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arXiv:2408.14912 · Nanomaterials

Numerical Modeling of Vortex-Based Superconducting Memory Cells: Dynamics and Geometrical Optimization

Aiste Skog, Razmik A. Hovhannisyan, V. M. Krasnov

Published Oct 12, 2024• 4 citations
arXivHTMLPDF

Abstract

The lack of dense random-access memory is one of the main obstacles to the development of digital superconducting computers. It has been suggested that AVRAM cells, based on the storage of a single Abrikosov vortex-the smallest quantized object in superconductors-can enable drastic miniaturization to the nanometer scale. In this work, we present the numerical modeling of such cells using time-dependent Ginzburg-Landau equations. The cell represents a fluxonic quantum dot containing a small superconducting island, an asymmetric notch for the vortex entrance, a guiding track, and a vortex trap. We determine the optimal geometrical parameters for operation at zero magnetic field and the conditions for controllable vortex manipulation by short current pulses. We report ultrafast vortex motion with velocities more than an order of magnitude faster than those expected for macroscopic superconductors. This phenomenon is attributed to strong interactions with the edges of a mesoscopic island, combined with the nonlinear reduction of flux-flow viscosity due to the nonequilibrium effects in the track. Our results show that such cells can be scaled down to sizes comparable to the London penetration depth, ∼100 nm, and can enable ultrafast switching on the picosecond scale with ultralow energy per operation, ∼10-19 J.

DOI
10.3390/nano14201634

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The lack of dense random-access memory is one of the main obstacles to the development of digital superconducting computers. It has been suggested that AVRAM cells, based on the storage of a single Abrikosov vortex-the smallest quantized object in superconductors-can enable drastic miniaturization to the nanometer scale. In this work, we present the numerical modeling of such cells using time-dependent Ginzburg-Landau equations. The cell represents a fluxonic quantum dot containing a small superconducting island, an asymmetric notch for the vortex entrance, a guiding track, and a vortex trap. We determine the optimal geometrical parameters for operation at zero magnetic field and the conditions for controllable vortex manipulation by short current pulses. We report ultrafast vortex motion with velocities more than an order of magnitude faster than those expected for macroscopic superconductors. This phenomenon is attributed to strong interactions with the edges of a mesoscopic island, combined with the nonlinear reduction of flux-flow viscosity due to the nonequilibrium effects in the track. Our results show that such cells can be scaled down to sizes comparable to the London penetration depth, ∼100 nm, and can enable ultrafast switching on the picosecond scale with ultralow energy per operation, ∼10-19 J.
Superconductivity is an electronic state of matter arising from the existence of a common wave function with a coherent phase extending on a truly macroscopic scale. One major manifestation of this striking quantum phenomenon is the dissipationless transport of electrical current, an asset deserving particular attention in the present times where the efficient energy distribution has become of utmost importance. Unfortunately, the motion of quantum units of magnetic flux (so-called vortices or fluxons), which is an unavoidable side-effect found in superconductors in the presence of transport currents and magnetic fields, severely limits the conditions to preserve dissipationless transport. This poses a challenge for achieving the functionalization of superconducting materials and threatens their spectrum of applications. It is widely known that any inhomogeneities (either material imperfections, or ones made artificially), which locally suppress superconductivity on the scale comparable to the core of the vortex, can pin the vortex and delay the onset of the vortex motion to higher applied currents. In recent years a substantial effort has been made to minimize the effects of current-induced vortex motion by tailoring arrays of artificial pinning centers. Besides improving the critical parameters of the superconducting state, a pinning matrix can be used for the manipulation of vortex matter, thus directly affecting the vortex dynamics, such as rectification of vortex motion under an ac drive (vortex diode) by introducing asymmetric pinning landscapes. In the literature one can find that the realization of the anchoring of the vortices can be based on nanostructured arrays of perforations, chemically grown defects, permanent nanomagnets, or even pinning sites produced by heavy ion bombardment. All of those realizations are based on a permanent imprint on the superconductor, without any possibility for subsequent modifications in the distribution and strength of the pinning. The principal objective of this thesis is to investigate the dynamical behavior of vortex matter under an entirely new kind of pinning landscape consisting of spatial and temporal modulation of the superconducting condensate. A particular case of spatial modulation is considered in a constricted structure where current lensing can cause extremely high vortex velocities. Subsequently, a time-dependent thermal potential introduced to the superconducting condensate will cause stroboscopic resonances during the vortex motion - a phenomenon that cannot be observed in the systems with static pinning imprints. Finally, a study of electronic gating is presented, where the local properties of superconductor, such as mean free path, or electronic band structure in general, can be influenced electronically. This is a completely unexplored interdisciplinary research topic, which will eventually allow one to manipulate individual vortices in superconducting materials by means of spatially confined and temporally controlled thermal and electromagnetic excitations. Furthermore, such techniques can provide one fundamental insight in different states of the vortex matter with respect to variation of the transport current, highly relevant for understanding the resistive state of superconducting materials and their applications.
The demand for low-dissipation nanoscale memory devices is as strong as ever. As Moore’s law is staggering, and the demand for a low-power-consuming supercomputer is high, the goal of making information processing circuits out of superconductors is one of the central goals of modern technology and physics. So far, digital superconducting circuits could not demonstrate their immense potential. One important reason for this is that a dense superconducting memory technology is not yet available. Miniaturization of traditional superconducting quantum interference devices is difficult below a few micrometers because their operation relies on the geometric inductance of the superconducting loop. Magnetic memories do allow nanometer-scale miniaturization, but they are not purely superconducting (Baek et al 2014 Nat. Commun. 5 3888). Our approach is to make nanometer scale memory cells based on the kinetic inductance (and not geometric inductance) of superconducting nanowire loops, which have already shown many fascinating properties (Aprili 2006 Nat. Nanotechnol. 1 15; Hopkins et al 2005 Science 308 1762). This allows much smaller devices and naturally eliminates magnetic-field cross-talk. We demonstrate that the vorticity, i.e., the winding number of the order parameter, of a closed superconducting loop can be used for realizing a nanoscale nonvolatile memory device. We demonstrate how to alter the vorticity in a controlled fashion by applying calibrated current pulses. A reliable read-out of the memory is also demonstrated. We present arguments that such memory can be developed to operate without energy dissipation.
Purpose The lack of reliable and scalable superconducting random access memory (RAM) cells is the main obstacle for full implementation of superconducting rapid single flux quantum(RSFQ) computers. This work points the methodology and the structures that shall be used in future implementation of RSFQ RAM. Design/methodology/approach A new design for RAM using two ferromagnetic strips in proximity to the superconductor in a RSFQ computer is presented (1). The concept of using a RAM RSFQ cell as a tuneable superconducting qubit is also explored. Findings Two basic architectures for superconducting RAM cells were developed with integration schemes in two dimensions. Research limitations/implications The proposed RAM cells as depicted in Figures 7 and 16 offer smaller size and greater 3 scalability in comparison to other suggested schemes (4), (3), (2), (5). Practical implications Currently, the main obstacle in implementation of RSQF computer is lack of reliable RAM cell. RSQF computer shall have potential to take a large fraction of classical supercomputers, as it consumes much less power. Social implications Computation power shall be cheaper when one uses RSQF computers for big data and computational centres. It is a matter of some time. Originality/value The publication presents the new design of superconducting RAM cell for use in RSQF computer. The numerical relaxation method is used to solve biharmonic Ginzburg–Landau equation. The analytic approach as a solution of a specified problem is given.
Superconductors can host quantized magnetic flux tubes surrounded by supercurrents, called Abrikosov vortices. Vortex penetration into a superconducting film is usually limited to its edges and triggered by external magnetic fields or local electrical currents. With a view to novel research directions in quantum computation, the possibility to generate and control single flux quanta in situ is thus challenging. We introduce a far-field optical method to sculpt the magnetic flux or generate permanent single vortices at any desired position in a superconductor. It is based on a fast quench following the absorption of a tightly focused laser pulse that locally heats the superconductor above its critical temperature. We achieve ex-nihilo creation of a single vortex pinned at the center of the hotspot, while its counterpart opposite flux is trapped tens of micrometers away at its boundaries. Our method paves the way to optical operation of Josephson transport with single flux quanta.
Abstract Storage of a single magnetic flux quantum in a superconducting loop containing a Josephson junction represents a promising unit cell configuration for construction of a cryogenic memory of superconducting digital circuits. However, application of a DC bias current is required for operation of such a memory cell to maintain trapping of the flux quantum in the storage loop. In this work, we present a superconducting memory cell that uses a superconducting-magnetic π junction. The cell characteristics show flux quantum hysteresis centering at the zero-bias current. We develop a fabrication process that combines superconductor–ferromagnet–superconductor (SFS) junctions with superconductor–normal metal–superconductor (SNS) junctions. The critical current density of the SFS junctions shows a 0–π oscillation as a function of the ferromagnetic layer thickness. The formation of the π junction is confirmed further by the flux modulation curves of a superconducting quantum interference device made from SNS junctions with an additional SFS junction.
The talk is based on an overview which was published recently (1). For this reason, only an abstract is given here, which includes Later results not contained in the aforementioned overview. The presently-known Josephson memory cells store information as persistent currents in superconducting loops, or what is equivalent as a magnetic flux in the area of the ring. This method of storage is nonvolatile and has no power consumption in the storing state. In a superconducting ring system, the magnetic flux is quantized, and cells have been built which operate either with only one flux quantum, or with many of them. For the Latter cells with many flux quanta (ring cells), quite a number of designs exist. They have one or two Josephson junctions in the ring, which allow writing. An external junction which is controlled by the ring current serves for non-destructive reading of the information. The smallest cell realized had an area of 900 ?m2 with a 2 ?m minimum line width. Switching speed was ? 80 ps. Cells which store information as a single-flux quantum (single flux-quantum cells = SFQ cells) in the ring, usually contain two Josephson junctions used for reading and writing. Read-out in most of these cells is destructive, but methods of reading non-destructively have also been proposed. The smallest device made had an area of ? 150 ?m2 with a minimum line width of 2 ?m. The read signal had a rise time ? 100 ps.