Superconductivity in self-rolled nanoarchitectures

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Superconductivity is one of the most intriguing effects predicted by quantum theory. In a superconducting material, electrical currents can be sustained for an infinitely long time without dissipation. Prof Vladimir Fomin, at the Leibniz Institute for Solid State and Materials Research (IFW) Dresden, is pioneering the use of micro- and nanostructures by virtue of the appearance of topological defects, which can be used to control currents in superconductors. His fundamental results unveil the fascinating and hitherto unknown physical phenomena occurring in the man-made nanoarchitectures fabricated by state-of-the-art high-tech methods: strain-induced rolling up and focused ion/electron beam writing.

Superconductors are among the most exciting and widely studied subjects of modern physics and materials science. First identified in 1911, the materials feature an electrical resistance which suddenly drops to zero below a certain ‘critical temperature’, and also expel any magnetic fields contained within them. Together, these properties allow superconductors to sustain an electric current for indefinitely long periods of time, without any need for an external power source to keep the current from decaying.

When they were first discovered, the classical theory of electromagnetism was found to be incapable not only of predicting, but even explaining the existence of this exotic state of matter. It was only during the 1950s that two fully quantum-mechanical models of (conventional) superconductivity were developed; namely, the phenomenological Ginzburg-Landau theory and the microscopic Bardeen-Cooper-Schrieffer theory.

Nowadays, superconducting materials are integrated in several types of equipment and machinery, including magnets for nuclear magnetic resonance imaging machines, fusion reactors, and particle accelerators. They have also become excellent materials for magnetic levitation railway systems, energy storage, electrical power generation, magnetic sensors, high-frequency filters and switches, and in quantum computing devices.

“We report on a topological transition between the two types of topological defects: vortices and phase slips under a strong transport current in an open superconductor nanotube with a submicron-scale inhomogeneity of the normal-to-the-surface component of the applied magnetic field. When the magnetic field is orthogonal to the axis of the nanotube, which carries the transport current in the azimuthal direction, the induced voltage shows a pulse as a function of the magnetic field.” – V. M. Fomin

Superconductivity is already highly desirable in many modern technologies – yet in recent years, their performance has been advanced even further through the ability to fabricate superconductor micro- and nanostructures. “These emerging complex structures are leading to superconductors with novel, counterintuitive materials properties, promising a significant improvement in performance compared with available devices”, explains Prof Vladimir Fomin, at the Leibniz Institute for Solid State and Materials Research (IFW) Dresden.

“Micro- and nanostructured superconductors, like microtubes and nanohelices, exhibit unique mechanical, electrical, magnetic and optical properties.”

Introducing topological defects

Typically, superconducting materials need to be nanoengineered to achieve the levels of performance required in most of these advanced applications. In his research, Prof Fomin explores fascinating new ways to overcome the challenges presented by these requirements, through unfixable tears in superconductor nanostructures, named ‘topological defects’.

Topology plays a crucial role in the physics of superconductivity. It deals with the properties of a superconductor structure that are preserved under continuous deformations, like stretching or bending. The ‘topological defects’ occur when adjoining geometric structures within a material cannot seamlessly transition between each other without being cut or joined together in any way.

Figure 1. The superconductor open tube manifests diverse vortex patterns and superconducting screening currents (SSCs).

Prof Fomin has been conducting theoretical research in this pioneering field of superconductors for over ten years. “These defects are induced by the geometric designs of the curved micro- and nanostructures of superconductors”, he describes. “They give rise to unique spatial patterns and dynamics of the superconducting state, which can be observed experimentally.” This work has revealed a plethora of intriguing physical effects caused by the low dimensionality in conjunction with complex geometry of these high-tech materials.

In order to theoretically account for and to simulate the superconducting properties of these complex nanostructures, Prof Fomin and his collaborators have developed a powerful numerical approach linking time-dependent Ginzburg-Landau theory; the Poisson equation, describing the electric field; and Maxwell’s equations of electromagnetism. This platform has allowed the researchers to make quantitative predictions of the occurrence of topological defects within specific superconducting micro- and nanoarchitectures, and the new phenomena they cause.

Superconductors with finite resistance

In bulk, or 3D superconductors, topological defects take the form of structures named ‘vortices’, which describe tiny, closed loops of superconducting currents that allow magnetic fields to penetrate their cores. Vortices can also form in low-dimensional, for instance, 2D superconductors, alongside another type of extended topological defects, named ‘phase slips’. At these defects, the superconducting ‘order parameter’ – a quantity describing the difference in a material’s state on each side of its critical temperature – drops to zero. Subsequently, the order parameter’s phase will suddenly change by an integer multiple of 2 within a closed loop around each vortex core or across the phase-slip region.

Figure 2. The vortex-chain regime: the amplitude and phase of the order parameter and the SSC patterns in the Nb open microtube under the magnetic field 6

Remarkably, both moving vortices and phase slips bring about a finite electrical resistance, destroying superconductivity. However, unlike conventional conductors, in which the resistance decreases continuously with lowering temperature, the tendency of superconductors to resist electrical current as a function of temperature exhibits far richer and more diverse effects owing to topological defects.

In the simulations and experiments, Prof Fomin and his colleagues trigger topological defects by engineering superconductor structures on both micro- and nanoscales. In doing this, he has shown that topological defects lead to the appearance of entirely new physical properties, which defy our current understanding of superconductivity.

Topological phase transitions

In one intriguing example, topological defects play a key role in shaping the response of a superconductor to an applied magnetic field. The effect occurs within rolled-up niobium and tin microtubes, which consist of ultrathin bi- or trilayers. Using dedicated strain-induced self-organisation processes, these systems can be made to turn upon themselves, once or repeatedly, to form rolled-up tubular structures of unique geometry.

“Topological defects induced by virtue of a material’s geometry can be used to control the physical properties of a superconductor.”

The work of Prof Fomin and his colleagues has demonstrated the existence of a topological transition, which occurs when a magnetic field is applied at a right angle to the axis of the open microtubes. “Our investigations have unveiled transitions between vortex-chain and phase-slip regimes within curved superconductor nanostructures, which vary as a function of the applied magnetic field under a strong transport current”, Prof Fomin explains. “This opens up a possibility to efficiently tailor the superconducting properties of nanostructured materials.”

Figure 3. The phase-slip regime: the amplitude and phase of the order parameter and the superconductor screening current patterns in the Nb open microtube under the magnetic field 10 mT.

One of the consequences of this phenomenon, which determines the magnetic field–voltage and current–voltage characteristics of the superconductor microtubes, is the appearance of a pulse-like induced voltage in response to the applied magnetic field. Prof Fomin is currently expanding the study of superconductor nanostructures to the analysis of their response to transport currents which alternate in direction and magnitude. This work is providing fascinating new perspectives on how nanoengineered superconducting materials could be precisely tailored.

Superconducting nanohelices

Building on previous examinations of the occurrence and evolution of topological defects, Prof Fomin’s most recent work has focused on understanding and predicting the properties of superconductor micro- and nanohelices. These chiral (distinguishable from their mirror images) spiral-shaped structures exhibit unique mechanical, electrical, magnetic, and optical properties, and are of central interest in a large number of superconducting technologies. One of them is a microscopy-based technique, which uses focused beams of helium ions to fabricate three-dimensional tungsten carbide nanohelices of specific geometries.

Using this approach, extremely small and densely packed nanohelices were fabricated featuring diameters of 100 nanometres, and an aspect ratio of up to 65. Extensive simulations based on the numerical platform developed by Prof Fomin and his collaborators have also allowed researchers to identify the fingerprints of topologically distinct, experimentally observed vortex and phase-slip patterns, whose origin has been traced back to the helical geometry of the superconductor samples.

Prof Fomin’s team will now continue these efforts in their future research and hopes to shed soon even more light on how precisely engineered nanostructures can induce intriguing behaviours due to topological defects. Ultimately, their work takes us a step closer to unlocking the full potential of superconducting materials, and applying them across an even wider array of advanced technologies.

Figure 4. Simulated order parameter distributions plotted over the 2D surface of the tungsten carbide nanohelix at four values of the transport current (left panel) allow for interpretation of four steps in the experimentally measured resistance (right panel) for the magnetic field 2 T

What are the most important future directions and current challenges in the development of next-generation superconducting devices?

• To enhance by orders of magnitude sensitivity of superconductor nanosensors of the magnetic field and to design innovative superconductor quantum-interference filters and switchers (towards perfect switchers!) based, e.g., on the controlled vortex dynamics and topological transition between vortices and phase slips in superconductor open nanotubes and hybrid nanostructures.

• To develop novel robust elements for fluxon-based quantum information processing and quantum computing, e. g., self-assembled networks of Josephson Junctions, parametric amplifiers, memory elements, superconducting qubits or frequency generators, based on sustainable double fluxon transmission lines in superconductor open nanotubes.

• To develop sustainable superconducting nanostructured bolometers and THz-detectors, which possess a significant advancement in sensitivity and reduction in noise as compared to the available ones, e.g., using superconductor nanohelices.



  • Fomin, V. (2021). Self-rolled Micro- and Nanoarchitectures: Topological and Geometrical Effects. De Gruyter, Berlin-Boston. Available at: [Accessed 17 August 2021]
  • Rezaev, R; Smirnova, E; Schmidt, O; Fomin, V. (2020). Topological transitions in superconductor nanomembranes under a strong transport current. Communications Physics, 3, 144. Available at: [Accessed 17 August 2021]
  • Córdoba R; Mailly, D; Rezaev R; Smirnova, E; Schmidt, O; Fomin, V; Zeitler, U; Guillamón, I; Suderow, H; De Teresa, J. (2019). Three-Dimensional Superconducting Nanohelices Grown by H+-Focused-Ion-Beam Direct Writing. Nano Letters, 19, 8597-8604. Available at: [Accessed 17 August 2021]
  • Fomin, V. (2021). Prof Dr Vladimir Fomin [online]. Leibniz Institute for Solid State and Materials Research (IFW) Dresden. Available at: [Accessed 17 August 2021].

Research Objectives

Prof Vladimir Fomin researches topological defects in nanostructures in order to control currents in superconductors.


  • German Research Foundation (DFG)
  • European Cooperation in Science and Technology – COST Action #CA16218 (NANOCOHYBRI)


  • Prof Dr Oliver G. Schmidt (Dresden, Germany)
  • Dr Vladimir N. Gladilin (Antwerp, Belgium)
  • Dr Roman R. Rezaev (Moscow, Russia)
  • Prof Dr José María De Teresa (Zaragoza, Spain)
  • Dr Rosa Córdoba (Valéncia, Spain)
  • Prof Dr Hermann Suderow (Madrid, Spain)
  • Prof Dr Francesco Tafuri (Naples, Italy)
  • Prof Dr. Feo Kusmartsev (Loughborough, UK)
  • Priv.-Doz. Dr Habil Oleksandr V. Dobrovolskiy (Vienna, Austria)
  • Dr Nicola Poccia (Dresden, Germany)


Prof Vladimir Fomin is scientist and educator. His scientific interests lie in nanophysics, especially the theory of strain-induced self-rolled nano- and microarchitectures: rolled-up membranes and nanohelices and self-assembled quantum rings; optical properties of quantum dots and optical waveguides; persistent currents and magnetisation of quantum rings; topological defects and vortex matter in meso-, nanoscopic and patterned superconductors; phonons and thermoelectric effects in nanostructures.

Prof Vladimir Fomin

Prof Dr Vladimir M. Fomin
Institute for Integrative
Nanosciences (IIN)
Leibniz Institute for Solid State
and Materials Research (IFW)
Helmholtzstraße 20
D-01069 Dresden

T: +49 351 4659 780

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