Observation of superconducting vortices carrying a temperature-dependent fraction of the flux quantum

The magnetic response is a state-defining property of superconductors. The magnetic flux penetrates type-II bulk superconductors by forming quantum vortices when the enclosed magnetic flux is equal to the magnetic flux quantum. The flux quantum is the universal quantity that depends only on the ratio of fundamental constants: the electron charge and the Planck constant. This work investigates the vortex state in the hole-overdoped Ba$_{1-x}$K$_x$Fe$_2$As$_2$ by using scanning superconducting quantum interference device (SQUID) magnetometry. We observed quantum vortices that carry only a fraction of the flux quantum, which vary continuously with temperature. This finding establishes the phenomenon that superconductors support quantum vortices with non-universally quantized magnetic flux. Furthermore, the demonstrations of the mobility of the fractional vortices and the manipulability of their positions open up a route for future fluxonics applications.Comment: 19 pages, 9 figure

Piezoelectric-driven uniaxial pressure cell for muon spin relaxation and neutron scattering experiments

We present a piezoelectric-driven uniaxial pressure cell that is optimized for muon spin relaxation and neutron scattering experiments and that is operable over a wide temperature range including cryogenic temperatures. To accommodate the large samples required for these measurement techniques, the cell is designed to generate forces up to ∼1000 N. To minimize the background signal, the space around the sample is kept as open as possible. We demonstrate here that by mounting plate-like samples with epoxy, a uniaxial stress exceeding 1 GPa can be achieved in an active volume of at least 5 mm3. We show that for practical operation, it is important to monitor both the force and displacement applied to the sample. In addition, because time is critical during facility experiments, samples are mounted in detachable holders that can be rapidly exchanged. The piezoelectric actuators are likewise contained in an exchangeable cartridge. © 2020 Author(s)

Unsplit superconducting and time reversal symmetry breaking transitions in Sr2_2RuO4_4 under hydrostatic pressure and disorder

There is considerable evidence that the superconducting state of Sr$_2$RuO$_4$ breaks time reversal symmetry. In the experiments showing time reversal symmetry breaking its onset temperature, $T_\text{TRSB}$, is generally found to match the critical temperature, $T_\text{c}$, within resolution. In combination with evidence for even parity, this result has led to consideration of a $d_{xz} \pm id_{yz}$ order parameter. The degeneracy of the two components of this order parameter is protected by symmetry, yielding $T_\text{TRSB} = T_\text{c}$, but it has a hard-to-explain horizontal line node at $k_z=0$. Therefore, $s \pm id$ and $d \pm ig$ order parameters are also under consideration. These avoid the horizontal line node, but require tuning to obtain $T_\text{TRSB} \approx T_\text{c}$. To obtain evidence distinguishing these two possible scenarios (of symmetry-protected versus accidental degeneracy), we employ zero-field muon spin rotation/relaxation to study pure Sr$_2$RuO$_4$ under hydrostatic pressure, and Sr$_{1.98}$La$_{0.02}$RuO$_4$ at zero pressure. Both hydrostatic pressure and La substitution alter $T_\text{c}$ without lifting the tetragonal lattice symmetry, so if the degeneracy is symmetry-protected $T_\text{TRSB}$ should track changes in $T_\text{c}$, while if it is accidental, these transition temperatures should generally separate. We observe $T_\text{TRSB}$ to track $T_\text{c}$, supporting the hypothesis of $d_{xz} \pm id_{yz}$ order.Comment: 14 pages, 8 Figure

Elastoresistivity of Heavily Hole-Doped 122 Iron Pnictide Superconductors

Nematicity in heavily hole-doped iron pnictide superconductors remains controversial. Sizeable nematic fluctuations and even nematic orders far from magnetic instability were declared in RbFe2As2 and its sister compounds. Here, we report a systematic elastoresistance study of a series of isovalent- and electron-doped KFe2As2 crystals. We found divergent elastoresistance on cooling for all the crystals along their [110] direction. The amplitude of elastoresistivity diverges if K is substituted with larger ions or if the system is driven toward a Lifshitz transition. However, we conclude that none of them necessarily indicates an independent nematic critical point. Instead, the increased nematicity can be associated with another electronic criticality. In particular, we propose a mechanism for how elastoresistivity is enhanced at a Lifshitz transition

Hall-plot of the phase diagram for Ba(Fe1-xCox)2As2

The Hall effect is a powerful tool for investigating carrier type and density. For single-band materials, the Hall coefficient is traditionally expressed simply by $R_H^{-1} = -en$, where $e$ is the charge of the carrier, and $n$ is the concentration. However, it is well known that in the critical region near a quantum phase transition, as it was demonstrated for cuprates and heavy fermions, the Hall coefficient exhibits strong temperature and doping dependencies, which can not be described by such a simple expression, and the interpretation of the Hall coefficient for Fe-based superconductors is also problematic. Here, we investigate thin films of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ with compressive and tensile in-plane strain in a wide range of Co doping. Such in-plane strain changes the band structure of the compounds, resulting in various shifts of the whole phase diagram as a function of Co doping. We show that the resultant phase diagrams for different strain states can be mapped onto a single phase diagram with the Hall number. This universal plot is attributed to the critical fluctuations in multiband systems near the antiferromagnetic transition, which may suggest a direct link between magnetic and superconducting properties in the BaFe$_2$As$_2$ system.Comment: Accepted for publication in Scientific Reports, 6 main figures plus Supplemental Information (8 figures

High field superconducting properties of Ba(Fe1-xCox)2As2 thin films

The film investigated grew phase-pure and highly textured with in-plane and out-of-plane full width at half maximum, FWHM, of = 0.74° and = 0.9°, Suppl. S1. The sample, however, does contain a large density of ab-planar defects, as revealed by transition electron microscope (TEM) images of focused ion beam (FIB) cuts near the microbridges, Fig. 1. These defects are presumably stacking faults (i.e. missing FeAs layers)20. The reason for this defect formation (also observed on technical substrates)21 is not fully understood. Possible reasons are a partial As loss during deposition22, and relaxation processes in combination with the Fe buffer layer23. Estimating the distance between these intergrowths leads to values varying between 5 and 10 nm. Between the planar defects, an orientation contrast is visible in TEM (inset Fig. 1b), i.e. the brighter crystallites are slightly rotated either around (010) (out-of-plane spread, ) or around (001) (in-plane spread, ) and enclosed by dislocation networks or small-angle GBs. Since the crystallites are sandwiched between planar defects, an in-plane misorientation is most likely. The out-of-plane misorientation, on the other hand, is visible as a slight tilt of the ab-planar defects with respect to each other, especially in the upper part of the sample. No globular or columnar precipitates were found

Calorimetric evidence for two phase transitions in Ba1−x_{\rm 1-x}Kx_{\rm x}Fe2_{2}As2_{2} with fermion pairing and quadrupling states

Theoretically, materials that break multiple symmetries allow, under certain conditions, the formation of four-fermion condensates above the superconducting critical temperature. Such states can be stabilized by phase fluctuations. Recently a fermionic quadrupling condensate that breaks the $Z_2$ time-reversal symmetry was reported in Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ [V. Grinenko et al., Nat. Phys. 17, 1254 (2021)]. Evidence for the new state of matter comes from muon-spin rotation, transport, thermoelectric, and ultrasound experiments. Observing a specific heat anomaly is a very important signature of a transition to a new state of matter. However, a fluctuation-induced specific heat singularity is usually very challenging to resolve from a background of other contributions. Here, we report on detecting two anomalies in the specific heat of Ba$_{\rm 1-x}$K$_{\rm x}$Fe$_{2}$As$_{2}$ at zero magnetic field. The anomaly at the higher temperature is accompanied by the appearance of a spontaneous Nernst effect, indicating broken time-reversal ($Z_2$) symmetry. The second anomaly at the lower temperature coincides with the transition to a zero resistance state, indicating superconductivity breaking the $U(1)$ gauge symmetry. Our data provide calorimetric evidence for the $Z_2$ phase formation above the superconducting phase transition.Comment: 12 pages, 3 figures and Supplementary informatio