Low-temperature Superfluid Density Research Articles

Superconductivity of Co-Doped CaKFe4As4 Investigated via Point-Contact Spectroscopy and London Penetration Depth Measurements.

The iron-based superconductors (IBSs) of the recently discovered 1144 class, unlike many other IBSs, display superconductivity in their stoichiometric form and are intrinsically hole doped. The effects of chemical substitutions with electron donors are thus particularly interesting to investigate. Here, we study the effect of Co substitution in the Fe site of CaKFe4As4 single crystals on the critical temperature, on the energy gaps, and on the superfluid density by using transport, point-contact Andreev-reflection spectroscopy (PCARS), and London penetration depth measurements. The pristine compound (Tc≃36 K) shows two isotropic gaps whose amplitudes (Δ1 = 1.4-3.9 meV and Δ2 = 5.2-8.5 meV) are perfectly compatible with those reported in the literature. Upon Co doping (up to ≈7% Co), Tc decreases down to ≃20 K, the spin-vortex-crystal order appears, and the low-temperature superfluid density is gradually suppressed. PCARS and London penetration depth measurements perfectly agree in demonstrating that the nodeless multigap structure is robust upon Co doping, while the gap amplitudes decrease as a function of Tc in a linear way with almost constant values of the gap ratios 2Δi/kBTc.

Exploring superconductivity in Ba3Ir4Ge16: Experimental and theoretical insights

We explore both experimental and theoretical aspects of the superconducting properties in the layered caged compound, Ba3Ir4Ge16. Our approach integrates muon spin rotation and relaxation (μSR) measurements with magnetization and heat capacity experiments, accompanied by first-principle calculations. The compound’s bulk superconductivity is unequivocally established through DC magnetization measurements, revealing a critical temperature (TC) of 5.7 K. A noteworthy characteristic observed in the low-temperature superfluid density is its saturating behavior, aligning with the features typical of conventional Bardeen-Cooper-Schrieffer (BCS) superconductors. The assessment of moderate electron-phonon coupling superconductivity is conducted through transverse field μSR measurements, yielding a superconducting gap to TC ratio (2Δ(0)∕kBTC) of 4.04, a value corroborated by heat capacity measurements. Crucially, zero field μSR measurements dismiss the possibility of any spontaneous magnetic field emergence below TC, highlighting the preservation of time-reversal symmetry. Our experimental results are reinforced by first-principles density functional calculations, underscoring the intricate interplay between crystal structure and superconducting order parameter symmetry in caged compounds. This comprehensive investigation enhances our understanding of the relationship between crystal structure and superconductivity in such unique compounds.

Multigap superconductivity in the Mo5PB2 boron–phosphorus compound

The tetragonal Mo5PB2 compound was recently reported to show superconductivity with a critical temperature up to 9.2 K. In search of evidence for multiple superconducting gaps in Mo5PB2, comprehensive measurements, including magnetic susceptibility, electrical resistivity, heat capacity, and muon-spin rotation and relaxation measurements were carried out. Data from both low-temperature superfluid density and electronic specific heat suggest a nodeless superconducting ground state in Mo5PB2. Two superconducting energy gaps Δ0 = 1.02 meV (25%) and 1.49 meV (75%) are required to describe the low-T electronic specific-heat data. The multigap features are clearly evidenced by the field dependence of the electronic specific-heat coefficient and the Gaussian relaxation rate in the superconducting state (i.e., superfluid density), as well as by the temperature dependence of the upper critical field. By combining our extensive experimental results with numerical band-structure calculations, we provide compelling evidence of multigap superconductivity in Mo5PB2.

Crossover from multiple- to single-gap superconductivity in Nb5Ir3−xPtxO alloys

By using mostly the muon-spin rotation/relaxation ($\mu$SR) technique, we investigate the superconductivity (SC) of Nb$_5$Ir$_{3-x}$Pt$_x$O ($x = 0$ and 1.6) alloys, with $T_c = 10.5$ K and 9.1 K, respectively. At a macroscopic level, their superconductivity was studied by electrical resistivity, magnetization, and specific-heat measurements. In both compounds, the electronic specific heat and the low-temperature superfluid density data suggest a nodeless SC. The superconducting gap value and the specific heat discontinuity at $T_c$ are larger than that expected from the Bardeen-Cooper-Schrieffer theory in the weak-coupling regime, indicating strong-coupling superconductivity in the Nb$_5$Ir$_{3-x}$Pt$_x$O family. In Nb$_5$Ir$_3$O, multigap SC is evidenced by the field dependence of the electronic specific heat coefficient and the superconducting Gaussian relaxation rate, as well as by the temperature dependence of the upper critical field. Pt substitution suppresses one of the gaps, and Nb$_5$Ir$_{1.4}$Pt$_{1.6}$O becomes a single-gap superconductor. By combining our extensive experimental results, we provide evidence for a multiple- to single-gap SC crossover in the Nb$_5$Ir$_{3-x}$Pt$_x$O family.

Strong- to weak-coupling superconductivity in high- Tc bismuthates: Revisiting the phase diagram via μSR

Several decades after the discovery of superconductivity in bismuthates, the strength of their electron-phonon coupling and its evolution with doping remain puzzling. To clarify these issues, polycrystalline hole-doped Ba$_{1-x}$K$_{x}$BiO$_3$ ($0.1 \le x \le 0.6$) samples were systematically synthesized and their bulk- and microscopic superconducting properties were investigated by means of magnetic susceptibility and muon-spin rotation/relaxation ($\mu$SR), respectively. The phase diagram of Ba$_{1-x}$K$_{x}$BiO$_3$ was reliably extended up to $x = 0.6$, which is still found to be a bulk superconductor. The lattice parameter $a$ increases linearly with K-content, implying a homogeneous chemical doping. The low-temperature superfluid density, measured via transverse-field (TF)-$\mu$SR, indicates an isotropic fully-gapped superconducting state with zero-temperature gaps $\Delta_0/k_\mathrm{B}T_c$ = 2.15, 2.10, and 1.75, and magnetic penetration depths $\lambda_0$ = 219, 184, and 279 nm for $x$ = 0.3, 0.4, and 0.6, respectively. A change in the superconducting gap, from a nearly ideal BCS value (1.76 $k_\mathrm{B}$$T_c$ in the weak coupling case) in the overdoped $x$ = 0.6 region, to much higher values in the optimally-doped case, implies a gradual decrease in electron-phonon coupling with doping.

Scaling between Superfluid Density and Tc in Overdoped La2−xSrxCuO4 Films

We used an electronic phase separation approach to interpret the scaling between the low-temperature superfluid density average ρ sc ( 0 ) and the superconducting critical temperature T c on overdoped La 2 − x Sr x CuO 4 films. Guided by the observed nematic and incommensurate charge ordering (CO), we performed simulations with a free energy that reproduces charge domains with wavelength λ C O and provides a scale to local superconducting interactions. Under these conditions a complex order parameter with amplitude Δ d ( r i ) and phase θ ( r i ) may develop at a domain i. We assumed that these domains are coupled by Josephson energy E J ( r i j ) , proportional to the local superfluid density ρ sc ( r i j ) . Long-range order occured when the average E J ( T c ) is ∼ k B T c . The linear ρ s c ( 0 ) vs. T c relation was satisfied whenever CO was present, even with almost vanishing charge amplitudes.

Nodeless superconductivity and preserved time-reversal symmetry in the noncentrosymmetric Mo3P superconductor

We report a comprehensive study of the noncentrosymmetric superconductor Mo$_3$P. Its bulk superconductivity, with $T_c = 5.5$ K, was characterized via electrical resistivity, magnetization, and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation/relaxation ($\mu$SR) and nuclear magnetic resonance (NMR) techniques. In the normal state, NMR relaxation data indicate an almost ideal metallic behavior, confirmed by band-structure calculations, which suggest a relatively high electron density of states, dominated by the Mo $4d$-orbitals. The low-temperature superfluid density, determined via transverse-field $\mu$SR and electronic specific heat, suggest a fully-gapped superconducting state in Mo$_3$P, with $\Delta_0= 0.83$ meV, the same as the BCS gap value in the weak-coupling case, and a zero-temperature magnetic penetration depth $\lambda_0 = 126$ nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined from zero-field $\mu$SR measurements, indicates a preserved time-reversal symmetry in the superconducting state of Mo$_3$P and, hence, spin-singlet pairing.

Time-Reversal Symmetry Breaking in Re-Based Superconductors.

To trace the origin of time-reversal symmetry breaking (TRSB) in Re-based superconductors, we performed comparative muon-spin rotation and relaxation (μSR) studies of superconducting noncentrosymmetric Re_{0.82}Nb_{0.18} (T_{c}=8.8 K) and centrosymmetric Re (T_{c}=2.7 K). In Re_{0.82}Nb_{0.18}, the low-temperature superfluid density and the electronic specific heat evidence a fully gapped superconducting state, whose enhanced gap magnitude and specific-heat discontinuity suggest a moderately strong electron-phonon coupling. In both Re_{0.82}Nb_{0.18} and pure Re, the spontaneous magnetic fields revealed by zero-field μSR below T_{c} indicate time-reversal symmetry breaking and thus unconventional superconductivity. The concomitant occurrence of TRSB in centrosymmetric Re and noncentrosymmetric ReT (T=transition metal), yet its preservation in the isostructural noncentrosymmetric superconductors Mg_{10}Ir_{19}B_{16} and Nb_{0.5}Os_{0.5}, strongly suggests that the local electronic structure of Re is crucial for understanding the TRSB superconducting state in Re and ReT. We discuss the superconducting order parameter symmetries that are compatible with the experimental observations.

Nodeless superconductivity in the noncentrosymmetric Mo3Rh2N superconductor: A μSR study

The noncentrosymmetric superconductor Mo$_3$Rh$_2$N, with $T_c = 4.6$ K, adopts a $\beta$-Mn-type structure (space group $P$4$_1$32), similar to that of Mo$_3$Al$_2$C. Its bulk superconductivity was characterized by magnetization and heat-capacity measurements, while its microscopic electronic properties were investigated by means of muon-spin rotation and relaxation ($\mu$SR). The low-temperature superfluid density, measured via transverse-field (TF)-$\mu$SR, evidences a fully-gapped superconducting state with $\Delta_0 = 1.73 k_\mathrm{B}T_c$, very close to 1.76 $k_\mathrm{B}T_c$ - the BCS gap value for the weak coupling case, and a magnetic penetration depth $\lambda_0 = 586$ nm. The absence of spontaneous magnetic fields below the onset of superconductivity, as determined by zero-field (ZF)-$\mu$SR measurements, hints at a preserved time-reversal symmetry in the superconducting state. Both TF-and ZF-$\mu$SR results evidence a spin-singlet pairing in Mo$_3$Rh$_2$N.

Magnetic-field-induced reduction of the low-temperature superfluid density in cuprate superconductors

The weak magnetic field induced reduction of the low-temperature superfluid density in cuprate superconductors is studied based on the kinetic energy driven superconducting mechanism. The electromagnetic response kernel is evaluated by considering both couplings of the electron charge and electron magnetic momentum with a weak magnetic field and employed to calculate the superfluid density, then the main features of the weak magnetic field induced reduction of the low-temperature superfluid density are well reproduced. The theory also shows that the striking behavior of the weak magnetic field induced reduction of the low-temperature superfluid density is intriguingly related to both depairing due to the Pauli spin polarization and nonlocal response in the vicinity of the d-wave gap nodes on the Fermi surface to a weak magnetic field.

Electromagnetic response of high-Tcsuperconductors: Slave-boson and doped-carrier theories

We evaluate the doping dependence of the quasiparticle current and low-temperature superfluid density in two slave-particle theories of the $t{t}^{\ensuremath{'}}{t}^{\ensuremath{''}}J$ model---the slave-boson theory and doped-carrier theory. In the slave-boson theory, the nodal quasiparticle current renormalization factor $\ensuremath{\alpha}$ proportionally vanishes to the zero temperature superfluid density ${\ensuremath{\rho}}_{S}(0)$; however, we find that away from the ${\ensuremath{\rho}}_{S}(0)\ensuremath{\rightarrow}0$ limit, $\ensuremath{\alpha}$ displays a much weaker doping dependence than ${\ensuremath{\rho}}_{S}(0)$. A similar conclusion applies to the doped-carrier theory, which differentiates the nodal and antinodal regions of momentum space. Due to its momentum space anisotropy, the doped-carrier theory enhances the value of $\ensuremath{\alpha}$ in the hole doped regime, bringing it to quantitative agreement with experiments, and reproduces the asymmetry between hole and electron doped cuprate superconductors. Finally, we use the doped-carrier theory to predict a specific experimental signature of local staggered spin correlations in doped Mott insulator superconductors, which, we propose, should be observed in scanning tunneling microscopy measurements of underdoped high-${T}_{c}$ compounds. This experimental signature distinguishes the doped-carrier theory from other candidate mean-field theories of high-${T}_{c}$ superconductors, such as the slave-boson theory and the conventional BCS theory.

Magnetic penetration depth and self-induced irradiation effects in superconducting [formula omitted] probed by muon spin rotation

Freshly prepared samples of PuCoGa 5 have the highest superconducting critical temperature T c ≅ 19 K of all f-electron superconductors. In addition, this material undergoes self-irradiation from the radioactive decay of the Pu nuclei. We report muon spin rotation ( μ SR ) measurements of the superconducting penetration depth λ in 400 day-old single crystalline samples of PuCoGa 5 ( T c ≅ 15.5 K ) , and compare these results to μ SR measurements taken on the same samples after only 25 days of aging ( T c ≅ 18.5 K ) , in order to elucidate the symmetry of the order parameter and its dependence on aging. The experiments show that the low-temperature superfluid density n s decreases linearly with increasing T in both fresh and aged PuCoGa 5 , consistent with a line of nodes in the order parameter.

Quantum Phase Transition in the BCS-to-BEC Evolution of p-wave Fermi Gases

We discuss the possibility of a quantum phase transition in ultra-cold spin-polarized Fermi gases which exhibit a p-wave Feshbach resonance. We show that when fermionic atoms form a condensate that can be externally tuned between the BCS and BEC limits, the zero temperature compressibility and the spin susceptibility of the fermionic gas are non-analytic functions of the two-body bound state energy. This non-analyticity is due to a massive rearrangement of the momentum distribution in the ground state of the system. Furthermore, we show that the low temperature superfluid density is also non-analytic and exhibits a dramatic change in behavior when the critical value of the bound state energy is crossed.

Field Induced Reduction of the Low-Temperature Superfluid Density inYBa2Cu3O6.95

A novel high magnetic field (8 T) spectrometer for muon spin rotation has been used to measure the temperature dependence of the in-plane magnetic penetration depth in YBa2Cu3O6.95. At low H and low T, the penetration depth exhibits the characteristic linear T dependence associated with the energy gap of a d_x^2-y^2-wave superconductor. However, at higher fields the penetration depth is essentially temperature independent at low T. We discuss possible interpretations of this surprising new feature in the low-energy excitation spectrum.

Two-dimensional superfluidity and localization in the hard-core boson model: A quantum Monte Carlo study.

Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled clean system becomes superfluid via a finite temperature Kosterlitz-Thouless transition. The relationship between low temperature superfluid density and particle density is symmetric and appears parabolic about the half filling point. Disorder appears to break the superfluid phase up into two distinct localized states, depending on the particle density. We find that these results strongly correlate with the results of several experiments on high-$T_c$ superconductors.

Superfluidity versus localization of two-dimensional hard-core boson model: a quantum Monte Carlo study

Quantum Monte Carlo simulations are used to investigate two-dimensional superfluidity of the hard-core boson model, that depends on particle density and disorder. It is definitely found that the clean system at half filling becomes superfluid via finite temperature Kosterlitz-Thouless transition. The low temperature superfluid density, as a function of particle density, displays a symmetric and parabolic shape about half filling. Disorder alters the superfluid phase into two distinct localized phases, depending on particle density. The universal relationship between T c and carrier-density, as experimentally reported for high-T c superconductors, appears to correlate with the computational result.

Low-Temperature Superfluid Density in a Restricted Geometry

Low-Temperature Superfluid Density in a Restricted Geometry