Materials with flat electronic bands often exhibit exotic quantum phenomena owing to strong correlations. An isolated low-energy flat band can be induced in bilayer graphene by simply rotating the layers by 1.1°, resulting in the appearance of gate-tunable superconducting and correlated insulating phases. In this study, we demonstrate that in addition to the twist angle, the interlayer coupling can be varied to precisely tune these phases. We induce superconductivity at a twist angle larger than 1.1°—in which correlated phases are otherwise absent—by varying the interlayer spacing with hydrostatic pressure. Our low-disorder devices reveal details about the superconducting phase diagram and its relationship to the nearby insulator. Our results demonstrate twisted bilayer graphene to be a distinctively tunable platform for exploring correlated states.

https://science.sciencemag.org/content/sci/early/2019/01/23/science.aav1910.full.pdf

Tuning superconductivity in twisted bilayer graphene.

This review considers unusual effects in superconductor-ferromagnet structures, in particular, the triplet component of the condensate generated in those systems. This component is odd in frequency and even in momentum, which makes it insensitive to nonmagnetic impurities. If the exchange field is not homogeneous in the system, the triplet component is not destroyed even by a strong exchange field and can penetrate the ferromagnet over long distances. Some other effects considered here and caused by the proximity effect are enhancement of the Josephson current due to the presence of the ferromagnet, induction of a magnetic moment in superconductors resulting in a screening of the magnetic moment, and formation of periodic magnetic structures due to the influence of the superconductor. Finally, theoretical predictions are compared with existing experiments.

https://arxiv.org/pdf/cond-mat/0506047.pdf

Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures

This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

/pdf/the-current-phase-relation-in-josephson-junctions-40zrgv4v2s.pdf

The current-phase relation in Josephson junctions

Traditional studies that combine spintronics and superconductivity have mainly focused on the injection of spin-polarized quasiparticles into superconducting materials However, a complete synergy between superconducting and magnetic orders turns out to be possible through the creation of spin-triplet Cooper pairs, which are generated at carefully engineered superconductor interfaces with ferromagnetic materials Currently, there is intense activity focused on identifying materials combinations that merge superconductivity and spintronics to enhance device functionality and performance The results look promising: it has been shown, for example, that superconducting order can greatly enhance central effects in spintronics such as spin injection and magnetoresistance Here, we review the experimental and theoretical advances in this field and provide an outlook for upcoming challenges in superconducting spintronics

/pdf/superconducting-spintronics-3kqdqwe8bp.pdf

Superconducting Spintronics

The superconductor-ferromagnet proximity effect describes the fast decay of a spin-singlet supercurrent originating from the superconductor upon entering the neighboring ferromagnet. After placing a conical magnet (holmium) at the interface between the two, we detected a long-ranged supercurrent in the ferromagnetic layer. The long-range effect required particular thicknesses of the spiral magnetically ordered holmium, consistent with spin-triplet proximity theory. This enabled control of the electron pairing symmetry by tuning the degree of magnetic inhomogeneity through the thicknesses of the holmium injectors.

https://science.sciencemag.org/content/sci/329/5987/59.full.pdf

Controlled Injection of Spin-Triplet Supercurrents into a Strong Ferromagnet

Coupling of Two Superconductors through a Ferromagnet

Under certain conditions, the order parameter induced by a superconductor (S) in a ferromagnet (F) can be inhomogeneous and oscillating, which results e.g. in the so-called π -coupling in S/F/S junctions. In principle, the inhomogeneous state can be induced at T c as function of the F-layer thickness d F in S/F bilayers and multilayers, which should result in a dip-like characteristic of T c ( d F ). We show the results of measurements on the S/F system Nb/Cu 1− x Ni x , for Ni-concentrations in the range x =0.5–0.7, where such effects might be expected. We find that the critical thickness for the occurrence of superconductivity is still relatively high, even for these weak ferromagnets. The resulting dip then is intrinsically shallow and difficult to observe, which explains the lack of a clear signature in the T c ( d F ) data.

/pdf/inhomogeneous-superconductivity-induced-in-a-weak-jlay1lo73r.pdf

Inhomogeneous superconductivity induced in a weak ferromagnet

We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-$\ensuremath{\pi}$ junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, nonvanishing supercurrent and half-integer Shapiro steps at the $0\text{\ensuremath{-}}\ensuremath{\pi}$ transition self-consistently point to an intrinsic second harmonic term, making it possible to rule out common alternative origins of half-periodic behavior. While surprising for diffusive multimode junctions, the large second harmonic is in agreement with theory predictions for thin ferromagnetic interlayers.

https://link.aps.org/accepted/10.1103/PhysRevLett.121.177702

Second-Harmonic Current-Phase Relation in Josephson Junctions with Ferromagnetic Barriers.

We have observed and studied critical supercurrents, I c , in cross-type Nb–Cu/Ni–Nb junctions with Josephson layers prepared from diluted ferromagnetic alloys. For suitable values of the exchange energy in the ferromagnet and the F-layer thickness we have observed I c ( T ) oscillation with vanishing I c for definite values of T and d F .

Supercurrents through the superconductor–ferromagnet–superconductor (SFS) junctions

We have investigated superconductor/ferromagnetic bilayers consisting of $\mathrm{Nb}∕{\mathrm{Pd}}_{81}{\mathrm{Ni}}_{19}$ with varying thickness of the ferromagnet (F) layer ${d}_{F}$ in order to compare the behavior of the superconducting transition temperature ${T}_{c}$ with that of the depairing current density ${J}_{\mathit{dp}}$. For ${T}_{c}({d}_{F})$, we find the usual behavior, with a minimum around ${d}_{F}=3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, which signifies the transition to an oscillatory order parameter in the $F$ layer. For ${J}_{\mathit{dp}}$, which was measured down to $T∕{T}_{c}\ensuremath{\approx}0.5$ using a pulsed-current technique, we find that the behavior can be well described by the Kupriyanov-Lukichev (KL) theory (Fiz. Nizk. Temp. 6, 445 (1980) [Sov. J. Low Temp. Phys. 6, 210 (1980)]), and therefore also by ${J}_{\mathit{dp}}\ensuremath{\propto}{(1\ensuremath{-}T∕{T}_{c})}^{3∕2}$ in the Ginzburg-Landau (GL) regime close to ${T}_{c}$. Extrapolating the GL regime to $T=0$ yields ${J}_{\mathit{dp}}^{\mathit{GL}}(0)$, which, as a function of ${d}_{F}$, behaves similarly to ${T}_{c}({d}_{F})$ with a shallow minimum around ${d}_{F}=3\char21{}4\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. At some temperature below ${T}_{c}$, most samples break away from the KL curve to higher values of ${J}_{\mathit{dp}}$, indicating a current-induced breakdown of the inhomogeneous state. Moreover, we find a significantly increased width of the transition to the normal state in the regime of the oscillatory order parameter.

/pdf/depairing-current-behavior-in-superconducting-nb-pd81ni19-1ofugsrpad.pdf

Alexander Yu. Rusanov

Papers

Coupling of Two Superconductors through a Ferromagnet

Inhomogeneous superconductivity induced in a weak ferromagnet

Second-Harmonic Current-Phase Relation in Josephson Junctions with Ferromagnetic Barriers.

Supercurrents through the superconductor–ferromagnet–superconductor (SFS) junctions

Depairing current behavior in superconducting Nb/Pd81Ni19 bilayers