Anomalous Josephson effect controlled by an Abrikosov vortex

Abstract

The possibility of a fast and precise Abrikosov vortex manipulation by a focused laser beam opens the way to create laser-driven Josephson junctions. We theoretically demonstrate that a vortex pinned in the vicinity of the Josephson junction generates an arbitrary ground state phase which can be equal not only to 0 or π but to any desired ϕ 0 value in between. Such ϕ 0 junctions have many peculiar properties and may be effectively controlled by the optically driven Abrikosov vortex. Also we theoretically show that the Josephson junction with the embedded vortex can serve as an ultrafast memory cell operating at sub THz frequencies. I. INTRODUCTIONJosephson junctions (JJs) with nonzero spontaneous phase difference between the superconducting electrodes in the ground state (the so-called π , ϕ 0 , and ϕ JJs) have become the subject of intensive theoretical and experimental study during the past decade [1,2]. The most striking feature of such junctions is their ability to generate a current in the superconducting circuit, thus acting as a phase battery [3][4][5][6]. In addition, relatively small variation of the system parameters may provoke dramatic changes in the ground state phase difference, which is believed to provide new effective tools for controlling the currents in microelectronic devices (see, e.g., Refs. [7,8]).There are several generic mechanisms leading to the spontaneous appearance of nonzero Josephson phase. The basic one reveals when the superconducting (S) electrodes are separated by a ferromagnetic (F) layer. The exchange field inside the ferromagnet produces the spatial oscillations of the Cooper pair wave function, and depending on the ratio between the oscillation period and the F-layer thickness the ground state phase is equal to 0 or π (these cases are referred as 0 or π JJs, respectively) [9][10][11]. A peculiar situation is realized when the thickness d of the ferromagnet varies along the junction in a way that in some parts of the ferromagnet the value of d corresponds to the 0 state while in other parts to the π state (see Ref. [12] and references therein). If there is only a slight difference between the areas of the "0" and "π " regions the phase frustration can result in the appearance of a state with the spontaneous phase difference φ = ±ϕ = 0,π which is degenerate (ϕ JJ) (see Ref.[13] and references therein). A similar effect takes place in Josephson junctions with the current injectors acting as an effective source of the phase jumps along the junction (see and references therein). One can also obtain a ϕ 0 JJ, where the ground state phase φ = ϕ 0 is not degenerate, e.g., using the JJs with broken inversion symmetry [17]. In this case the superconducting current I through the junction should not be necessarily an odd function of the phase difference φ and can take the form I = I c sin(φ + ϕ 0 ) [17]. Such situation is realized in the S|F|S junctions with strong spin-orbit coupling (see and references therein) or complicated noncollinear distribution of the magnetization (see an...

Two mechanisms of Josephson phase shift generation by an Abrikosov vortex

“…Thus, there is no magnetic field neither inside, nor outside the vortex and current makes the only contribution to the phase shift. All previous theoretical studies considered a similar case [41,42,[44][45][46]. We note that junctions studied here and earlier [17,43] have intermediate electrode thickness d ∼ λ [53] and their sizes L x ∼ 5−6 µm are significantly larger that λ * ∼ 100 − 300 nm.…”

“…(1,8) and decays in a long-range manner ∝ 1/r, this is not a long range phenomenon because it is valid only at r λ * . In principle, the image method can be extended to r > λ * provided there are no stray fields [41,42,46]. This is the case for infinite-size objects with zero demagnetization factor.…”

“…An Abrikosov vortex (AV), having a 2π phase rotation, can induce a phase shift in a nearby Josephson junction (JJ) [41][42][43][44][45][46]. The vortex-induced phase shift depends on the distance and geometry [43,44].…”

“…The vortex-induced phase shift depends on the distance and geometry [43,44]. Since vortices can be easily and controllably manipulated (displaced, introduced or removed) by magnetic field [43,47], current [17,47,48], light or heat [46,49] pulses, they can be used for creation of memory cells [17] and tunable but persistent phase batteries. However, the mechanism of vortex-induced Josephson phase shift is still not well understood.…”

Josephson critical currents in annular superconductors with Pearl vortices

“…In several works, [4][5][6][7] it has been shown that the above features find a natural explanation when one considers the full gauge invariant phase variation (∆φ in what follows) across the junction. In these papers, by resorting to the Josephson's zero voltage supercurrent I J = I c sin(∆φ), and after evaluating ∆φ, which characterizes the superconducting condensate and ultimately depends on the magnetic flux, the above properties have been theoretically reproduced.…”