic orders that may play a key role in the pairing mechanism. In this work, we investigate the magnetic properties of the alternating monolayer-trilayer phase of La$_3$Ni$_2$O$_7$ (1313-La$_3$Ni$_2$O$_7$) using muon-spin rotation/relaxation ($\mu$SR) under both ambient and hydrostatic pressure conditions. The monolayer-trilayer phase develops incommensurate magnetic order below approximately 150 K, with a mean ordering temperature of $T_{SDW} \simeq 123$ K and a transition width of $\Delta T_{SDW} \simeq 15$ K. The abrupt onset of the internal magnetic field indicates a first-order-like transition. Hydrostatic pressure ($p$) suppresses the magnetic ordering temperature at a rate of $dT_{SDW}/d p \simeq -3.9$ K/GPa, demonstrating a progressive destabilization of the ordered state. By comparison with the bilayer 2222-La$_3$Ni$_2$O$_7$ and the trilayer 3333-La$_4$Ni$_3$O$_{10}$ systems, and within a unified phenomenological framework, systematic trends are identified linking the pressure dependence of $T_{SDW}$, the (in)commensurability of the magnetic order, and the character of the magnetic transition. These trends consistently indicate a gradual reduction of electronic correlation strength from the bilayer to the monolayer-trilayer and trilayer nickelates. This hierarchy suggests that the higher superconducting transition temperature observed in the 2222 phase may be closely connected to its more strongly correlated electronic nature. These results position the alternating monolayer-trilayer 1313-La$_3$Ni$_2$O$_7$ as an intermediate member linking the magnetic behavior of the bilayer 2222-La$_3$Ni$_2$O$_7$ and the trilayer 3333-La$_4$Ni$_3$O$_{10}$ Ruddlesden-Popper compounds.

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arXiv2025

Muon Knight shift as a precise probe of the superconducting symmetry of Sr$_2$RuO$_4$

Muon spin rotation ($\mu$SR) measurements of internal magnetic field shifts, known as the muon Knight shift, is used for determining pairing symmetries in superconductors. While this technique has been especially effective for $f$-electron-based heavy-fermion superconductors, it remains challenging in $d$-electron-based superconductors such as Sr$_2$RuO$_4$, where the Knight shift is intrinsically small. Here, we report high-precision muon Knight shift measurements of superconducting Sr$_2$RuO$_4$. We observe that using multiple pieces of crystals, a common practice in $\mu$SR measurements, induces a substantial paramagnetic shift below the superconducting transition temperature, $T_c$, when a weak magnetic field is applied. We attribute such an unresolved paramagnetic shift to stray fields generated by neighboring diamagnetic crystals. To avoid this, one piece of crystal was used in this study. We experimentally determine the muon Knight shift of Sr$_2$RuO$_4$ in the normal state to be -116$\pm$7 ppm. By combining the observed muon Knight shift with independently determined bulk magnetization data from the same crystal used in $\mu$SR and carefully separating various contributions to the shift, we confirm a significant reduction in the spin Knight shift below $T_c$, consistent with spin-singlet-like pairing. This result constitutes the precise muon Knight shift measurement in a $d$-electron-based superconductor. Our results highlight the potential of $\mu$SR as a powerful complementary technique to the established method of nuclear magnetic resonance for probing the spin susceptibility in superconductors.

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arXiv2025

Pressure tuning of competing interactions on a honeycomb lattice

Magnetic exchange interactions are mediated via orbital overlaps across chemical bonds. Thus, modifying the bond angles by physical pressure or strain can tune the relative strength of competing interactions. Here we present a remarkable case of such tuning between the Heisenberg (J) and Kitaev (K) exchange, which respectively establish magnetically ordered and spin liquid phases on a honeycomb lattice. We observe a rapid suppression of the Neel temperature (TN) with pressure in Ag3LiRh2O6, a spin-1/2 honeycomb lattice with both J and K couplings. Using a combined analysis of x-ray data and first-principles calculations, we find that pressure modifies the bond angles in a way that increases the |K/J| ratio and thereby suppresses TN. Consistent with this picture, we observe a spontaneous onset of muon spin relaxation (muSR) oscillations below TN at low pressure, whereas in the high-pressure phase, oscillations appear only when T < TN/2. Unlike other candidate Kitaev materials, Ag3LiRh2O6 is tuned toward a quantum critical point by pressure while avoiding a structural dimerization in the relevant pressure range.

cond-mat.str-el↗

arXiv2025

Oxygen-isotope effect on density wave transitions in La$_3$Ni$_2$O$_{7}$

TThe isotope effect is a powerful probe of electron-phonon interactions in solid-state systems, offering key insights into how atomic mass influences emergent quantum states. Here, the impact of oxygen isotope substitution ($^{16}{\rm O}\rightarrow \; ^{18}{\rm O}$) on charge- and spin-density wave (CDW and SDW) transitions in the double-layer Ruddlesden-Popper nickelate La$_3$Ni$_2$O$_7$ is investigated. A clear isotope effect is observed in the CDW transition: the transition temperature ($T_{\rm CDW}$) increases upon $^{18}$O substitution. In contrast, the SDW transition temperature remains unaffected within experimental uncertainty. These findings point to a strong involvement of lattice vibrations in the formation of charge order, while spin order appears to be predominantly of electronic origin. The results suggest that electron-phonon coupling, manifested through the CDW response to isotope substitution, may be relevant to the superconducting pairing mechanism in Ruddlesden-Popper nickelates.

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arXiv2025

Pressure Effect on the Spin Density Wave Transition in La$_2$PrNi$_2$O$_{6.96}$

High-pressure studies reveal a stark contrast between the superconducting properties of double-layer Ruddlesden-Popper (RP) nickelates La$_2$PrNi$_2$O$_7$ and La$_3$Ni$_2$O$_7$. While La$_2$PrNi$_2$O$_7$ exhibits bulk superconductivity, La$_3$Ni$_2$O$_7$ displays filamentary behavior, suggesting that superconductivity is confined to phase interfaces rather than the bulk. Since magnetism emerges near the superconducting phase, understanding its differences in La$_3$Ni$_2$O$_7$ and La$_2$PrNi$_2$O$_7$ is essential for clarifying their underlying electronic and magnetic properties. In this work we study the magnetic responce of La$_2$PrNi$_2$O$_{6.96}$ under pressures up to 2.3 GPa using the muon-spin rotation/relaxation ($\mu$SR) technique. The application of external pressure increases the N\'{e}el temperature $T_{\rm N}$ from approximately 161 K at ambient pressure ($p=0$) to about 170 K at $p=2.3$ GPa. The temperature dependence of the internal magnetic field $B_{\rm int}(T)$ (i.e., the magnetic order parameter) follows the power-law relation $B_{\rm int} = B_{\rm int}(0) \left(1 - \left[T/T_{\rm N}\right]^\alpha \right)^\beta$, with consistent exponent values of $\alpha\simeq 1.95$ and $\beta\simeq 0.35$ across different pressures. The value of the ordered moments at the Ni sites, which is proportional to $B_{\rm int}$, remain unaffected by pressure. Our findings suggest that the magnetic properties of double-layer RP nickelate La$_3$Ni$_2$O$_7$ are broadly unaffected by Pr to La substitution.

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arXiv2025

Unraveling Spin Density Wave Order in Layered Nickelates $\mathrm{La_3Ni_2O_7}$ and $\mathrm{La_2PrNi_2O_7}$ via Neutron Diffraction

The discovery of pressure-induced superconductivity in two- and three-layer Ruddlesden-Popper nickelates has generated significant interest in these materials as a platform for unconventional superconductivity. While their ground state exhibits magnetism, a direct determination of their magnetic structure remains elusive. Understanding this aspect is crucial, as magnetism may play a role in the pairing mechanism of superconductivity in these compounds. We resolve the magnetic structures of the bilayer (2222) polymorphs of La3Ni2O7 and La2PrNi2O7 using neutron powder diffraction (NPD) and muon-spin rotation/relaxation (muSR). Magnetic neutron scattering appears below approximately 150 K in both compounds and is observed at the (qx, 1/2, 0) position, with qx = 0 and 1/2 for La3Ni2O7 and qx = 0 for La2PrNi2O7. Within a single layer, alternating low (0.05 - 0.075 muB) and high (0.66 muB) magnetic moment stripes form. These layers stack antiferromagnetically along the c-direction to form bilayers. The presence of two propagation vectors (qx = 0 and 1/2) in undoped La3Ni2O7 suggests the coexistence of two magnetic stacking polymorphs within a single crystallographic phase. The muSR spectra further confirm these magnetic structures. Our findings provide a detailed understanding of the magnetic ground state in bilayer nickelates, offering insights into possible precursor states that may influence the emergence of superconductivity in these materials.

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arXiv2025

Effect of Pressure and Oxygen-Isotope Substitution on Density-Wave Transitions in La$_4$Ni$_3$O$_{10}$

Understanding the interplay between magnetism and superconductivity in nickelate systems is a key objective in condensed matter physics. Here, we present a systematic muon-spin rotation/relaxation ($\mu$SR) and resistivity study of the trilayer Ruddlesden-Popper nickelate La$_4$Ni$_3$O$_{10}$ under ambient and applied pressure, combined with oxygen-isotope substitution. At ambient pressure, two incommensurate spin-density-wave (SDW) transitions are identified at $T_{SDW}\simeq132$ K and $T^\ast\simeq80-90$ K. Comparison of the internal magnetic fields with dipole-field calculations reveals a magnetic structure consistent with antiferromagnetically coupled SDW order on the outer two Ni layers, with smaller moments on the inner layer. Above $T^\ast$, the moments lie mainly in the $ab$ plane, whereas below this temperature they develop a $c$-axis component. The internal fields at the muon stopping sites appear abruptly at $T_{SDW}$, suggesting a first-order-like SDW transition closely linked to the charge-density-wave (CDW) order occurring at the same temperature ($T_{SDW}=T_{CDW}$). Under pressure, all transition temperatures -- $T_{SDW}$, $T^\ast$, and $T_{CDW}$ -- are suppressed at a nearly uniform rate of $\simeq-13$ K/GPa. This contrasts with bilayer La$_3$Ni$_2$O$_7$, where pressure enhances the separation between the SDW and CDW transitions. Oxygen-isotope substitution ($^{16}$O $\rightarrow$ $^{18}$O) shifts $T_{CDW}$ to higher values. The isotope effect on $T_{SDW}$ and $T^\ast$ differs markedly: when CDW and SDW are intertwined, a notable isotope effect is observed on $T_{SDW}$, yielding nearly identical isotope shifts for $T_{CDW}$ and $T_{SDW}$, whereas no isotope effect is detected at $T^\ast$, where the SDW transition occurs independently of the CDW.

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arXiv2025

Emergence of a Fluctuating Ground State in Y-kapellasite under Pressure

Y-kapellasite (Y$_3$Cu$_9$(OH)$_{19}$Cl$_8$), which hosts an original anisotropic kagome sublattice, is a promising candidate for studying elusive and complex correlated physics. It exhibits a theoretically predicted in-plane $(1/3, 1/3)$ magnetic order [1] but its magnetic interaction values place it close to a phase boundary to a spin liquid state [2]. Our $\mu$SR measurements under hydrostatic pressure demonstrate the complete suppression of static magnetism in favor of a fully dynamical ground state at $2.3$~GPa. Complementary high-pressure x-ray and optical phonon measurements reveal a gradual reduction of the kagome anisotropy, enhancing magnetic frustration without structural transitions. Our results establish Y-kapellasite as a rare clean kagome model in which long-range order is suppressed by pressure-tuned frustration, the first fingerprint for the realization of a quantum spin liquid without strong disorder.

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arXiv2025

Influence of pressure on properties of multi-gap type-I superconductor BeAu

We report on studies of the superconducting and normal state properties of the noncentrosymmetric superconductor BeAu under hydrostatic pressure conditions. The room-temperature equation of state (EOS) reveals the values of the bulk modulus ($B_0$) and its first derivative ($B^\prime_0$) at ambient pressure to be $B_0 \simeq 132$~GPa and $B^\prime_0 \simeq 30$, respectively. Up to the highest pressures studied ($p \simeq 2.2$~GPa), BeAu remains a multi-gap type-I superconductor. The analysis of $B_{\rm c}(T, p)$ data within the self-consistent two-gap approach suggests the presence of two superconducting energy gaps, with the gap-to-$T_{\rm c}$ ratios $\Delta_1/k_{\rm B}T_{\rm c} \sim 2.3$ and $\Delta_2/k_{\rm B}T_{\rm c} \sim 1.1$ for the larger and smaller gaps, respectively [$\Delta = \Delta(0)$ is the zero-temperature value of the gap and $k_{\rm B}$ is the Boltzmann constant]. With increasing pressure, $\Delta_1/k_{\rm B}T_{\rm c}$ increases while $\Delta_2/k_{\rm B}T_{\rm c}$ decreases, suggesting that pressure enhances (weakens) the coupling strength between the superconducting carriers within the bands where the larger (smaller) superconducting energy gap has opened. The superconducting transition temperature $T_{\rm c}$, \textcolor{black}{the zero-temperature values of the superconducting gaps $\Delta_1$ and $\Delta_2$} and the zero-temperature value of the thermodynamic critical field $B_{\rm c}(0)$ decrease with increasing pressure, with the rates of ${\rm d}T_{\rm c}/{\rm d}p \simeq -0.195$~K/GPa, \textcolor{black}{${\rm d}\Delta_1/{\rm d}p \simeq -0.034$~meV/GPa, ${\rm d}\Delta_2/{\rm d}p \simeq -0.029$~meV/GPa,} and ${\rm d}B_{\rm c}(0)/{\rm d}p = -2.65(1)$~mT/GPa, respectively. The measured $B_{\rm c}(0)$ values plotted as a function of $T_{\rm c}$ follow an empirical scaling relation established for conventional type-I superconductors.

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arXiv2024

Pressure weakens coupling strength in In and Sn elemental superconductors

Pressure dependence of the thermodynamic critical field $B_{\rm c}$ in elemental indium (In) and tin (Sn) superconductors was studied by means of the muon-spin rotation/relaxation. Pressure enhances the deviation of $B_{\rm c}(T)$ from the parabolic behavior, expected for a typical type-I superconductor, suggesting a weakening of the coupling strengths $\alpha=\langle\Delta\rangle /k_{\rm B}T_{\rm c}$ ($\langle\Delta\rangle$ is the average value of the superconducting energy gap, $T_{\rm c}$ is the transition temperature and $k_{\rm B}$ is the Boltzmann constant). As pressure increases from 0.0 to $\simeq 3.0$ GPa $\alpha$ decreases linearly, by approaching the limiting weak-coupling BCS value $\alpha_{\rm BCS}=1.764$. Analysis of the data within the framework of the Eliashberg theory reveals that only part of the pressure effect on $\alpha$ can be attributed to the effect of hardening of the phonon spectra, which is reflected by a decrease of the electron-phonon coupling constant. Nearly 40% of the effect is caused by increased anisotropy of the superconducting energy gap.

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