3D nano-superconductors, with non-trivial geometry-driven topological phenomena, stand as promising systems for the future evolution of efficient and multifunctional technologies. However, the substantial challenges inherent in the experimental work, particularly regarding the fabrication and characterization of 3D nanoscale geometries and unconventional topologies of superconducting states, have confined the majority of investigations in this domain until recently to the realms of computational and theoretical studies. We overview the recent advancements in fabricating superconductor 3D nanoarchitectures and unveiling their fascinating physical properties that occur due to the geometry-induced topology and chirality, which offer a broad spectrum of applications of these nanostructures for the front-line development of various modern technologies.

Topics
Quantum vortices, Superconducting devices, Superconductors, Focused ion beam, Topological properties, Electron beam-induced deposition, Nanotubes, Nanowires, Quantum nanostructures, Chirality

This Letter is devoted to the revolutionizing penetration of two mathematical concepts in physics: “topology,” which embraces the properties of a geometric object that are preserved under continuous deformations,1 and “chirality” that identifies the property of asymmetry of a system, which is distinguishable from its mirror image.2 The both concepts have led to unprecedented wealth of results in physics. The realm of topological matter can be conventionally subdivided into two categories.3 First, topologically protected surface/edge states governed by Dirac physics and/or topologically non-trivial electronic structure in the momentum space underlie the origin of quantum Hall effect, quantum spin Hall effect, quantum anomalous Hall effect, nonmagnetic topological insulators, topological crystalline insulators, topological semimetals4 as well as topological superconductors and Majorana fermions. Second, non-trivial topology occurs due to a complex geometry of structures or fields in real space, e.g., quantum rings, Möbius bands,5 metamaterials of interlocked hollow semiconducting tori, optical waveguides, arrays of Josephson junctions, Skyrmions, and other topologically non-trivial spin and magnetic textures.6 Here, an overview is provided of topology- and chirality-driven effects in the complex man-made geometries in real space, implemented by the recently developed high-tech methods to fabricate superconductor three-dimensional (3D) micro- and nanoarchitectures.

The incorporation of the third dimension into nano-superconductivity enables the deliberate manipulation of topology and chirality through the formulation of curved geometries. As a result, the integration of nanoscale dimensions with three-dimensional and curvilinear structures for the development of 3D nano-superconductors constitutes a noteworthy frontier in emerging physics.3,7

It has been theoretically predicted that superconducting properties on 3D micro-superconductors, such as spherical shells,8 curved mesoscopic strips,9 hollow cylinders,10 thin-walled open cylinders,11,12 helices,13 and Möbius strips,14 are cardinally different from those observed in analogous 2D structures. Particularly, the Josephson effect can be regulated, with control over both the amplitude and phase of the supercurrent, and the confinement-induced curvature effects through the curved geometry of superconductors.15 In addition, the distinctive vortex dynamics identified in curved geometries with particular topologies has been recognized as one of the most promising areas for research.16 

Experimental evidence, when conducted, has predominantly been confined to rudimentary 3D nano-superconductors or, in some instances, to 3D micro-superconductors that incompletely elucidate the boundless potential offered by a transition of nano-geometries into three dimensions.

In the subsequent two sections, we will first delineate the advancements achieved in fabricating genuine superconductor 3D nanoarchitectures. Second, we will expound upon the innovative properties experienced by these 3D nanoarchitectures induced by curved nano-geometries.

Experimental evidence has demonstrated that the pathways for fabricating complex SC 3D nanoarchitectures rely on sophisticated methodologies:

  1. The utilization of chemical synthesis based on solid-gas reactions, notably evident in the fabrication of Transition Metal Dichalcogenide nanotubes, particularly WS2.17 

  2. The employment of freestanding superconducting rolled-up technology,18,19 which allowed for the fabrication of the first superconductor niobium radial superlattices20,21 and seamlessly integrates the 2D superconducting layer with a helical spiral curvature, as exemplified in the fabrication of microwave radiation detectors.22 

  3. The adoption of the conventional Dolan bridge technique for the nanofabrication of 3D superconducting circuit suspended from the substrate.23 This ground-breaking technique has facilitated the introduction of the elusive Blochnium superconducting qubit.24 

  4. The utilization of a methodology based on DNA self-assembly to create 3D arrays of Josephson junctions, yielding niobium cubic superlattices with a 48 nm unit cell.25 

  5. The strategic deployment of 3D nanoprinting techniques to grow 3D nano-superconductors in a single step.26,27 This approach has been used in fabricating wires,28–32 hollow nanocylinders,33,34 and nanohelices.35 

Several representative 3D superconductor nanoarchitectures are depicted in Fig. 1.

FIG. 1.
Examples of 3D superconductor nanoarchitectures. (a) TEM image of a chemically synthesized chiral superconducting WS2 nanotube. Contrast image shows the cylindrical structure with a diameter of about 100 nm. Scale bar, 50 nm. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) SEM image of a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948–2955 (2019). Copyright 2019 American Chemical Society. (c) SEM image 3D superconducting superlattices (with simple cubic symmetry and 48 nm unit cell) using self-assembly of 3D DNA frames. Adapted with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (d) SEM image of a hollow nanocylinder with outer diameter down to 32 nm grown using He+ FIBID as a 3D nanoprinting technique. Inset: TEM image of the cross sectional view of the hollow nanocylinder with inner diameter down to 6 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379–1386 (2018). Copyright 2018 American Chemical Society. (e) STEM images of hollow nanocylinders with different inner and outer diameters grown using He+ FIBID. Adapted with permission from R. Córdoba et al., Beilstein J. Nanotechnol. 11, 1198–1206 (2020). Copyright 2020 Beilstein-Institut. (f) SEM image of a fabricated Blochnium device using Dolan bridge technique. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368–371 (2020). Copyright 2020 Springer Nature. (g) SEM image of a freestanding 3D nanowire of width 170 nm grown using Ga+ FIBID as a 3D nanoprinting technique. Reproduced with permission from F. Porrati et al., ACS Nano 13, acsnano.9b00059 (2019). Copyright 2019 American Chemical Society. (h) SEM images of individual WC nanohelices with nanowire diameter of 45 nm and a nanohelices array grown using He+ FIBID. Δ V represents the locations of the voltage contacts. Inset: the top view of the nanohelix. Scale bar: 100 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597–8604 (2019). Copyright 2019 American Chemical Society.
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Examples of 3D superconductor nanoarchitectures. (a) TEM image of a chemically synthesized chiral superconducting WS2 nanotube. Contrast image shows the cylindrical structure with a diameter of about 100 nm. Scale bar, 50 nm. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) SEM image of a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948–2955 (2019). Copyright 2019 American Chemical Society. (c) SEM image 3D superconducting superlattices (with simple cubic symmetry and 48 nm unit cell) using self-assembly of 3D DNA frames. Adapted with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (d) SEM image of a hollow nanocylinder with outer diameter down to 32 nm grown using He+ FIBID as a 3D nanoprinting technique. Inset: TEM image of the cross sectional view of the hollow nanocylinder with inner diameter down to 6 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379–1386 (2018). Copyright 2018 American Chemical Society. (e) STEM images of hollow nanocylinders with different inner and outer diameters grown using He+ FIBID. Adapted with permission from R. Córdoba et al., Beilstein J. Nanotechnol. 11, 1198–1206 (2020). Copyright 2020 Beilstein-Institut. (f) SEM image of a fabricated Blochnium device using Dolan bridge technique. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368–371 (2020). Copyright 2020 Springer Nature. (g) SEM image of a freestanding 3D nanowire of width 170 nm grown using Ga+ FIBID as a 3D nanoprinting technique. Reproduced with permission from F. Porrati et al., ACS Nano 13, acsnano.9b00059 (2019). Copyright 2019 American Chemical Society. (h) SEM images of individual WC nanohelices with nanowire diameter of 45 nm and a nanohelices array grown using He+ FIBID. Δ V represents the locations of the voltage contacts. Inset: the top view of the nanohelix. Scale bar: 100 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597–8604 (2019). Copyright 2019 American Chemical Society.

FIG. 1.
Examples of 3D superconductor nanoarchitectures. (a) TEM image of a chemically synthesized chiral superconducting WS2 nanotube. Contrast image shows the cylindrical structure with a diameter of about 100 nm. Scale bar, 50 nm. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) SEM image of a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948–2955 (2019). Copyright 2019 American Chemical Society. (c) SEM image 3D superconducting superlattices (with simple cubic symmetry and 48 nm unit cell) using self-assembly of 3D DNA frames. Adapted with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (d) SEM image of a hollow nanocylinder with outer diameter down to 32 nm grown using He+ FIBID as a 3D nanoprinting technique. Inset: TEM image of the cross sectional view of the hollow nanocylinder with inner diameter down to 6 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379–1386 (2018). Copyright 2018 American Chemical Society. (e) STEM images of hollow nanocylinders with different inner and outer diameters grown using He+ FIBID. Adapted with permission from R. Córdoba et al., Beilstein J. Nanotechnol. 11, 1198–1206 (2020). Copyright 2020 Beilstein-Institut. (f) SEM image of a fabricated Blochnium device using Dolan bridge technique. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368–371 (2020). Copyright 2020 Springer Nature. (g) SEM image of a freestanding 3D nanowire of width 170 nm grown using Ga+ FIBID as a 3D nanoprinting technique. Reproduced with permission from F. Porrati et al., ACS Nano 13, acsnano.9b00059 (2019). Copyright 2019 American Chemical Society. (h) SEM images of individual WC nanohelices with nanowire diameter of 45 nm and a nanohelices array grown using He+ FIBID. Δ V represents the locations of the voltage contacts. Inset: the top view of the nanohelix. Scale bar: 100 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597–8604 (2019). Copyright 2019 American Chemical Society.
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Examples of 3D superconductor nanoarchitectures. (a) TEM image of a chemically synthesized chiral superconducting WS2 nanotube. Contrast image shows the cylindrical structure with a diameter of about 100 nm. Scale bar, 50 nm. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) SEM image of a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948–2955 (2019). Copyright 2019 American Chemical Society. (c) SEM image 3D superconducting superlattices (with simple cubic symmetry and 48 nm unit cell) using self-assembly of 3D DNA frames. Adapted with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (d) SEM image of a hollow nanocylinder with outer diameter down to 32 nm grown using He+ FIBID as a 3D nanoprinting technique. Inset: TEM image of the cross sectional view of the hollow nanocylinder with inner diameter down to 6 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379–1386 (2018). Copyright 2018 American Chemical Society. (e) STEM images of hollow nanocylinders with different inner and outer diameters grown using He+ FIBID. Adapted with permission from R. Córdoba et al., Beilstein J. Nanotechnol. 11, 1198–1206 (2020). Copyright 2020 Beilstein-Institut. (f) SEM image of a fabricated Blochnium device using Dolan bridge technique. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368–371 (2020). Copyright 2020 Springer Nature. (g) SEM image of a freestanding 3D nanowire of width 170 nm grown using Ga+ FIBID as a 3D nanoprinting technique. Reproduced with permission from F. Porrati et al., ACS Nano 13, acsnano.9b00059 (2019). Copyright 2019 American Chemical Society. (h) SEM images of individual WC nanohelices with nanowire diameter of 45 nm and a nanohelices array grown using He+ FIBID. Δ V represents the locations of the voltage contacts. Inset: the top view of the nanohelix. Scale bar: 100 nm. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597–8604 (2019). Copyright 2019 American Chemical Society.

Close modal

3D nanoprinting techniques rely on focused beams of charged particles, including ions, to form Focused Ion Beam (FIB) and to effectively address the significant limitations associated with traditional “top-bottom” nanofabrication methods in the development of 3D nano-superconductors.36 The noteworthy advantage of 3D nanoprinting, in contrast to direct competitors like two-photon lithography37 and electrodeposition,38 lies in its exceptionally high resolution (down to a few tens of nanometers33–35) and the ability to create shapes of arbitrary complexity.39 Ga+ FIB induced deposition (FIBID) (probe size ≈ 5 nm) has already been used to grow individual superconducting 3D W-C28–30,32 and Nb-C31 wires with Tc and Bc2 similar to those obtained for planar nanostructures. However, the resolution in this process is primarily constrained by the Ga+ beam diameter and its high lateral scattering, thus far preventing the growth of sub-100 nm 3D structures.

He+ FIBID has demonstrated its significance in the development of 3D superconducting nanostructures characterized by intricate geometries, higher aspect ratios, and exceptional superconducting properties (Tc ≈ 6.2–7.1 K, Bc2(0) ≈ 12–15 T), exemplified by structures like hollow nanocylinders33,34 and nanohelices.35 This success is attributed to its diminutive probe size (⁠ ≈ 0.3 nm)40 and minimal proximity effect.41 Thus, He+ FIBID marks a substantial leap forward in the direct-writing of 3D nano-objects when juxtaposed with Ga+ FIBID.

An illustrative demonstration of these capabilities lies in the production of tailored 3D hollow nanocylinders, featuring diameters as small as 32 nm, wall thicknesses down to 13 nm, and an aspect ratio ≈ 200.33,34 The presence of a 6 nm diameter hole at the center of the standing cylinder results from a delicate balance between milling and deposition processes. The resulting material exhibits a higher tungsten content (reaching up to 70 at. %) compared to that achieved through Ga+ FIBID. Moreover, the presence of 20–30 nm-sized crystalline grains of the face-centered cubic WC1−x phase is noted.

Another remarkable example involves the precise patterning of 3D nanohelices, achieved through meticulous adjustment of key deposition parameters such as dwell time and pattern diameter.35 The geometry of the nanohelices is effectively controlled, with turn lengths ranging from 200 nm to 2.3 μm, nanohelix diameters spanning from 100 to 295 nm, and nanowire diameter as small as 45 nm. Notably, the fabrication of the smallest and most densely packed superconducting nanohelix to date is reported, measuring as tiny as 100 nm in diameter and exhibiting an impressive aspect ratio of 65. These nanohelices demonstrate superconductivity below 7 K, along with high upper critical magnetic fields μ 0 H c 2 ≈ 15 T and large critical current densities J c ≈ 0.2 MA/cm2. To date, acquiring experimental evidence for 3D nano-superconductors through focused electron beam induced deposition (FEBID) has proven elusive, although the technique holds the potential to achieve this in the near future. Only a few studies have been reported, focusing on planar W-C42,43 (Tc ≈ 2–4.5 K), Pb-C44 (Tc ≈ 7.3 K), and Mo-C45 (Tc ≈ 10 K) FEBID superconducting materials using W(CO)6, (CH3CH2)4Pb, and Mo(CO)6 as precursors, respectively. However, it is noteworthy that, at present, only simple 3D nano-superconductors have been created through trial and error methodologies. The fabrication of complex 3D superconductor nanoarchitectures remains elusive, as the current repertoire of patterning tools in FIB46 and FEB47–49 necessitates further exploration of available precursors that could enable the production of more sophisticated 3D nano-superconductors.

Figure 2 illustrates various experimental instances showcasing geometry-induced topological phenomena in 3D superconductor nanoarchitectures.

FIG. 2.
Examples of geometry-driven topological phenomena of 3D superconductor nanoarchitectures. (a) Superconductor chiral nanotube [shown in Fig. 1(a)]. The upper panel displays a plot of R ω and R 2 ω in the low-magnetic field region at T = 4 K. Periodic oscillations are observed for both signals in the superconducting state. In the lower panel, the temperature variation of the resistance and magnitude of the quantum oscillations in R ω and R 2 ω is depicted. Both oscillating signals are enhanced around Tc. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) Hollow nanocylinders grown using He+ FIBID. The upper panel shows the Jc as a function of the applied magnetic field at 0.5 K for a hollow nanocylinder with an outer diameter of 32 nm. The behavior of Jc below the critical value B * (where B * = 2.63 T, representing the field at which Jc is 0.9 Jc at 0 T) is influenced by the strong confinement potential of a single row of vortices at the core of the hollow nanocylinder. Whereas for B above B *, Jc is subjected to fitting using a potential equation indicative of collective vortex pinning. An inset illustration depicts the penetration of magnetic flux into the hollow nanocylinder, with a single vortex row forming at B   <   B *. Lower panel illustrates the dependence of n values on R N / L for three nanocylinders. This dependency strongly indicates that smallest nanocylinders are approaching quasi-one-dimensional superconducting behavior. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379 (2018). Copyright 2019 American Chemical Society. (c) The Blochnium superconducting qubit [shown in Fig. 1(f)]. In the left panel, transition frequencies extracted from the two-tone spectroscopy data are presented as a function of the external flux through the loop, along with the fit to the spectrum. The right panel displays a zoomed-in-view of the raw data. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368 (2020). Copyright 2020 Springer Nature. (d) 3D arrays of Josephson junctions [shown in Fig. 1(c)]. The I–V characteristics were measured over the temperature range of 1.9–3.7 K. In the right inset, the V–I characteristics at 1.9 and 3.7 K are shown. In the left inset, the critical current derived from the I–V curves is presented as a function of temperature. Reproduced with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (e) Nanohelices. R–I characteristic is presented in the left panel for a nanohelix, while simulated order parameter distributions are depicted over the 2D surface of the helical structure in the right panel for magnetic field of 2 T. Various vortex and phase-slip patterns are associated with steps of resistance, as indicated by the red arrows. Inset: the tilted view of the nanohelix. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597 (2019). Copyright 2019 American Chemical Society.
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Examples of geometry-driven topological phenomena of 3D superconductor nanoarchitectures. (a) Superconductor chiral nanotube [shown in Fig. 1(a)]. The upper panel displays a plot of R ω and R 2 ω in the low-magnetic field region at T = 4 K. Periodic oscillations are observed for both signals in the superconducting state. In the lower panel, the temperature variation of the resistance and magnitude of the quantum oscillations in R ω and R 2 ω is depicted. Both oscillating signals are enhanced around Tc. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) Hollow nanocylinders grown using He+ FIBID. The upper panel shows the Jc as a function of the applied magnetic field at 0.5 K for a hollow nanocylinder with an outer diameter of 32 nm. The behavior of Jc below the critical value B * (where B * = 2.63 T, representing the field at which Jc is 0.9 Jc at 0 T) is influenced by the strong confinement potential of a single row of vortices at the core of the hollow nanocylinder. Whereas for B above B *⁠, Jc is subjected to fitting using a potential equation indicative of collective vortex pinning. An inset illustration depicts the penetration of magnetic flux into the hollow nanocylinder, with a single vortex row forming at B   <   B *⁠. Lower panel illustrates the dependence of n values on R N / L for three nanocylinders. This dependency strongly indicates that smallest nanocylinders are approaching quasi-one-dimensional superconducting behavior. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379 (2018). Copyright 2019 American Chemical Society. (c) The Blochnium superconducting qubit [shown in Fig. 1(f)]. In the left panel, transition frequencies extracted from the two-tone spectroscopy data are presented as a function of the external flux through the loop, along with the fit to the spectrum. The right panel displays a zoomed-in-view of the raw data. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368 (2020). Copyright 2020 Springer Nature. (d) 3D arrays of Josephson junctions [shown in Fig. 1(c)]. The I–V characteristics were measured over the temperature range of 1.9–3.7 K. In the right inset, the V–I characteristics at 1.9 and 3.7 K are shown. In the left inset, the critical current derived from the I–V curves is presented as a function of temperature. Reproduced with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (e) Nanohelices. R–I characteristic is presented in the left panel for a nanohelix, while simulated order parameter distributions are depicted over the 2D surface of the helical structure in the right panel for magnetic field of 2 T. Various vortex and phase-slip patterns are associated with steps of resistance, as indicated by the red arrows. Inset: the tilted view of the nanohelix. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597 (2019). Copyright 2019 American Chemical Society.

FIG. 2.
Examples of geometry-driven topological phenomena of 3D superconductor nanoarchitectures. (a) Superconductor chiral nanotube [shown in Fig. 1(a)]. The upper panel displays a plot of R ω and R 2 ω in the low-magnetic field region at T = 4 K. Periodic oscillations are observed for both signals in the superconducting state. In the lower panel, the temperature variation of the resistance and magnitude of the quantum oscillations in R ω and R 2 ω is depicted. Both oscillating signals are enhanced around Tc. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) Hollow nanocylinders grown using He+ FIBID. The upper panel shows the Jc as a function of the applied magnetic field at 0.5 K for a hollow nanocylinder with an outer diameter of 32 nm. The behavior of Jc below the critical value B * (where B * = 2.63 T, representing the field at which Jc is 0.9 Jc at 0 T) is influenced by the strong confinement potential of a single row of vortices at the core of the hollow nanocylinder. Whereas for B above B *, Jc is subjected to fitting using a potential equation indicative of collective vortex pinning. An inset illustration depicts the penetration of magnetic flux into the hollow nanocylinder, with a single vortex row forming at B   <   B *. Lower panel illustrates the dependence of n values on R N / L for three nanocylinders. This dependency strongly indicates that smallest nanocylinders are approaching quasi-one-dimensional superconducting behavior. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379 (2018). Copyright 2019 American Chemical Society. (c) The Blochnium superconducting qubit [shown in Fig. 1(f)]. In the left panel, transition frequencies extracted from the two-tone spectroscopy data are presented as a function of the external flux through the loop, along with the fit to the spectrum. The right panel displays a zoomed-in-view of the raw data. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368 (2020). Copyright 2020 Springer Nature. (d) 3D arrays of Josephson junctions [shown in Fig. 1(c)]. The I–V characteristics were measured over the temperature range of 1.9–3.7 K. In the right inset, the V–I characteristics at 1.9 and 3.7 K are shown. In the left inset, the critical current derived from the I–V curves is presented as a function of temperature. Reproduced with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (e) Nanohelices. R–I characteristic is presented in the left panel for a nanohelix, while simulated order parameter distributions are depicted over the 2D surface of the helical structure in the right panel for magnetic field of 2 T. Various vortex and phase-slip patterns are associated with steps of resistance, as indicated by the red arrows. Inset: the tilted view of the nanohelix. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597 (2019). Copyright 2019 American Chemical Society.
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Examples of geometry-driven topological phenomena of 3D superconductor nanoarchitectures. (a) Superconductor chiral nanotube [shown in Fig. 1(a)]. The upper panel displays a plot of R ω and R 2 ω in the low-magnetic field region at T = 4 K. Periodic oscillations are observed for both signals in the superconducting state. In the lower panel, the temperature variation of the resistance and magnitude of the quantum oscillations in R ω and R 2 ω is depicted. Both oscillating signals are enhanced around Tc. Reproduced with permission from F. Qin et al., Nat. Commun. 8, 14465 (2017). Copyright 2017 Springer Nature. (b) Hollow nanocylinders grown using He+ FIBID. The upper panel shows the Jc as a function of the applied magnetic field at 0.5 K for a hollow nanocylinder with an outer diameter of 32 nm. The behavior of Jc below the critical value B * (where B * = 2.63 T, representing the field at which Jc is 0.9 Jc at 0 T) is influenced by the strong confinement potential of a single row of vortices at the core of the hollow nanocylinder. Whereas for B above B *⁠, Jc is subjected to fitting using a potential equation indicative of collective vortex pinning. An inset illustration depicts the penetration of magnetic flux into the hollow nanocylinder, with a single vortex row forming at B   <   B *⁠. Lower panel illustrates the dependence of n values on R N / L for three nanocylinders. This dependency strongly indicates that smallest nanocylinders are approaching quasi-one-dimensional superconducting behavior. Adapted with permission from R. Córdoba et al., Nano Lett. 18, 1379 (2018). Copyright 2019 American Chemical Society. (c) The Blochnium superconducting qubit [shown in Fig. 1(f)]. In the left panel, transition frequencies extracted from the two-tone spectroscopy data are presented as a function of the external flux through the loop, along with the fit to the spectrum. The right panel displays a zoomed-in-view of the raw data. Adapted with permission from I. V. Pechenezhskiy et al., Nature 585, 368 (2020). Copyright 2020 Springer Nature. (d) 3D arrays of Josephson junctions [shown in Fig. 1(c)]. The I–V characteristics were measured over the temperature range of 1.9–3.7 K. In the right inset, the V–I characteristics at 1.9 and 3.7 K are shown. In the left inset, the critical current derived from the I–V curves is presented as a function of temperature. Reproduced with permission from L. Shani et al., Nat. Commun. 11, 5697 (2020). Copyright 2020 Springer Nature. (e) Nanohelices. R–I characteristic is presented in the left panel for a nanohelix, while simulated order parameter distributions are depicted over the 2D surface of the helical structure in the right panel for magnetic field of 2 T. Various vortex and phase-slip patterns are associated with steps of resistance, as indicated by the red arrows. Inset: the tilted view of the nanohelix. Adapted with permission from R. Córdoba et al., Nano Lett. 19, 8597 (2019). Copyright 2019 American Chemical Society.

Close modal

Superconductivity in chiral nanotubes. Chiral WS2 nanotubes reveal non-identical current behaviors under paraxial magnetic fields due to chirality.17 Nonreciprocal superconducting transport, detected through second harmonic signals in AC magnetoresistance, reveals a chirality-induced effect on superconductivity. The nonreciprocal signals are notably enhanced in the superconducting state, featuring oscillations with a period equal to the magnetic flux quantum and increased magnitude around Tc, indicating quantum interference of the superconducting current. These chiral WS2 nanotubes hold promise for superconductivity modulation via nonreciprocity [Fig. 2(a)].

Hollow nanocylinders33,34 display superconducting characteristics below the critical temperature of Tc = 6.3 K, accompanied by a substantial critical magnetic field μ 0 H c 2 ( 0 ) ≈ 13.9 T and critical current density J c ≈ 0.23 MA/cm, which exceeds by 1.5 times the value for planar nanowires of comparable dimensions fabricated using Ga+ FIBID. Below the critical value B * = 2.6 T (defined as, the field, at which J c ( B ) is 0.9 Jc at 0 T), the behavior of Jc is influenced by the strong confinement potential of a single row of vortices at the core of the hollow nanocylinder50 [Fig. 2(b)].

In a rolled-up nanohelix, the low-dimensionality of the superconducting niobium layer is combined with a helical spiral curvature in a transition-edge sensor.22 The standalone sensor features an exceptionally low heat capacity and achieves an ultrafast response time. The supporting bilayer of the nanohelix is 50 nm, and the chiral geometry dictates minimal contact points between the transition-edge sensor and the substrate.

The Blochnium superconducting qubit exploits the coherent insulating response of a single Josephson Junction, resulting from the extension of phase fluctuations beyond 2 π [Fig. 2(c)]. A significant technological advancement of this research involves integrating a weak junction shunted with an exceptionally high inductance in a 3D superconducting circuit.24 The radio frequency excitation spectrum is analyzed while manipulating the external magnetic flux passing through the 3D loop, aligning with a duality mapping of Blochnium onto a transmon, which substitutes the external flux with the offset charge and introduces an alternative collective quasicharge variable.

The DNA-based self-assembly facilitates the formation of precisely organized 3D arrays of Josephson Junctions [Fig. 2(d)]. Each pair of superconducting octahedra is intricately connected by a weak link, surpassing the niobium superconducting coherence length of approximately 40 nm. The low-temperature I–V curves of the array exhibit behavior similar to that of an individual Josephson Junction.25 

Nanohelices. An enhancement of the magnetic field values (35% larger compared to hollow nanocylinders33), at which the resistance reaches 10% of its normal-state value, is observed for a nanohelix of a specific type.35 Additionally, tilting the magnetic field reveals a significant influence on the upper critical magnetic field. At the same time, a nanohelix of a different type reveals characteristic features of vortex- and phase-slip-regimes, experimentally discerned through resistance steps in the I–V curves. These patterns are attributed to topologically non-trivial screening currents and confinement potentials in the helical 3D geometry. The experimental observations are supported by numerical simulations based on the time-dependent Ginzburg–Landau equation coupled with the Poisson equation. Simulations unveil various patterns of the order parameter corresponding to the spatial distribution of the normal-to-the-surface component of the magnetic field over the surface of the nanohelix at different values of the transport current [Fig. 2(e)].

Dynamic topological transitions. Dynamic geometry-driven topological transitions in open superconductor nanotubes occur under a combined dc+ac transport current.51 The key effect is a transition between two regimes of superconducting dynamics [Fig. 3(a)]. The first regime is characterized by a pronounced first harmonic in the FFT spectrum of the induced voltage at the ac frequency. The second regime is represented by a rich FFT spectrum of the induced voltage with pronounced low-frequency components. The unveiled transitions between vortex- and phase-slip-based transport regimes in 3D nanoarchitectures governed by the global superconducting screening currents flowing over the entire structures are of topological nature and, therefore, are robust with respect to defects and impurities.

FIG. 3.
Computationally unveiled geometry-driven topological phenomena. (a) Effect of the ac frequency on the dynamics of topological defects in open Nb superconductor nanotubes. Adapted with permission from V. M. Fomin et al., Sci. Rep. 12, 10069 (2022). Copyright 2022 Springer Nature. The time-dependent voltage (panels 1–3) and its FFT spectra (panels 4–6) at the magnetic field B = 2 mT, the dc transport current j0 = 2.1 GAm2, and the transport current modulation depth j 1 / j 0 = 0.5 for the ac frequencies 3, 6, and 10 GHz. The second- and third-highest peaks are indicated by arrows in the inset of panel (5). (b) The frequency spectrum f U ( B ) as a function of the magnetic induction B for the nanotube with R = 390 nm at the transport current densities 16 and 20 GA/m2. Adapted with permission from I. Bogush et al., Phys. Rev. B 109, 104516 (2024). Copyright 2024 American Physical Society. (c) Snapshots of the absolute value of the superconducting order parameter | ψ | overlaid with the accumulated vortex paths for the nanotube with R = 390 nm at the transport current density j tr = 16 GA/m2 under tiled magnetic fields. L: left; R: right (half-tube); M: middle; b: bifurcations; m: multifurcations. The number in the jet name corresponds to the number of vortex chains in the jet. Direction of the vortex motion is indicated by the arrows. The dash-dotted lines are the midlines. Adapted with permission from I. Bogusch et al., Nanomaterials 14, 420 (2024). Copyright 2024 MDPI.
View largeDownload slide

Computationally unveiled geometry-driven topological phenomena. (a) Effect of the ac frequency on the dynamics of topological defects in open Nb superconductor nanotubes. Adapted with permission from V. M. Fomin et al., Sci. Rep. 12, 10069 (2022). Copyright 2022 Springer Nature. The time-dependent voltage (panels 1–3) and its FFT spectra (panels 4–6) at the magnetic field B = 2 mT, the dc transport current j0 = 2.1 GAm2, and the transport current modulation depth j 1 / j 0 = 0.5 for the ac frequencies 3, 6, and 10 GHz. The second- and third-highest peaks are indicated by arrows in the inset of panel (5). (b) The frequency spectrum f U ( B ) as a function of the magnetic induction B for the nanotube with R = 390 nm at the transport current densities 16 and 20 GA/m2. Adapted with permission from I. Bogush et al., Phys. Rev. B 109, 104516 (2024). Copyright 2024 American Physical Society. (c) Snapshots of the absolute value of the superconducting order parameter | ψ | overlaid with the accumulated vortex paths for the nanotube with R = 390 nm at the transport current density j tr = 16 GA/m2 under tiled magnetic fields. L: left; R: right (half-tube); M: middle; b: bifurcations; m: multifurcations. The number in the jet name corresponds to the number of vortex chains in the jet. Direction of the vortex motion is indicated by the arrows. The dash-dotted lines are the midlines. Adapted with permission from I. Bogusch et al., Nanomaterials 14, 420 (2024). Copyright 2024 MDPI.

FIG. 3.
Computationally unveiled geometry-driven topological phenomena. (a) Effect of the ac frequency on the dynamics of topological defects in open Nb superconductor nanotubes. Adapted with permission from V. M. Fomin et al., Sci. Rep. 12, 10069 (2022). Copyright 2022 Springer Nature. The time-dependent voltage (panels 1–3) and its FFT spectra (panels 4–6) at the magnetic field B = 2 mT, the dc transport current j0 = 2.1 GAm2, and the transport current modulation depth j 1 / j 0 = 0.5 for the ac frequencies 3, 6, and 10 GHz. The second- and third-highest peaks are indicated by arrows in the inset of panel (5). (b) The frequency spectrum f U ( B ) as a function of the magnetic induction B for the nanotube with R = 390 nm at the transport current densities 16 and 20 GA/m2. Adapted with permission from I. Bogush et al., Phys. Rev. B 109, 104516 (2024). Copyright 2024 American Physical Society. (c) Snapshots of the absolute value of the superconducting order parameter | ψ | overlaid with the accumulated vortex paths for the nanotube with R = 390 nm at the transport current density j tr = 16 GA/m2 under tiled magnetic fields. L: left; R: right (half-tube); M: middle; b: bifurcations; m: multifurcations. The number in the jet name corresponds to the number of vortex chains in the jet. Direction of the vortex motion is indicated by the arrows. The dash-dotted lines are the midlines. Adapted with permission from I. Bogusch et al., Nanomaterials 14, 420 (2024). Copyright 2024 MDPI.
View largeDownload slide

Computationally unveiled geometry-driven topological phenomena. (a) Effect of the ac frequency on the dynamics of topological defects in open Nb superconductor nanotubes. Adapted with permission from V. M. Fomin et al., Sci. Rep. 12, 10069 (2022). Copyright 2022 Springer Nature. The time-dependent voltage (panels 1–3) and its FFT spectra (panels 4–6) at the magnetic field B = 2 mT, the dc transport current j0 = 2.1 GAm2, and the transport current modulation depth j 1 / j 0 = 0.5 for the ac frequencies 3, 6, and 10 GHz. The second- and third-highest peaks are indicated by arrows in the inset of panel (5). (b) The frequency spectrum f U ( B ) as a function of the magnetic induction B for the nanotube with R = 390 nm at the transport current densities 16 and 20 GA/m2. Adapted with permission from I. Bogush et al., Phys. Rev. B 109, 104516 (2024). Copyright 2024 American Physical Society. (c) Snapshots of the absolute value of the superconducting order parameter | ψ | overlaid with the accumulated vortex paths for the nanotube with R = 390 nm at the transport current density j tr = 16 GA/m2 under tiled magnetic fields. L: left; R: right (half-tube); M: middle; b: bifurcations; m: multifurcations. The number in the jet name corresponds to the number of vortex chains in the jet. Direction of the vortex motion is indicated by the arrows. The dash-dotted lines are the midlines. Adapted with permission from I. Bogusch et al., Nanomaterials 14, 420 (2024). Copyright 2024 MDPI.

Close modal

Deduction of vortex configurations from global observables. Various vortex chains, vortex jets, and phase-slip regimes52 occur in superconductor open nanotubes due to the inhomogeneity of the normal magnetic induction component B n⁠,11 which determines the topology of screening currents.53,54 Traversing of the half-tubes by dc-driven vortices induces GHz-frequency voltage U oscillations with spectrum f U ( B ) [Fig. 3(b)]. Integer harmonics nf1 (f1 is the vortex nucleation frequency, n ≥ 2⁠) correspond to a single vortex-chain regime at low B. At higher fields, non-integer harmonics n m f 1 (⁠ m ≥ 2 , m ≠ n⁠) are indicative of the presence of m chains in the vortex jets. Peaks in dU/dB and jumps in the frequency of microwave generation occur when the number of fluxons moving in the half-tubes increases by one. Thus, vortex jets can be efficiently constrained and steered using the curvature of 3D superconductor membranes.

Steering of vortices by magnetic-field tiltings. Steering of vortex chains and jets in superconductor open nanotubes55 is provided by tilting of the magnetic field B at an angle α in the plane perpendicular to the axis of a nanotube carrying an azimuthal transport current. An increase in α displaces the areas with the close-to-maximum normal component | B n | to the close(opposite)-to-slit regions. At lower B, close-to-slit vortex chains disappear, yielding f U ( B ) consisting of integer harmonics nf1. At higher B, f f ( U ) is largely blurry because of multifurcations of vortex trajectories, giving rise to coexistence of a vortex jet with two vortex chains at α = 90 °⁠. This behavior is explained by the analysis of the modulus of the order parameter | ψ ( x , y ) | as a function of α and B overlaid with the accumulated vortex trajectories [Fig. 3(c)].

Sensitive superconducting bolometers. In Ref. 22, a significant improvement of the microwave radiation detection has been demonstrated through the fabrication of a superconducting bolometer by self-rolling 2D superconductor structures into 3D helical belts. The sensitivity measurements [Fig. 4(a)] revealed that the nanohelix features a noise equivalent power (NEP) of ∼ 2 × 1010 WHz1/2 at a microwave radiation power of 9 W m–2, which is four orders of magnitude smaller than the NEP of the commercially available QMC Instruments Ltd. sensor at a similar radiation power. The reason is the extremely low heat capacity of the 50 nm thick supporting material and the few contact points between the transition-edge-sensor and the substrate.

FIG. 4.
(a) Sensitivity vs temperature (inset: details for low-current densities) for a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948 (2019). Copyright 2019 American Chemical Society. (b) Geometry of a suspended Ti gated superconductor transistor. Inset: switching currents IC1, IC2, and IC3 as a function of VG measured at very low bath temperatures. Reproduced with permission from M. Rocci et al., ACS Nano 14, 12621 (2020). Copyright 2020 American Chemical Society. (c) The instability velocity v* as a function of the magnetic field in Nb-C microwires grown with Ga+ FIBID. Reproduced with permission from O. V. Dobrovolskiy et al., Nat. Commun. 11, 3291 (2020). Copyright 2020 Springer Nature.
View largeDownload slide

(a) Sensitivity vs temperature (inset: details for low-current densities) for a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948 (2019). Copyright 2019 American Chemical Society. (b) Geometry of a suspended Ti gated superconductor transistor. Inset: switching currents IC1, IC2, and IC3 as a function of VG measured at very low bath temperatures. Reproduced with permission from M. Rocci et al., ACS Nano 14, 12621 (2020). Copyright 2020 American Chemical Society. (c) The instability velocity v* as a function of the magnetic field in Nb-C microwires grown with Ga+ FIBID. Reproduced with permission from O. V. Dobrovolskiy et al., Nat. Commun. 11, 3291 (2020). Copyright 2020 Springer Nature.

FIG. 4.
(a) Sensitivity vs temperature (inset: details for low-current densities) for a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948 (2019). Copyright 2019 American Chemical Society. (b) Geometry of a suspended Ti gated superconductor transistor. Inset: switching currents IC1, IC2, and IC3 as a function of VG measured at very low bath temperatures. Reproduced with permission from M. Rocci et al., ACS Nano 14, 12621 (2020). Copyright 2020 American Chemical Society. (c) The instability velocity v* as a function of the magnetic field in Nb-C microwires grown with Ga+ FIBID. Reproduced with permission from O. V. Dobrovolskiy et al., Nat. Commun. 11, 3291 (2020). Copyright 2020 Springer Nature.
View largeDownload slide

(a) Sensitivity vs temperature (inset: details for low-current densities) for a rolled-up Nb nanohelix. Reproduced with permission from S. Lösch et al., ACS Nano 13, 2948 (2019). Copyright 2019 American Chemical Society. (b) Geometry of a suspended Ti gated superconductor transistor. Inset: switching currents IC1, IC2, and IC3 as a function of VG measured at very low bath temperatures. Reproduced with permission from M. Rocci et al., ACS Nano 14, 12621 (2020). Copyright 2020 American Chemical Society. (c) The instability velocity v* as a function of the magnetic field in Nb-C microwires grown with Ga+ FIBID. Reproduced with permission from O. V. Dobrovolskiy et al., Nat. Commun. 11, 3291 (2020). Copyright 2020 Springer Nature.

Close modal

Superconducting memory elements. A miniaturized superconducting memory cell employing a 3D Nb nano-Superconducting Quantum Interference Device (SQUID) is presented, featuring tunable hysteresis between flux quantum states.56 The measured current-phase relations of nano-SQUIDs exhibit skewness correlated with critical current and hysteresis loop size. These skewed relations enable further memory cell miniaturization by overcoming loop inductance limitations and advancing superconducting memory technology.

Superconducting thermoelectric elements. Including a curved 3D geometry enhances performance of superconducting tunnel junctions, which exhibit significant bipolar thermoelectricity under thermal gradients due to particle-hole symmetry breaking. Integrated into Josephson interferometers, they could act as bipolar thermoelectric Josephson engines.57 

Superconducting quantum circuits. Exploring macroscopic quantum dynamics in ultrahigh-impedance circuits is suggested for application in quantum computing and metrology. The Blochnium qubit utilizes hyperinductance (⁠ L ≈ 2.5 μH, ω / 2 π > 13 GHz, and L ω > 200   k Ω⁠), enabling fault-tolerant operations on superconducting qubits.24 

Electric field-induced control of superconductivity. An initiative involves integrating advanced superconductors into 3D Field-Effect Transistors58 to control the superconducting transition as well as vortex and phase slip dynamics using an electric field.59 The 3D geometry aims to mitigate challenges from planar structures,60 enhancing electrical characteristics and addressing reliability concerns [Fig. 4(b)].

High-sensitivity magnetic-field sensors. Nanosystems are perspective as building blocks for constructing 3D Josephson Junctions, aiming to control phase slip events for reversible decoherence in Josephson weak links using an electric field.61 These components could offer high stability and operational robustness, serving various applications, such as scanning probe microscopy tips and sensitive SQUID-on-tip (SOT) devices.62,63 Imaging of superconducting vortices in amorphous MoSi thin films with a SOT sensor was demonstrated.64 Functioning at low temperatures and under high magnetic fields, these sensors could serve as ideal probes for electron spin sensing and vortex imaging in superconductors.

Single-photon detectors. Ultrafast vortex motion is demonstrated in Nb-C microwires grown with Ga+ FIBID,65 presenting an opportunity to study non-equilibrium superconducting systems [Fig. 4(c)]. Incorporating a curved 3D geometry is expected to enhance their weak vortex pinning, critical currents near the depairing current, and rapid heat dissipation from heated electrons, making them promising candidates for fast single-photon detectors.

To fully harness the potential of transition into three dimensions, addressing substantial experimental challenges related to the fabrication and characterization of intricate 3D nanoscale geometries and topological configurations is imperative.66,67

  • Advanced nanofabrication methods: a self-spooling of NbSe3 Möbius-stripes and other architectures on spontaneously emerging Se balls;68 a physical vapor deposition technique called Glancing Angle Deposition (GLAD);69 3D roll-up self-organization;18,19,22 direct-writing techniques using FEBID; automated design of 3D DNA-based origami with non-rasterized 2D curvature.70 To obtain reproducible results, precise control over experimental conditions is required ensuring consistent production of superconductor 3D nanoarchitectures with desired physical and chemical properties.

  • Advanced characterization methodology: The characterization of 3D curved superconductors at the nanoscale has, thus far, been constrained to a limited set of experimental techniques, as detailed in Section II of the current article. These include electrical magnetotransport measurements [Figs. 2(a), 2(b), 2(d), 2(e), 4(b), and 4(c)], two-tone radiofrequency spectroscopy [Fig. 2(f)], and microwave radiation detection [Fig. 4(a)]. At present, the direct application of other well-established characterization methods, such as SQUID for superconductors at the microscale, has not yet demonstrated its suitability for 3D curved superconductors at the nanoscale. Consequently, there is an urgent need to advance the adaptation of microscale techniques or propose original approaches to facilitate the comprehensive characterization of 3D superconducting nanoarchitectures.

  • Application design.

    1. To enhance by orders of magnitude sensitivity of superconductor nanosensors of the magnetic field53 and to design innovative superconductor quantum interference filters and switches based, e.g., on the controlled vortex dynamics and topological transition between vortex-chain- and phase-slip-regimes in superconductor open nanotubes and hybrid nanostructures.51 

    2. To develop 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, and frequency generators, based on sustainable double fluxon transmission lines in superconductor open nanotubes.11 

    3. To design superconductor nanostructured bolometers and THz-detectors, which provide a significant advancement in sensitivity and reduction in noise as compared to the available ones, e.g., using superconductor nanohelices.22 

    4. To extend the fascinating topological properties of quantum fields, including unprecedented continuous control of the Berry phase, revealed recently in Möbius-stripe waveguides5 onto superconductor Möbius-like nanoarchitectures.

  1. To model and simulate the physical phenomena inherent in fabrication methods for the creation of 3D superconductor nanoarchitectures, which anticipate proximity and heating effects.

  2. To expedite optimization and improve reproducibility in FIB processing using Deep Learning, which may be deployed in near-real time.71 

  3. To explore the physics of superconducting fluctuations, in particular, to unveil the effects of fluctuations of the order parameter on properties of 3D nanoarchitectures above Tc.72 To understand the role of correlated disorder and ordered impurities in superconductor 3D nanoarchitectures toward targeted design of their functional properties for responsive media, thermoelectrics and topological phases.73 To analyze edge defects, which determine vortex (de)nucleation in superconductor 3D nanoarchitectures.

  4. To investigate the impact of confinement of superconductors into 3D nanoarchitectures on the amplitude (or Higgs) mode of the order parameter fluctuation through the nonlinear light-Higgs coupling.74,75

  5. To incorporate the (dc+ac)-driven escape of quasiparticles from the vortex cores, leading to the complex dynamics of vortices surrounded by a cloud of quasiparticles (the flux-flow instability) in superconductor 3D nanoarchitectures.76 

  6. To study the interplay between superconductivity and chirality or noncentrosymmetry aimed at prediction of nonreciprocal transport effects in superconductor 3D nanoarchitectures.

  7. To develop efficient high-performance methods for the numerical simulations of superconductor 3D nanoarchitectures of complicated geometry, like the algorithm based on the differential-geometry formalism.77 

In conclusion, our manuscript presents a comprehensive overview of recent advancements in the fabrication and characterization of 3D nano-superconductors with unconventional topologies of superconducting states. We have highlighted the significant challenges faced in the experimental work in this field and emphasized the importance of overcoming these obstacles to unlock the full potential of these materials for various technological applications. By elucidating the fascinating physical properties arising from geometry-induced topology and chirality, our work aims to catalyze further research in this area and contribute to the front-line development of modern technologies. We believe that it will serve as a valuable resource for researchers and engineers working in the field of applied physics and nanotechnologies.

This article is based upon work supported by the Generalitat Valenciana (SEJIGENT/2021/012T), MCIN/AEI/10.13039/501100011033 and “ESF Investing in your future” (RYC2020-029075-I) and the European Cooperation in Science and Technology COST Actions CA21144 (SuperQuMap) and CA16218 (FIT4NANo). The authors are grateful to numerous current and former collaborators on the present topic over the past years: J. M. De Teresa, I. Guillamón, D. Mailly, P. Orús, R. O. Rezaev, O. G. Schmidt, E. I. Smirnova, H. Suderow, and U. Zeitler. R.C. thanks A. Arroyo-Fructuoso, G. Hlawacek, and A. Ibarra. V.M.F. thanks I. A. Bogush, M. D. Croitoru, V. N. Gladilin, D. Grimm, O. V. Dobrovolskiy, and R. Wördenweber.

The authors have no conflicts to disclose.

Rosa Córdoba: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (supporting); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Vladimir M. Fomin: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (lead); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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