🔬 mesoscale physics

Anomalous vortex shape in a frustrated superconductor hosting chiral multicomponent order parameters

Using spectroscopic scanning tunneling microscopy at 0.3 K, researchers discovered that the spinel superconductor LiTi2O4 hosts triangular Abrikosov vortices with orientations locked to crystallographic domains rather than the magnetic field, providing evidence for a hidden chiral selectivity in its multicomponent order parameter.

Original authors: Yuita Fujisawa, Anjana Krishnadas, Tomonori Nakamura, Chia-Hsiu Hsu, Yen-Yu Lai, Barnaby R. M. Smith, Markel Pardo-Almanza, Yukiko Obata, Dyon van Dinter, Guoqing Chang, Chun-Liang Lin, Robert. Joynt

Published 2026-09-03

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CC BY 4.0

Original authors: Yuita Fujisawa, Anjana Krishnadas, Tomonori Nakamura, Chia-Hsiu Hsu, Yen-Yu Lai, Barnaby R. M. Smith, Markel Pardo-Almanza, Yukiko Obata, Dyon van Dinter, Guoqing Chang, Chun-Liang Lin, Robert. Joynt, Yuki Nagai, Tadashi Machida, Yoshinori Okada

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Superconductors are materials that conduct electricity with zero resistance, a property that usually emerges when they are cooled to extremely low temperatures. In many of these materials, when a magnetic field is applied, the field does not penetrate the entire solid uniformly. Instead, it squeezes through in tiny, discrete tubes called vortices. Inside each of these tubes, the superconducting state is temporarily broken, creating a small core where the material behaves like a normal metal. For decades, scientists have studied the shapes of these vortices to understand the hidden rules governing the electrons inside the material. In the most common types of superconductors, these vortices are perfectly round or slightly stretched, reflecting the symmetry of the crystal lattice that holds the atoms together. However, a more exotic class of materials exists where the electrons pair up in a more complex, twisted way. In these systems, theory predicts that the vortices should take on strange, multi-lobed shapes that defy the simple symmetry of the crystal, acting as a direct window into a hidden form of electronic order.

A team of researchers has now captured the first clear images of these exotic vortices in a specific superconductor called lithium titanium oxide. This material, which becomes superconducting at about 13 Kelvin, is unique because its atoms are arranged in a structure that creates a high degree of frustration among the electrons, meaning the electrons cannot settle into a single, simple pattern. The scientists used a powerful microscope called a scanning tunneling microscope, which can map the flow of electrons on a surface with atomic precision, to look at the material at a temperature of 0.3 Kelvin. They applied a magnetic field and watched how the vortices formed. Instead of finding the expected round or six-sided shapes, they discovered that the vortices were distinctly triangular. This triangular shape was not a random defect; it was a robust feature that appeared consistently across the sample.

The researchers went further to determine what caused this unusual shape. They examined the surface of the material to see if the triangular vortices were simply a result of bumps or steps on the crystal surface, but found no such connection. They also checked if the shape was an artifact of the material's surface layers, but the data suggested the phenomenon was happening deep within the bulk of the material. The most striking discovery came when they looked at the boundaries between different regions, or domains, of the crystal. In one domain, the triangular vortices pointed in one direction. When the researchers crossed a boundary into a neighboring domain, the triangles rotated by 180 degrees, pointing in the opposite direction. This rotation happened regardless of which way the magnetic field was pointing. The orientation of the vortices was locked to the internal structure of the crystal domain itself, not to the external magnetic field.

This behavior points to a specific type of superconductivity where the electrons pair up in two different ways simultaneously, creating a chiral state. In this state, the two pairing components compete with each other inside the vortex. One component tries to push the other away, while the other tries to stay close, resulting in a compromise where the core of the vortex splits into three distinct parts, forming the triangular shape. The researchers propose that even before the magnetic field is turned on, the material has already "chosen" a specific direction for this chiral state within each domain, a hidden selectivity that only becomes visible once the magnetic field forces the vortices to form. The study suggests that lithium titanium oxide hosts a complex, multi-component superconducting order that was previously only a theoretical prediction. By visualizing these triangular vortices, the team has provided strong evidence for a hidden electronic order that exists in frustrated materials, opening a new path for understanding how electrons behave in these complex, geometrically constrained environments.

Technical Summary: Anomalous Vortex Shape in a Frustrated Superconductor Hosting Chiral Multicomponent Order Parameters

Problem and Motivation
Understanding hidden electronic ordering and symmetry in superconductors remains a central challenge in quantum materials science. While the visualization of Abrikosov vortices (AVs) has proven powerful for probing single-component superconductors, the experimental landscape for superconductors with chiral multicomponent order parameters (CMOP), defined as $\Psi_{\pm} = \Psi_1 \pm i\Psi_2$ , remains largely unexplored. Theoretical predictions suggest that such systems can host unconventional vortex textures forbidden in conventional single-component paradigms. The spinel superconductor LiTi $_2$ O $_4$ (LTO), with a critical temperature ( $T_c$ ) of approximately 13 K and a formal 3d $^{0.5}$ electronic configuration on a pyrochlore lattice, presents a unique platform for this investigation. Unlike its related compound MgTi $_2$ O $_4$ , which is a Mott insulator with long-range chiral order, LTO exhibits highly frustrated and degenerate electronic states in the anomalous metallic regime above $T_c$ . The study aims to determine whether LTO hosts a chiral multicomponent superconducting state and to visualize the resulting unconventional vortex structures.

Methodology
The researchers employed in situ spectroscopic scanning tunneling microscopy (STM) and spectroscopy (STS) on atomically flat (111)- and ($-1-1-1$)-oriented LiTi $_2$ O $_4$ thin films at a temperature of 0.3 K. The study focused on the mixed state of the superconductor under applied magnetic fields ranging from 0.2 T to 1.0 T, a regime where vortex-vortex interactions are minimized to preserve intrinsic single-vortex shapes.
Key methodological steps included:

Domain Characterization: Identifying coexisting crystalline domains with (111) and ($-1-1-1$) orientations, which correspond to opposite out-of-plane polarities.
Vortex Imaging: Acquiring zero-bias conductance ( $g(0)$ ) maps to visualize the spatial distribution of low-energy quasiparticle states within vortex cores.
Quantitative Analysis: Constructing polar intensity plots of the conductance and integrating the signal up to 30 nm (approximately three coherence lengths, $\xi \approx 10$ nm) to optimize signal-to-noise ratios. Fourier analysis was performed on these integrated curves to quantify anisotropy components, specifically looking for a threefold component ( $I_{C3}$ ).
Control Comparisons: Comparing observations against surface morphology to rule out surface-driven effects and against theoretical simulations for single-component order parameters to rule out conventional bulk descriptions.

Key Results

Triangular Abrikosov Vortices (tr-AVs): Contrary to the sixfold-symmetric vortices expected for single-component superconductivity based on the calculated electronic structure of LTO, the study directly visualized triangular Abrikosov vortices. Fourier analysis confirmed a robust threefold anisotropy ( $I_{C3}$ ) in the vortex core structure.
Domain-Locked Orientation: The orientation of the triangular vortices was found to be locked to the crystallographic domains rather than the direction of the applied magnetic field. Specifically, the vortex orientation rotated by 180° across domain boundaries separating (111) and ($-1-1-1$) regions.
Magnetic Field Independence: The orientation of the tr-AVs remained invariant when the magnetic field polarity was inverted (comparing $+0.5$ T and $-0.5$ T), indicating that the selectivity is intrinsic to the crystalline domain structure rather than the external field vector.
Zero-Field Electronic State: At zero magnetic field, the superconducting gap appeared nearly isotropic and nodeless across domain boundaries, with no pronounced in-gap states or spectroscopic anomalies distinguishing the domains. This suggests that the chirality selectivity is "hidden" in the zero-field state.
Exclusion of Alternatives: The study ruled out surface-related effects (such as step edges or surface electronic states) and conventional single-component descriptions (which preserve inversion symmetry and cannot generate net threefold anisotropy) as the primary causes of the observed triangular shapes.

Interpretation and Mechanism
The authors propose that the observed tr-AVs arise from a chiral multicomponent order parameter ( $\Psi_1 \pm i\Psi_2$ ). In this framework, the vortex structure results from a competition between two energy minimization tendencies:

Condensation Energy: The tendency to spatially separate the singular regions (zeros) of the individual components $|\Psi_1(\mathbf{r})|$ and $|\Psi_2(\mathbf{r})|$ to maintain a large total superconducting amplitude.
Gradient Energy: The tendency to keep these singular regions locked in space.
This competition leads to a multiple-core-like structure within a single vortex, resulting in the triangular shape. The authors suggest that the two chiral states ( $\Psi_+$ and $\Psi_-$ ) are degenerate in zero field but become electronically active and distinct under a magnetic field, with the specific chirality selected by the underlying crystalline domain orientation.

Significance and Claims
The paper claims that the observation of triangular Abrikosov vortices provides strong evidence for chiral multicomponent superconductivity in LiTi $_2$ O $_4$ . Furthermore, it proposes the existence of a "hidden chirality selectivity" embedded in the zero-field electronic state, which is only revealed under an applied magnetic field. The findings establish epitaxial spinel-oxide thin films as a promising platform for investigating exotic superconductivity in strongly correlated 3d-electron systems on geometrically frustrated lattices. The work opens avenues for exploring how such phenomena evolve as electronic filling is tuned between the 3d $^0$ and 3d $^1$ limits, particularly in connection with anomalous metallic and superconducting states. The authors note that while the detailed microscopic nature of the order parameters (e.g., specific pairing channels) remains to be fully clarified, the phenomenological picture of a CMOP-driven vortex structure is strongly supported by the data.

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