Superconducting Coherence Length Research Articles

Superconducting density of states and vortex lattice of LaRu2P2observed by Scanning Tunneling Spectroscopy.

We provide the superconducting density of states of the pnictide superconductor LaRu2P2(Tc= 4.1 K), measured using millikelvin Scanning Tunneling Microscopy. From the tunneling conductance, we extract a density of states which shows the opening of a s-wave single superconducting gap. The temperature dependence of the gap also follows BCS theory. Under magnetic fields, vortices present Caroli de Gennes Matricon states, although these are strongly broadened by defect scattering. From the vortex core size we obtain a superconducting coherence length of ξ= 50 nm, compatible with the value extracted from macroscopic Hc2measurements. We discuss the comparison between s-wave LaRu2P2and pnictide unconventional multiple gap and strongly correlated Fe based superconductors.

Multiphase superconductivity at the interface between ultrathin FeTe islands and Bi2Te3

FeTe monolayer islands situated on a topological insulator Bi2Te3 (0001) surface were recently reported to exhibit the opening of an energy gap below temperatures T ~ 6 K, which could be due to a superconducting phase transition. In this work, we present a magnetic field dependent transport study proving that this gap is indeed of superconducting origin. Upon cooling, several drops in resistance are observed in the temperature range between 6 K and 2 K, indicating multiple transitions. Using the Ginzburg-Landau theory, we show that the critical magnetic field of the dominant high-temperature transition at ~ 6 K is governed by orbital Cooper pair breaking in larger FeTe islands, large enough to exceed the superconductive coherence length ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi$$\\end{document}. At smaller island sizes, transitions at lower temperatures < 6 K become more prominent, showing significantly increased critical fields dominated by paramagnetic pair breaking. The multiphase superconducting behaviour is in line with an observed wide distribution of FeTe islands width 5–100 nm and seems to reflect disorder effects at the interface to Bi2Te3. The proof of local superconductivity makes the FeTe interface to the topological insulator Bi2Te3 substrate a potential host of topological superconductivity.

Induced superconducting correlations in a quantum anomalous Hall insulator

AbstractThin films of ferromagnetic topological insulator materials can host the quantum anomalous Hall effect without the need for an external magnetic field. Inducing Cooper pairing in such a material is a promising way to realize topological superconductivity with the associated chiral Majorana edge states. However, finding evidence of the superconducting proximity effect in such a state has remained a considerable challenge due to inherent experimental difficulties. Here we demonstrate crossed Andreev reflection across a narrow superconducting Nb electrode that is in contact with the chiral edge state of a quantum anomalous Hall insulator. In the crossed Andreev reflection process, an electron injected from one terminal is reflected out as a hole at the other terminal to form a Cooper pair in the superconductor. This is a compelling signature of induced superconducting pair correlation in the chiral edge state. The characteristic length of the crossed Andreev reflection process is found to be much longer than the superconducting coherence length in Nb, which suggests that the crossed Andreev reflection is, indeed, mediated by superconductivity induced on the quantum anomalous Hall insulator surface. Our results will invite future studies of topological superconductivity and Majorana physics, as well as for the search for non-abelian zero modes.

Probing magnetic and triplet correlations in spin-split superconductors with magnetic impurities

A superconductor (SC) in proximity to a ferromagnetic insulator (FMI) is predicted to exhibit mixed singlet and triplet correlations. The magnetic proximity effect of FMI spin splits the energy of Bogoliubov excitations and leads to a spin polarization at the surface for superconducting films that are thinner than the superconducting coherence length. In this work, we study manifestations of these phenomena in the properties of a magnetic impurity coupled via Kondo coupling to this FMI/SC system. Using the numerical renormalization group (NRG) method, we compute the properties of the ground state and low-lying excited states of a model that incorporates the Kondo interaction and a Ruderman-Kittel-Kasuya-Yosida (RKKY)-like interaction with the surface spin polarization. Our main finding is an energy splitting of the lowest even fermion-parity states caused by the proximity to the FMI. As the Kondo coupling increases, the splitting grows and saturates to a universal value equal to twice the exchange field of the FMI. We introduce a two-site model that can be solved analytically and provides a qualitative understanding of this and other NRG results. In addition, using perturbation theory, we demonstrate that the mechanism behind the splitting involves the RKKY field and the triplet correlations of the spin-split superconductor. A scaling analysis combined with NRG shows that the splitting can be written as a single-parameter scaling function of the ratio of the Kondo temperature and the superconducting gap, which is also numerically obtained. Published by the American Physical Society 2024

Monoclinic LaSb2 Superconducting Thin Films.

Rare-earth diantimondes exhibit coupling between structural and electronic orders, which are tunable under pressure and temperature. Here we present the discovery of a new polymorph of LaSb2 stabilized in thin films synthesized using molecular beam epitaxy. Using diffraction, electron microscopy, and first-principles calculations we identify a YbSb2-type monoclinic lattice as a yet-uncharacterized stacking configuration. The material hosts superconductivity with a Tc = 2 K, which is enhanced relative to the bulk ambient phase, and a long superconducting coherence length of 1730 Å. This result highlights the potential thin film growth has in stabilizing novel stacking configurations in quasi-two-dimensional compounds with competing layered structures.

Controllable Andreev Bound States in Bilayer Graphene Josephson Junctions from Short to Long Junction Limits.

We demonstrate that the mode number of Andreev bound states in bilayer graphene Josephson junctions can be modulated by controlling the superconducting coherence length insitu. By exploiting the quadratic band dispersion of bilayer graphene, we control the Fermi velocity and thus the coherence length via the application of electrostatic gating. Tunneling spectroscopy of the Andreev bound states reveals a crossover from short to long Josephson junction regimes as we approach the charge neutral point of the bilayer graphene. Furthermore, analysis of different mode numbers of the Andreev energy spectrum allows us to estimate the phase-dependent Josephson current quantitatively. Our Letter provides a new way for studying multimode Andreev levels by tuning the Fermi velocity.

Stoichiometric control of electron mobility and 2D superconductivity at LaAlO3-SrTiO3 interfaces

SrTiO3-based conducting interfaces, which exhibit coexistence of gate-tunable 2D superconductivity and strong Rashba spin-orbit coupling (RSOC), are candidates to host topological superconductive phases. Yet, superconductivity is usually in the dirty limit, which tends to suppress nonconventional pairing and therefore challenges these expectations. Here we report on LaAlO3/SrTiO3 (LAO/STO) interfaces with large mobility and mean free paths comparable to the superconducting coherence length, approaching the clean limit for superconductivity. We further show that the carrier density, mobility, and formation of the superconducting condensate are controlled by the fine-tuning of La/Al chemical ratio in the LAO film. We find a region in the superconducting phase diagram where the critical temperature is not suppressed below the Lifshitz transition, at odds with previous experimental investigations. These findings point out the relevance of achieving a clean-limit regime to enhance the observation of unconventional pairing mechanisms in these systems.

Nanoscale spin ordering and spin screening effects in tunnel ferromagnetic Josephson junctions

Magnetic Josephson junctions (MJJs) have emerged as a prominent playground to explore the interplay between superconductivity and ferromagnetism. A series of fascinating experiments have revealed striking phenomena at the superconductor/ferromagnet (S/F) interface, pointing to tunable phase transitions and to the generation of unconventional spin-triplet correlations. Here, we show that the Josephson effect, being sensitive to phase space variation on the nanoscale, allows a direct observation of the spin polarization of the S/F interface. By measuring the temperature dependence of the Josephson magnetic field patterns of tunnel MJJs with strong and thin F-layer, we demonstrate an induced nanoscale spin order in S along the superconducting coherence length at S/F interface, i.e., the inverse proximity effect, with the first evidence of full spin screening at very low temperatures, as expected by the theory. A comprehensive phase diagram for spin nanoscale ordering regimes at S/F interfaces in MJJs has been derived in terms of the magnetic moment induced in the S-layer. Our findings contribute to drive the design and the tailoring of S/F interfaces also in view of potential applications in quantum computing.

Superconducting properties of bismuthate/manganite epitaxial multilayers

We report epitaxial growth and superconducting properties of superconductor/ferromagnet (S/F) multilayers consisting of an s-wave superconducting bismuthate BaPb0.75Bi0.25O3 (BPBO) and a ferromagnetic insulating manganite La0.875Sr0.125MnO3 (LSMO). We demonstrate that the superconductivity of BPBO sandwiched by LSMO is preserved down to a thickness close to the superconducting coherence length. The superconducting transition temperature of BPBO is unaffected by the magnetization alignment of the LSMO layers, which is in sharp contrast to YBa2Cu3O7 showing a clear magnetic exchange interaction. While the stable s-wave superconductivity in the S/F oxide multilayer demonstrated in this work is promising for the development of quantum spin devices with strong spin–orbit coupling, the absence of the magnetic exchange field effect highlights the importance of interface engineering for the realization of a strongly exchange-coupled s-wave S/F oxide interface.

Crossover from clean to dirty superconducting limit in YBCO films with modulated disorder

Magnetotransport measurements have been carried out for pristine and irradiated Y Ba2Cu3O7−x films. The measurements reveal a crossover from the clean superconducting limit to the dirty one with an increase in the impurity scattering rate Γ produced by a certain dose of irradiation. For the clean limit, the critical temperature Tc0 decreases with Γ, while the initial slope K=|dHc2/dT|Tc0 increases. We find a nice agreement between these experimental data and a model of d-wave superconductors with anisotropic impurity scattering. Such dose-dependencies of Tc0 and K reveal the superconducting coherence length ξ0 to be quasi-invariant in the clean limit. For the dirty limit, ξ0 increases with Γ due to a decrease in both the quantities Tc0 and K. Though, this decrease appears slower than predicted by the textbook picture of d-wave superconductors. Such discrepancy can be produced by an irradiation-induced modulated disorder responsible for the formation of (d+s)-wave pairing.

Superconducting Proximity Effect and Long-Ranged Triplets in Dirty Metallic Antiferromagnets.

Antiferromagnets have no net spin splitting on the scale of the superconducting coherence length. Despite this, antiferromagnets have been observed to suppress superconductivity in a similar way as ferromagnets, a phenomenon that still lacks a clear understanding. We find that this effect can be explained by the role of impurities in antiferromagnets. Using quasiclassical Green's functions, we study the proximity effect and critical temperature in diffusive superconductor-metallic antiferromagnet bilayers. The nonmagnetic impurities acquire an effective magnetic component in the antiferromagnet. This not only reduces the critical temperature but also separates the superconducting correlations into short-ranged and long-ranged components, similar to ferromagnetic proximity systems.

Demonstration of the Nonlocal Josephson Effect in Andreev Molecules.

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.

ZrNb(CO) RF Superconducting Thin Film with High Critical Temperature in the Theoretical Limit

AbstractSuperconducting radio‐frequency (SRF) resonators are critical components for particle accelerator applications, such as free‐electron lasers, and for emerging technologies in quantum computing. Developing advanced materials and their deposition processes to produce RF superconductors that yield nΩ surface resistances is a key metric for the wider adoption of SRF technology. Here, ZrNb(CO) RF superconducting films with high critical temperatures (Tc) achieved for the first time under ambient pressure are reported. The attainment of a Tc near the theoretical limit for this material without applied pressure is promising for its use in practical applications. A range of Tc, likely arising from Zr doping variation, may allow a tunable superconducting coherence length that lowers the sensitivity to material defects when an ultra‐low surface resistance is required. The ZrNb(CO) films are synthesized using a low‐temperature (100 – 200 °C) electrochemical recipe combined with thermal annealing. The phase transformation as a function of annealing temperature and time is optimized by the evaporated Zr‐Nb diffusion couples. Through phase control, one avoids hexagonal Zr phases that are equilibrium‐stable but degrade Tc. X‐ray and electron diffraction combined with photoelectron spectroscopy reveal a system containing cubic β‐ZrNb mixed with rocksalt NbC and low‐dielectric‐loss ZrO2. Proof‐of‐concept RF performance of ZrNb(CO) on an SRF sample test system is demonstrated. BCS resistance trends lower than reference Nb, while quench fields occur at approximately 35 mT. The results demonstrate the potential of ZrNb(CO) thin films for particle accelerators and other SRF applications.

What is measured when measuring a thermoelectric coefficient?

A thermal gradient generates an electric field in any solid hosting mobile electrons. In presence of a finite magnetic field (or Berry curvature) this electric field has a transverse component. These are known as Seebeck and Nernst coefficients. As Callen argued, back in 1948, the Seebeck effect quantifies the entropy carried by a flow of charged particles in absence of thermal gradient. Similarly, the Nernst conductivity, α xy , quantifies the entropy carried by a flow of magnetic flux in absence of thermal gradient. The present paper summarizes a picture in which the rough amplitude of the thermoelectric response is given by fundamental units and material-dependent length scales. Therefore, knowledge of material-dependent length scales allows predicting the amplitude of the signal measured by experiments. Specifically, the Nernst conductivity scales with the square of the mean-free-path in metals. Its anomalous component in magnets scales with the square of the fictitious magnetic length. Ephemeral Cooper pairs in the normal state of a superconductor generate a signal, which scales with the square of the superconducting coherence length and smoothly evolves to the signal produced by mobile vortices below the critical temperature.

Subgap states and quantum phase transitions in one-dimensional superconductor–ferromagnetic insulator heterostructures

We theoretically study the spectral properties of a one dimensional semiconductor-superconductor-ferromagnetic insulator (SE-SU-FMI) hybrid nanostructure, motivated by recent experiments where such devices have been fabricated using epitaxial growing techniques. We model the hybrid structure as a one-dimensional single-channel semiconductor nanowire under the simultaneous effect of two proximity-induced interactions: superconducting pairing and a (spatially inhomogeneous) Zeeman exchange field. The coexistence of these competing mechanisms generates a rich quantum phase diagram and a complex subgap Andreev bound state (ABS) spectrum. By exploiting the symmetries of the problem, we classify the solutions of the Bogoliubov-de Gennes equations into even and odd ABS with respect to the spatial inversion symmetry $x\ensuremath{\rightarrow}\ensuremath{-}x$. We find the ABS spectrum of the device as a function of the different parameters of the model: the length $L$ of the coexisting SU-FMI region, the induced Zeeman exchange field ${h}_{0}$, and the induced superconducting coherence length $\ensuremath{\xi}$. In particular we analyze the evolution of the subgap spectrum as a function of the length $L$. Interestingly, we generically find spin-polarized ABS emerging in the subgap region, which, depending on the ratio ${h}_{0}/\mathrm{\ensuremath{\Delta}}$, can eventually cross below the Fermi energy at certain critical values ${L}_{c}$, and induce spin- and fermion parity-changing quantum phase transitions. We argue that this type of device constitute a promising highly-tunable platform to engineer subgap ABS.

Phase fluctuations in two-dimensional superconductors and pseudogap phenomenon

We study the phase fluctuations in the normal state of generic two-dimensional superconducting systems with $s$-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the two-dimensional Berezinskii-Kosterlitz-Thouless transition lead to a significant broadening of the single-particle spectrum, giving birth to the pseudogap phenomenon. Quantitatively, the broadening of spectral weights near the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the fermionic attractive-$U$ Hubbard model on the square lattice, using the unbiased determinant quantum Monte Carlo method and stochastic analytic continuation.

Bosonic spectrum of a correlated multiband system, BaFe1.80Co0.20As2, obtained via infrared spectroscopy

We investigated a single crystal BaFe2−xCoxAs2 (Co-doped BaFe2As2: Co-doped Ba122) with x=0.20 using infrared spectroscopy. We obtained the bosonic spectrum from the measured spectrum using an extended Drude–Lorentz model for the normal state and a two-parallel-channel approach for the superconducting (SC) state, based on the generalized Allen formula. The coupling constant, maximum SC transition temperature, SC coherence length, and upper critical field were extracted from the bosonic spectrum. The superfluid plasma frequency and the London penetration depth were obtained from the optical conductivity. We compared the physical quantities of Co-doped Ba122 and K-doped Ba122 and found some interesting differences. Our results may be helpful for understanding superconductivity in doped Ba122 systems and may provide useful information on doped Ba122 systems for their applications.

Joule spectroscopy of hybrid superconductor–semiconductor nanodevices

Hybrid superconductor-semiconductor devices offer highly tunable platforms, potentially suitable for quantum technology applications, that have been intensively studied in the past decade. Here we establish that measurements of the superconductor-to-normal transition originating from Joule heating provide a powerful spectroscopical tool to characterize such hybrid devices. Concretely, we apply this technique to junctions in full-shell Al-InAs nanowires in the Little-Parks regime and obtain detailed information of each lead independently and in a single measurement, including differences in the superconducting coherence lengths of the leads, inhomogeneous covering of the epitaxial shell, and the inverse superconducting proximity effect; all-in-all constituting a unique fingerprint of each device with applications in the interpretation of low-bias data, the optimization of device geometries, and the uncovering of disorder in these systems. Besides the practical uses, our work also underscores the importance of heating in hybrid devices, an effect that is often overlooked.

Superconductors with a Topological Gap

I review a new superconductivity mechanism in which the gap is opened through a topological mechanism and not through the Landau mechanism of spontaneous symmetry breaking. As a consequence, the low-energy effective theory which describes these new superconductors is not the Landau–Ginzburg theory, formulated in terms of a local-order parameter, but a topological-field theory formulated in terms of emerging gauge fields. This new mechanism is realized as global superconductivty in Josephson junction arrays and in thin superconducting films with thicknesses comparable to the superconducting coherence length, which exhibits emergent granularity.

Superconductivity and Fermi Surface Studies of β″-(BEDT-TTF)2[(H2O)(NH4)2Cr(C2O4)3]·18-Crown-6

We report rf-penetration depth measurements of the quasi-2D organic superconductor β″-(BEDT-TTF)2[(H2O)(NH4)2Cr(C2O4)3]·18-crown-6, which has the largest separation between consecutive conduction layers of any 2D organic metal with a single packing motif. Using a contactless tunnel diode oscillator measurement technique, we show the zero-field cooling dependence and field sweeps up to 28 T oriented at various angles with respect to the crystal conduction planes. When oriented parallel to the layers, the upper critical field, Hc2=7.6 T, which is the calculated paramagnetic limit for this material. No signs of inhomogeneous superconductivity are seen, despite previous predictions. When oriented perpendicular to the layers, Shubnikov–de Haas oscillations are seen as low as 6 T, and from these we calculate Fermi surface parameters such as the superconducting coherence length and Dingle temperature. One remarkable result from our data is the high anisotropy of Hc2 in the parallel and perpendicular directions, due to an abnormally low Hc2⊥=0.4 T. Such high anisotropy is rare in other organics and the origin of the smaller Hc2⊥ may be a consequence of a lower effective mass.