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Register a new userZero-field superfluid density in d-wave superconductor evaluated from the results of muon-spin-rotation experiments in the mixed state
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We report on measurements of the in-plane magnetic penetration lambda_{ab} in the optimally doped cuprate superconductor (BiPb)_2(SrLa)_2CuO_6+delta (OP Bi2201) by means of muon-spin rotation (muSR). We show that in unconventional $d-$wave superconductors (like OP Bi2201), muSR experiments conducted in various magnetic fields allow to evaluate the zero-field magnetic penetration depth lambda_0, which relates to the zero-field superfluid density in terms of rho_sproptolambda_0^-2.
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We argue that claims about magnetic field dependence of the magnetic field penetration depth lambda, which were made on the basis of moun-spin-rotation studies of some superconductors, originate from insufficient accuracy of theoretical models employed for the data analysis. We also reanalyze some of already published experimental data and demonstrate that numerical calculations of Brandt [E.H. Brandt, Phys. Rev. B 68, 54506 (2003)] may serve as a reliable and powerful tool for the analysis of the data collected in experiments with conventional superconductors. Furthermore, one can use this approach in order to distinguish between conventional and unconventional superconductors. It is unfortunate that these calculations have practically never been employed for such analyses.
We show that the low-energy density of quasiparticle states in the mixed state of ultra-clean d-wave superconductors is characterized by pronounced quantum oscillations in the regime where the cyclotron frequency $hbaromega_c ll Delta_0$, the d-wave pairing gap. Such oscillations as a function of magnetic field B are argued to be due to the internodal scattering of the d-wave quasiparticles near wavevectors $(pm k_D,pm k_D)$ by the vortex lattice as well as their Zeeman coupling. The periodicity of the oscillations is set by the condition $k_D sqrt{hc/(eB)} equiv k_D sqrt{hc/(eB)}pmod {2pi}$. We find that there is additional structure within each period which grows in complexity as the Dirac node anisotropy increases.
Muon-spin rotation (muSR) experiments are often used to study the magnetic field distribution in type-II superconductors in the vortex state. Based on the determination of the magnetic penetration depth it is frequently speculated---also controversially---about the order-parameter symmetry of the studied superconductors. This article reports on a combined muSR and magnetization study of the mixed state in the cuprate high-temperature superconductor La_{1.83}Sr_{0.17}CuO_{4} in a low magnetic field of 20 mT applied along the c axis of a single crystal. The macroscopic magnetization measurements reveal substantial differences for various cooling procedures. Yet, indicated changes in the vortex dynamics between different temperature regions as well as the results of the microscopic muSR experiments are virtually independent of the employed cooling cycles. Additionally, it is found that the mean magnetic flux density, locally probed by the muons, strongly increases at low temperatures. This can possibly be explained by a non-random sampling of the spatial field distribution of the vortex lattice in this cuprate superconductor caused by intensified vortex pinning.
Neutron scattering is used to probe antiferromagnetic spin fluctuations in the d-wave heavy fermion superconductor CeCoIn$_{5}$ (T$_{c}$=2.3 K). Superconductivity develops from a state with slow ($hbarGamma$=0.3 $pm$ 0.15 meV) commensurate (${bf{Q_0}}$=(1/2,1/2,1/2)) antiferromagnetic spin fluctuations and nearly isotropic spin correlations. The characteristic wavevector in CeCoIn$_{5}$ is the same as CeIn$_{3}$ but differs from the incommensurate wavevector measured in antiferromagnetically ordered CeRhIn$_{5}$. A sharp spin resonance ($hbarGamma<0.07$ meV) at $hbar omega$ = 0.60 $pm$ 0.03 meV develops in the superconducting state removing spectral weight from low-energy transfers. The presence of a resonance peak is indicative of strong coupling between f-electron magnetism and superconductivity and consistent with a d-wave gap order parameter satisfying $Delta({bf q+Q_0})=-Delta({bf q})$.
We report transverse-field (TF) muon spin rotation experiments on single crystals of the topological superconductor Sr$_x$Bi$_2$Se$_3$ with nominal concentrations $x=0.15$ and $0.18$ ($T_c sim 3$ K). The TF spectra ($B= 10$ mT), measured after cooling to below $T_c$ in field, did not show any additional damping of the muon precession signal due to the flux line lattice within the experimental uncertainty. This puts a lower bound on the magnetic penetration depth $lambda geq 2.3 ~mu$m. However, when we induce disorder in the vortex lattice by changing the magnetic field below $T_c$ a sizeable damping rate is obtained for $T rightarrow 0$. The data provide microscopic evidence for a superconducting volume fraction of $sim 70~ %$ in the $x=0.18$ crystal and thus bulk superconductivity.
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