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Physics of the Solid State

Josephson junctions with nonsinusoidal current-phase relations based on heterostructures with a ferromagnetic spacer and their applications

N. V. Klenov, Н. Г. Пугач, Aleksei Sharafiev, Sergey V. Bakurskiy, Victor K. Kornev

Published Nov 1, 2010• 24 citations
Publisher

Abstract

A detailed review of theories describing the current-phase relations in Josephson junctions based on heterostructures with ferromagnetic layers is presented. The particular attention has been focused on the possibilities of making the so-called ϕ-junctions in which the ground state in the absence of the current is realized when the Josephson phase ϕ is nonzero. The recently popular speculations concerning the possibility of applying the Josephson π- and ϕ-junctions, which are made on the basis of heterostructures with ferromagnetic layers, to the formation of quantum bits (qubits) have been illustrated. An attempt to formulate the requirements for the characteristics of the Josephson heterostructures based on the first principles of the quantum-mechanical description of superconducting interferometers with a low inductance has been made.

DOI
10.1134/s1063783410110053

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A detailed review of theories describing the current-phase relations in Josephson junctions based on heterostructures with ferromagnetic layers is presented. The particular attention has been focused on the possibilities of making the so-called ϕ-junctions in which the ground state in the absence of the current is realized when the Josephson phase ϕ is nonzero. The recently popular speculations concerning the possibility of applying the Josephson π- and ϕ-junctions, which are made on the basis of heterostructures with ferromagnetic layers, to the formation of quantum bits (qubits) have been illustrated. An attempt to formulate the requirements for the characteristics of the Josephson heterostructures based on the first principles of the quantum-mechanical description of superconducting interferometers with a low inductance has been made.
π-junction qubit based on superconducting quantum interference device ring has been already proposed. In this qubit, a quantum two-level system is spontaneously generated without any bias flux applied. Flux qubit with a single π-junction concerns the large inductance L of the loop, which makes the qubit vulnerable to decoherence caused by magnetic fluctuations in the environment. To overcome this difficulty one can use three-junction π-qubit, comprising three π-junctions in a loop with negligible small inductance or unharmonic two-junction interferometer exploiting non-sinusoidal current-phase relations of the junctions. In the paper we theoretically investigate the macroscopic quantum dynamics of proposed qubits. The measurement process in two types of qubits has been analyzed in the frame of Lindblad equation formalism. Different mechanisms giving a non-sinusoidal CPR in SFS structures are analyzed as well. It is shown, that the largest second harmonic can be obtained for the SFS junction in the "clean" limit with a thin ferromagnet layer at low temperature.
This review provides a theoretical basis for understanding the current-phase relation (C\ensuremath{\Phi}R) 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 C\ensuremath{\Phi}R from the standard sinusoidal form. A new experimental tool for measuring the C\ensuremath{\Phi}R 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 C\ensuremath{\Phi}R measurements for both fundamental physics and applications.
We review the physical basis of and recent developments in ferromagnetic Josephson junctions with a focus on the π state, which is useful for applications to superconducting devices. Among various novel phenomena that emerge from the interaction between the superconductor and ferromagnet, the π state (junction) works as a phase shifter in superconducting devices, and several proposals and demonstrations of applications to quantum computing elements (qubits), classical superconducting logic circuits, and cryogenic memory have been presented. As a new research trend in superconducting spintronics, we also introduce recent interesting works on the long-range Josephson effect caused by spin-triplet Cooper pairs.
In recent years, various novel phenomena such as π-state (π-junction) and long-ranged supercurrents emerged in ferromagnetic Josephson junctions (superconductor/ferromagnet/superconductor junctions) have been studied so actively. An attractive device application of the ferromagnetic π-junction is a flux-bias-free superconducting flux quantum bit (qubit). By inserting the π-junction in the superconducting loop of the flux qubit, an external flux bias corresponding to half flux quantum, which is required for the operation of the conventional flux qubits, becomes unnecessary. This flux-bias-free feature is a great advantage in the realization of large-scale quantum circuits with many qubits. In the talk, we will present recent progress on the development of NbN-based ferromagnetic Josephson junctions which is suitable for the quantum circuits. We also show the experimental results on the several types of the quantum circuits with the NbN-based ferromagnetic π-junction.
Josephson junctions are used as active devices in superconducting electronics and quantum information technology. Outstanding properties are their distinct non-linear electrical characteristics and a usually sinusoidal relation between the current and the superconducting phase difference across the junction. In general the insertion of ferromagnetic material in the barrier of a Josephson junction is associated with a suppression of superconducting correlations. But also new phenomena can arise which may allow new circuit layouts and enhance the performance of applications. This thesis presents a systematic investigation for two concepts to fabricate Josephson junctions with a rather uncommon negative critical current. Such devices exhibit an intrinsic phase slip of Pi between the electrodes, so they are also known as Pi-junctions. Both studies go well beyond existing experiments and in one system a Pi-junction is shown for the first time. All the thin film junctions are based on superconducting Nb electrodes. In a first approach, barriers made from Si and Fe were investigated with respect to the realisation of Pi-junctions by spin-flip processes. The distribution of Fe in the Si matrix was varied from pure layers to disperse compounds. The systematic fabrication of alloy barriers was facilitated by the development of a novel timing-based combinatorial sputtering technique for planetary deposition systems. An orthogonal gradient approach allowed to create binary layer libraries with independent variations of thickness and composition. Second, Nb | AlOx | Nb | Ni60Cu40 | Nb (SIsFS) double barrier junctions were experimentally studied for the occurrence of proximity effect induced order parameter oscillations. Detailed dependencies of the critical current density on the thickness of s-layer and F-layer were acquired and show a remarkable agreement to existing theoretical predictions. Especially a variation of jc and IcRn by the s-layer thickness up to the value of nonmagnetic SIS junctions is notable. Additionally information on the emergence of superconductivity with the s-layer thickness was acquired.
Results on analytical and computational investigations of high frequency dynamics of Josephson junctions, characterized by nonzero capacitance and the second harmonic in the current-phase relation are presented. These attributes each influence on behaviour of integer Shapiro steps and lead to formation of non-integer Shapiro steps. Analytic theory of the integer and non-integer Shapiro steps has been developed for so-called high frequency limit. The analytical and numerical results are compared with experimental data for hybrid heterostructures YBCO/Au/Nb. Detector response for the case of high fluctuation level has been considered as well.