Session H25: Josephson Tunneling: SQUIDS and Superconductor-ferromagnetic Interactions

Controlling Hysteresis in Superconducting Weak Links and $\mu $-Superconducting Quantum Interference Devices.

We have fabricated and studied the current-voltage characteristics of a number of niobium film based weak-link devices and $\mu $-SQUIDs showing a critical current and two re-trapping currents. We have proposed a new understanding for the re-trapping currents in terms of thermal instabilities in different portions of the device. We also find that the superconducting proximity effect and the phase-slip processes play an important role in dictating the temperature dependence of the critical current in the non-hysteretic regime. The proximity effect helps in widening the temperature range of hysteresis-free characteristics. Finally we demonstrate control on temperature-range with hysteresis-free characteristics in two ways: 1) By using a parallel shunt resistor in close vicinity of the device, and 2) by reducing the weak-link width. Thus we get non-hysteretic behavior down to 1.3 K temperature in some of the studied devices.   

Phase-engineering artificial topology in a three-terminal Josephson interferometer.

The fundamental aspects of Majoranas with their non-Abelian statistics offer great applications for the future of quantum computation. Current theories on multi-terminal Josephson junctions emphasize the possibility of engineering non trivial states in the spectrum of a proximized normal metal giving rise to an artificial topological superconductor which is able to support Majorana bound states, and points out the importance of a first experimental agreement with the theoretical speculations [1,2]. Here we report on the realization of a three-terminal Josephson interferometer based on proximity effect and fully controlled by phase-coherence. Our device shows a non trivial phase-tunable switch from a regime where the normal metal spectrum shows a gap in the density of states to a gapless regime in full agreement with recent predictions [1,2,3,4], and represents the first essential step towards phase engineering of an artificial topological superconductor hosting Majorana bound states. [1] arXiv:1508.00146. [2] arXiv:1503.06862. [3] Phys. Rev. B 90, 155450 (2014). [4] arXiv:1508.03289.   

Tunable microstrip SQUID amplifiers for the Gen 2 Axion Dark Matter eXperiment (ADMX)

We present a series of tunable microstrip SQUID amplifiers (MSAs) for installation in ADMX. The axion dark matter candidate is detected via Primakoff conversion to a microwave photon in a high-Q ($\approx $100,000) tunable microwave cavity cooled with a dilution refrigerator in the presence of a 7-tesla magnetic field. The microwave photon frequency $\nu $ is a function of the unknown axion mass, so both the cavity and amplifier must be scanned over a wide frequency range. An MSA is a linear, phase-preserving amplifier consisting of a superconducting, resonant microstrip flux-coupled to a resistively-shunted dc SQUID biased into the voltage state. Tunability is achieved by terminating the microstrip with low inductance GaAs varactor diodes that operate below 100 mK. By varying the bias voltage of the varactors we vary their capacitance, allowing a reflected phase varying from nearly 0 to $\pi $, thus achieving a tunability close to a factor of 2. We demonstrate several devices operating below 100 mK, matched to the discrete operating bands of ADMX at frequencies ranging from 560 MHz to 1 GHz, that exhibit gains exceeding 20 dB. The associated noise temperatures, measured with a hot/cold load, approach the standard quantum limit ($h\mathrm{\nu }{/k}_{B})$ for a linear phase-preserving amplifier.   

Transparency and Coherence in rf SQUID Metamaterials

We have developed active metamaterials capable of quickly tuning their electrical and magnetic responses over a wide frequency range [1]. These metamaterials are based on superconducting elements to form low loss, physically and electrically small, highly tunable structures for fundamental studies of extraordinarily nonlinear media. The meta-atoms are rf superconducting quantum interference devices (SQUIDs) that incorporate the Josephson effect. RF SQUIDs have an inductance which is strongly tunable with dc and rf magnetic fields and currents. The rf SQUID metamaterial is a richly nonlinear effective medium introducing qualitatively new macroscopic quantum phenomena into the metamaterials community, namely magnetic flux quantization and the Josephson effect. The coherent oscillation of the meta-atoms is strongly sensitive to the environment and measurement conditions, and we have developed several strategies to improve the coherence experimentally by exploiting ideas from nonlinear dynamics [2]. The metamaterials also display a unique form of transparency whose development can be manipulated through multiple parametric dependences [3]. We discuss these qualitatively new metamaterial phenomena. [1] Melissa Trepanier, \textit{et al}., Phys. Rev. X 3, 041029 (2013). [2] Melissa Trepanier, \textit{et al}., in preparation. [3] Daimeng Zhang, \textit{et al}., Phys. Rev. X (in press). arXiv:1504.08301   

Multi-tone response of Nonlinear rf-SQUID metamaterials

We study the multi-tone response over a broad microwave frequency range of a nonlinear superconducting meta-atom and a metamaterial composed of Radio Frequency Superconducting QUantum Interference Devices (rf-SQUIDs). Nonlinearity in the SQUID metamaterial gives rise to large-range tunable resonance via dc/rf magnetic field and temperature [1] [2], it also results in signal mixing through intermodulation distortion (IMD). Our metamaterial responds to multi-frequency signals and generates strong higher order intermodulation signals in a certain range of applied rf power. However, our meta-atom and metamaterial show a reduced third-order IMD generation around the resonance, which is unusual for typical nonlinear systems. The numerical simulation predicts the same IMD gap feature as in experiment. A comprehensive analytical model is applied to explain the phenomena, and methods to enhance, or reduce, intermodulation levels are explored. [1] M. Trepanier, Daimeng Zhang, Oleg Mukhanov, Steven M. Anlage, Phys. Rev. X 3, 041029 (2013). [2] Daimeng Zhang, M. Trepanier, Oleg Mukhanov, Steven. M. Anlage, Anlage, arXiv:1504.08301 (2015).   

Stochastic Resonance Magnetic Force Microscopy imaging of Josephson Arrays

Vortex interactions are key to explaining the behavior of many two dimensional superconducting systems. We report on the development of a technique to locally probe vortex interactions in a 2D array of Josephson junctions. Scanning a magnetic tip attached to an ultra-soft cantilever over the array produces changes in the frequency of the cantilever along certain lines, forming geometric patterns in the scans. Different tip-surface separations and external magnetic fields produce a number of different patterns. These patterns correspond to tip locations in which two configurations of vortices in the lattice have degenerate energies. By imaging the locations of these degeneracies, information on the local vortex interactions may be obtained.   

Phase-coherent engineering of electronic heat currents with a Josephson modulator.

In this contribution we report the realization of the first balanced Josephson heat modulator designed to offer full control at the nanoscale over the phase-coherent component of electronic thermal currents.\footnote{A. Fornieri \textit{et al.}, arXiv:1507.00199, to be published in \textit{Nature Nanotechnology}.} The ability to master the amount of heat transferred through two tunnel-coupled superconductors by tuning their phase difference\footnote{F. Giazotto and M.-J. Mart\'inez-P\'erez, \textit{Nature} \textbf{492}, 401-405 (2012).} is the core of coherent caloritronics, and is expected to be a key tool in a number of nanoscience fields, including solid state cooling, thermal isolation, radiation detection, quantum information and thermal logic. Our device provides magnetic-flux-dependent temperature modulations up to 40 mK in amplitude with a maximum of the flux-to-temperature transfer coefficient reaching 200 mK per flux quantum at a bath temperature of 25 mK. Foremost, it demonstrates the exact correspondence in the phase-engineering of charge and heat currents, breaking ground for advanced caloritronic nanodevices such as thermal splitters, heat pumps and time-dependent electronic engines.   

Josephson current in parallel SFS junctions

We study a Josephson junction between superconductors connected by two parallel ferromagnetic arms. If the ferromagnets are fully polarised, supercurrent can only flow via Cooper pair splitting between the differently polarised arms. The disorder-average current is suppressed, but mesoscopic fluctuations lead to a significant typical current. We extract the typical current from a current-current correlator. The current is proportional to $\sin^2 \alpha/2$, where $\alpha$ is the angle between the polarisations of the two arms, revealing the spin dependence of crossed Andreev reflection. Compared to an SNS device of the same geometry, the typical SFS current is small by a factor determined by the properties of the superconducting leads alone. The current is insensitive to the flux threading the area between the ferromagnetic arms of the junction. However, if the ferromagnetic arms are replaced by metal with magnetic impurities, or partially polarised ferromagnets, the Josephson current starts depending on the flux with a period of $h/e$, i.e. twice the superconducting flux quantum.   

Critical Current Oscillations of Josephson Junctions with Ferromagnetic Layers

Josephson junctions containing ferromagnetic layers are of considerable interest for the development of practical cryogenic memory and superconducting qubits. Such junctions exhibit a phase shift of $\pi$ for certain ranges of ferromagnetic layer thickness. We present studies of Nb based micron-scale Josephson junctions using ferromagnetic layers of Ni, Ni$_{81}$Fe$_{19}$, or Ni$_{65}$Co$_{20}$Fe$_{15}$. By applying an external magnetic field, the critical current of the junctions containing Ni$_{81}$Fe$_{19}$ and Ni$_{65}$Co$_{20}$Fe$_{15}$ is found to follow a characteristic Fraunhofer pattern, and displays the clear switching behavior expected of single-domain magnets. However, the junctions containing Ni exhibit more complex behaviors. The maximum value of the critical current, extracted from the Fraunhofer patterns, oscillates as a function of the ferromagnetic layer thickness, indicating transitions in the phase difference across the junction between values of zero and $\pi$. We compare the data to previous work and to models of the 0-$\pi$ transitions based on existing clean and dirty limit theories.   

Controlling the Phase of Ferromagnetic Josephson Junctions for Cryogenic Memory Applications

Josephson junctions containing ferromagnetic layers are currently of interest for use in cryogenic memory where either the phase or critical current can be switched between two distinct states. We present the first direct phase measurements of such a junction demonstrating control of the phase [1]. If a junction contains one ferromagnetic layer, the thickness of that layer dictates the ground state phase between the superconducting electrodes, which can be either 0 or $\pi $. If the junction contains two ferromagnetic layers and the layer thicknesses are carefully chosen, then the phase of a single junction can be switched between 0 and $\pi $ by changing the relative magnetization directions of the two layers from antiparallel to parallel. We have successfully fabricated and directly measured the relative phase of two such spin valve junctions in a SQUID loop to confirm the phase change from $\pi $ to 0 and back again of each junction. We report our continued progress in optimizing the control of such systems. [1] E. C. Gingrich, B. M. Niedzielski, J. A. Glick, Y. Wang, D. L. Miller, R. Loloee. W. P. Pratt Jr., and N. O. Birge, arXiv:1509.05368   

Effects of a rotating magnetization on pair correlations in a ballistic regime Josephson Junction

Pair correlations in clean superconducting-magnetic proximity systems are studied with a focus on the singlet-triplet mixing resulting from magnetic inhomogeneities. The system is modeled in the clean limit using a tight-binding Hamiltonian and the Bogoliubov$-$de Gennes equations are solved to determine the Gor'kov functions of the system. Three different magnetic configurations are considered: an exchange spring, a helical magnet, and misaligned homogeneous ferromagnetic layers; each is sandwiched between two superconductors to form a Josephson junction. The goal of the study is to revisit how pair correlations are affected by different magnetization configurations and magnitudes in the clean limit. We discuss our results in the light of those obtained in the diffusive regime [1,2].\\[0.2cm] [1] T.E. Baker, A. Richie-Halford, A. Bill New J. Phys. 16, 093048 (2014).\\ [2] T.E. Baker, A. Richie-Halford, O.E. Icreverzi, A. Bill Europhys. Lett., 107, 17001 (2014).   

Nanoscale investigation of mesoscopic phenomena in superconductor/ferromagnet hybrid structures using low-temperature scanning tunneling microscopy and spectroscopy

Superconductor/ferromagnet (S/F) heterostructures exhibit unique electronic phenomena which strongly depend on the nature of the constituent materials and the coupling between the layers. Using low-temperature scanning tunneling microscopy and spectroscopy we have investigated S/F structures in the regimes of magnetic and proximity coupling. Here, in the case of S/F systems made of convential low-$T_c$ lead films with different ferromagnet materials, the spatial and temperature dependent effects on the local density of states which emerge at the nanoscale will be discussed.   

Josephson critical current of long SNS junctions in the presence of a magnetic field

We evaluate the Josephson critical current of a long and wide two-dimensional superconductor-normal metal-superconductor (SNS) junction, taking into account the effect of electron reflection off the side edges of the junction. Considering clean junctions, we find that the effect of edges alters the usual Fraunhofer-like dependence of the Josephson critical current~$I_c$ on the magnetic flux~$\Phi$. At relatively weak fields, $B\lesssim \Phi_0/W^2$, the edge effect lifts zeros of the $I_c(\Phi)$ dependence and gradually shifts the maxima of that function by $\Phi_0/2$. (Here $W$ is the width of the junction and $\Phi_0$ the magnetic flux quantum.) At higher fields, $B\gtrsim\Phi_0/W^2$, the edge effect leads to an accelerated decay of the critical current $I_c(\Phi)$ with increasing $\Phi$. Our results are robust with respect to the roughness of realistic boundaries. Finally, we discuss the role of mesoscopic fluctuations of $I_c(\Phi)$ originating from the scattering off the edges, and compare our findings to recent experiments.