Fig .1  “Composite vortices” split into fractional vortices and form superconducting skyrmions.

Recently, a joint research team led by Professor Hong Ding, Tsung-Dao Lee Chair Professor at the Tsung-Dao Lee Institute, Shanghai Jiao Tong University, published a Research Article in Science entitled “Observation of quantum vortex core fractionalization and skyrmion formation in a superconductor.” Tsung-Dao Lee Institute (TDLI), School of Physics and Astronomy is the primary corresponding institution. Ph.D. student Yu Zheng, supervised by Associate Professor Chi Ming Yim, and postdoctoral researcher Quanxin Hu, supervised by Professor Hong Ding, are the co-first authors of the Article. Quanxin Hu, Associate Professor Baiqing Lv, Associate Professor Chi Ming Yim, and Professor Hong Ding are co-corresponding authors. Professor Vadim Grinenko, Associate Professor Noah F.Q. Yuan, and postdoctoral researcher Haijiao Ji, Yongwei Li and Ye Gao of TDLI; Professor Egor Babaev and Igor Timoshuk of Royal Institute of Technology (KTH), Sweden; Associate Researcher Rui Wu, Xin Yu and Hanxiang Xu from the Institute of Physics, Chinese Academy of Sciences; and Professor Xingye Lu from Beijing Normal University are co-authors. This work was supported by user facility at the Synergetic Extreme Condition User Facility in Huairou, and by grants from the Ministry of Science and Technology of China, the National Natural Science Foundation of China, the New Cornerstone Science Foundation, the Shanghai Research Center for Quantum Sciences, the China Postdoctoral Science Foundation, and Shanghai Jiao Tong University.

Magnetic vortices are among the most important concepts in superconductivity. In 1957, Abrikosov theoretically predicted that, in type-II superconductors, an external magnetic field can enter the material in the form of a flux-vortex lattice; this pioneering contribution later formed an important basis for his 2003 Nobel Prize in Physics [1]. In 1961, M. Fairbank [2] and M. Näbauer [3] independently discovered experimentally that the flux carried by superconducting vortices is quantized Φ₀=h/2e. In the same year, C. N. Yang theoretically showed that magnetic flux is quantized in units of h/2e because of electron pairing in superconductors [4]. Since then, it has become a standard paradigm in superconductivity that magnetic fields enter type-II superconductors as integer-flux-quantum vortices: each isolated vortex carries an integer flux quantum and behaves as a topological defect with a stable, mobile core.

This classic picture naturally raises a deeper question: must superconducting vortices always exist only as integer-flux objects? In single-component superconductors, the phase winding of a vortex is tightly linked to flux quantization, so an isolated vortex can normally carry only an integer multiple of the flux quantum. In multiband or multicomponent superconductors, however, the vortex properties can be much richer. Back in 2002, Professor Egor Babaev of KTH, Sweden theoretically proposed that a multicomponent superconductor contains multiple phase degrees of freedom, allowing phase winding to occur in only one superconducting component and thereby giving rise to fractional vortices that carry only a portion of a flux quantum [5]. Fractional vortices are of fundamental importance. Since the early development of anyon theory, it has been recognized that charge-fractional-flux composites in two-dimensional systems can exhibit fractional statistics intermediate between Bose-Einstein and Fermi-Dirac statistics [6]. Fractional vortices are therefore not only important prototypes for understanding fractional statistics, but are also considered closely relevant to topological quantum computation.

However, realizing movable and reorganizable fractional vortices with core singularities in real materials has long been a major challenge in condensed matter physics. In multiband superconductors, fractional vortices are usually not free to separate. As they are coupled to the same vector-potential field and constrained by interband Josephson coupling, different fractional vortices often experience an effective attractive interaction that grows approximately linearly with their separation, conceptually analogous to the attractive interaction between quarks. As a result, they are typically bound together into a “composite vortex” carrying one integer flux quantum. In other words, fractional vortices in multiband superconductors have long remained in a state that is “allowed in theory but difficult to realize experimentally,” resembling a form of quark confinement. To spatially separate them, one must identify a physical mechanism capable of stabilizing vortex splitting.

Multiband superconductors with broken time-reversal symmetry provide one possible route. In addition to breaking the usual gauge symmetry, such superconducting states also break a Z₂ discrete symmetry associated with time reversal, whose spontaneous breaking can generate domain walls. When a composite vortex intersects a domain wall, the relative-phase structure near the domain wall can relieve interband Josephson coupling, which in turn leads to phase frustration and causes splitting of each composite vortex into multiple fractional vortices [7]. Although this theoretical picture is highly appealing, direct evidence in real materials has long been lacking. In recent years, Professor Vadim Grinenko of TDLI and his collaborators, through μSR and transport measurements, provided experimental evidence(s) for a time-reversal-symmetry-breaking s ± is superconducting state in Ba_1-xK_xFe₂As₂ near x = 0.77 [8,9]. Then, a research team from Stanford University observed the formation of fractional-flux-carrying vortices in the same system from the SQUID measurements [10]. Nevertheless, how fractional vortices form and separate from composite vortices, and how their core structures evolve at the atomic scale, still lack direct real-space and spectroscopic evidence.

Fig.2 Different terminations of 122-type iron-based superconductor

In 2023, a joint research team led by Professor Hong Ding of TDLI employed scanning tunneling microscopy to conduct an in-depth study of Ba_1-xK_xFe₂As₂ (x ≈ 0.77). However, due to chemical disorder introduced by doping and the complexity of polar surfaces in 122-type iron arsenides, its superconducting Ba/K-terminated surface exhibits pronounced surface reconstruction and disorder, hindering high-resolution real-space imaging of superconducting flux vortices. Surprisingly, the research team discovered another type of cleavage surface in the same material: the As-terminated surface (Fig. 2). This surface hosts a charge-density wave (CDW), but does not exhibit superconductivity. Professor Ding recognized that this CDW originates from self-hole doping of the As-terminated surface, which loses electronic compensation originally provided by the overlying Ba/K layer. The hole-doping level of this surface is slightly higher than that of KFe₂As₂. This hole doping effect shifts the saddle points that originally lie below the Fermi level towards its vicinity, causing nesting between them, which in turn induces the formation of the CDW. This work was published in Nature Communications 16, 253 (2025) [11].

Fig. 3 Pronounced superconductivity enhancement and multiband superconductivity on the “1 × 1” K-termination.

Inspired by the self-hole-doping effect on the As cleavage surface, Professor Ding and the joint research team turned to the “1 × 1” K-terminated surface of stoichiometric KFe₂As₂. On this surface, additional K atoms donate electrons to the topmost FeAs layer, causing the near-surface electronic structure approach the key heavily hole-doped regime of Ba_1-xK_xFe₂As₂ near x ≈ 0.75, while retaining an atomically flat surface, making the system suitable for STM studies. Through tunneling spectroscopy and quasiparticle-interference measurements, and comparisons with theoretical calculations, the research team confirmed that the K-terminated surface exhibits enhanced superconductivity. This implies that this surface termination may host a superconducting state similar to that in Ba_1-xK_xFe₂As₂ (x = 0.77), thereby provide an opportunity to realize fractional vortices (Fig. 3).

It is worth noting that the Ph.D. theses of Limin Liu and Changjiang Zhu, supervised by Researcher Shuheng Pan at the Institute of Physics, Chinese Academy of Sciences, had reported similar phenomena of enhanced superconductivity and anomalously increased vortex counts in the same material system in June 2021 [12,13]. These early observations provided useful inspiration for the present study to further explore unconventional vortex behavior on the “1 × 1” K cleavage surface.

Fig. 4 Quantum vortex core fractionalization and characteristics of fractional vortices. 

The research team then carried out systematic low-temperature, high-magnetic-field STM studies of the vortex-core structures and their spectroscopic characteristics, ultimately revealing the real-space morphology of fractional vortices and the microscopic mechanism by which they form superconducting skyrmions (Fig. 4). Temperature-dependent experiments show that there exist two distinct types of vortices, one remains as isolated integer vortices throughout the experiment, while another, which also appear as isolated vortices at low temperature, split at increasing temperature. In particular, at a temperature of 4.2 K, some vortices split into two cores, whereas others into three cores. When the temperature is lowered again, the split vortices recombine into single isolated vortices. This reversible vortex splitting phenomenon reveals that the vortex cores contain a reconfigurable multicomponent structure.

The observed vortex-splitting behavior also leads to a discrepancy of the experimentally observed number of vortex cores with the theoretically predicted value, with the former far exceeding the latter. Through extensive controlled experiments, the team ruled out possible explanations such as vortex-antivortex pairs, rapid positional fluctuations, and ordinary pinning effects. Combining temperature evolution, spatial distribution, vortex counting, and spectroscopic features, the team attributed the split vortex cores to fractional vortices carrying only a portion of the magnetic flux.

Spectroscopic measurements further revealed an essential distinction between integer vortices and fractional vortices. Compared to ordinary integer vortices, fractional vortices exhibit much weaker vortex-bound-state signals, while superconducting coherence peaks remain more strongly preserved. These spectroscopic features are consistent with the picture of a “partial core singularity”: in a fractional vortex core, only some components of the superconducting order parameter vanish, whereas other components remain finite. This provides direct spectroscopic evidence for vortex-core fractionalization. More importantly, the team found that these fractional vortices are not randomly distributed; instead, they tend to arrange into chain-like structures. Theoretical analysis showed that such chains of fractional vortices possess nontrivial topological properties and form a new type of topological defect: a chiral superconducting skyrmion, whose topology can be characterized by a CP² topological invariant.

This work advances the research of fractional vortices from a long-standing theoretical concept and indirect observation to the stage of atomic-scale real-space imaging and spectroscopic characterization. It not only provides direct evidence for the formation of fractional vortices and chiral superconducting skyrmions in a multiband superconductor, but also shows that the “1 × 1” K cleavage surface of KFe₂As₂, assisted by surface charge-transfer doping, may support a two-dimensional superconducting state with broken time-reversal symmetry. This state not only promotes vortex-core fractionalization and the formation of CP² skyrmions, but also provides a new experimental platform for simulating fractionalized excitations, linearly confining interactions, topological-defect formation, and quark-confinement-like phenomena in condensed-matter systems.

Paper link:https://www.science.org/doi/10.1126/science.ads0189

References:

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[11] Q. Hu et al., Evidence for saddle point-driven charge density wave on the surface of heavily hole-doped iron arsenide superconductors, Nat Commun 16, 253 (2025).

[12] L. Liu, Scanning Tunneling Microscopy/Spectroscopy Study of Surface Enhanced Superconductivity of KFe2As2 and Charge-Density Wave of ZrTe3, Ph.D. thesis, University of Chinese Academy of Sciences (Institute of Physics, Chinese Academy of Sciences), 2022.

[13] C. Zhu, STM Study in Superconductor of NbC/TaC/ZrTe3/KFe2As2, Ph.D. thesis, University of Chinese Academy of Sciences (Institute of Physics, Chinese Academy of Sciences), 2022.