Tiny Vortices Reveal New Superconductivity Mechanism

Scientists are increasingly focused on understanding the unusual superconducting properties emerging in kagome materials, and a new theoretical study led by Frederik A. S. Philipsen and Mats Barkman, both from the Niels Bohr Institute, University of Copenhagen, alongside Andreas Kreisel from both the Niels Bohr Institute and the Department of Physics and Astronomy, Uppsala University, and Brian M. Andersen also of the Niels Bohr Institute, sheds light on the nature of vortices within these chiral systems. Their research details the existence of fractional 1/3 flux quantum vortices permeating the superconducting condensate, a phenomenon arising from the unique band structure and time-reversal symmetry breaking observed in kagome metals. These fractional vortices, each carrying one third of the expected flux, are linked to the kagome lattice’s sublattice degrees of freedom and offer a potential explanation for experimental observations made when these materials are subjected to magnetic fields, representing a significant step towards fully characterising the complex behaviour of this novel class of superconductors.

Superconductivity just gained a surprising new complexity. Exotic, fractional vortices, carrying a third of the usual quantum of magnetism, have been predicted within a specific class of metallic materials. Understanding these unusual states could unlock new avenues for controlling and harnessing superconductivity in future technologies. Scientists are examining the unusual behaviour of vortices within a specific type of superconductor found in kagome metals.

These materials, characterised by a distinctive kagome lattice structure, a pattern of corner-sharing triangles, exhibit properties that challenge conventional understandings of superconductivity. Recent experiments have indicated time-reversal symmetry breaking within these superconducting states, suggesting the presence of exotic phenomena. Investigations focus on understanding how magnetic fields interact with these materials at a fundamental level, potentially revealing new states of matter.

Theoretical work suggests a more complex picture for kagome materials, where vortices carry only a portion of the standard flux quantum. Calculations incorporating the unique band structure of the kagome lattice predict the emergence of fractional vortices. These fractional vortices are intimately linked to the chiral nature of the superconducting state and the arrangement of atoms within the lattice.

Scientists have employed self-consistent microscopic calculations to model the superconducting condensate under an applied field, revealing that fractional vortices permeate the material, each carrying one third of the superconducting flux quantum. Each vortex also displays a unique signature tied to one of the three sublattice degrees of freedom inherent to the kagome lattice geometry.

This discovery has implications extending beyond fundamental materials science. The ability to control and manipulate these fractional vortices could open avenues for novel superconducting devices and offer insights into the broader field of unconventional superconductivity, where materials defy traditional theoretical descriptions.

Kagome lattice electronic band structure from tight-binding calculations

A tight-binding model defines the electronic structure of the kagome lattice — a structure comprising corner-connecting triangles with a triangular Bravais lattice and three sublattices per unit cell. The normal state Hamiltonian, HTB, is constructed using only nearest-neighbour hopping terms, and by transforming this into reciprocal space yields HTB = X σ,k∈BZ ψ† kσHTB(k)ψkσ. With ψkσ expressed in terms of Bloch states and HTB(k) a 3×3 matrix dependent on the wavevector ‘k’.

Understanding the weight of electronic states on each sublattice is essential. Diagonalizing the Hamiltonian obtains the three electronic bands εn(k) and their corresponding eigenstates uαn(k). Such bands feature a flat band, a Dirac crossing, and van Hove singularities, critical points in the band structure. Also, the bands exhibit sublattice interference, where the weight |uαn(k)|2 of eigenstates on a given sublattice becomes momentum dependent.

Through modelling the superconducting state requires a mean-field treatment of the interaction Hamiltonian, Hint = X r,r′ Vrr′ c† r↑c† r′↓cr′↓cr↑, where Vrr′ represents an attractive interaction potential. Mean-field decoupling within the Cooper channel transforms this into the Bogoliubov-de Gennes (BdG) Hamiltonian, HBdG = Ψ† HTB ∆ ∆† −HT TB Ψ, utilising Nambu space and a 3N × 3N matrix representation of HTB.

In turn, the superconducting gap, ∆, is determined through the self-consistency equation ∆rr′ = Vrr′⟨cr′↓cr↑⟩, where angle brackets denote the expectation value — to classify possible homogeneous superconducting states, the symmetry of the kagome lattice, belonging to the D6h point group, is considered. Decomposition into irreducible representations reveals the lowest harmonics correspond to A1g, E1u, and E2g symmetries, and calculations favour the E2g (d-wave) pairing state, particularly in the vicinity of the upper van Hove singularity. Such fractional vortices exhibit a characteristic signature linked to the three sublattice degrees of freedom inherent to the kagome lattice geometry. Such vortices demonstrate a unique spatial distribution reflecting the underlying lattice symmetry.

Here, the observed fractional flux is not simply a consequence of symmetry breaking within the superconducting state, but is stabilised by the interaction between the chiral order parameter and the kagome lattice itself. At the boundary between regions with differing chiralities, d+id and d-id phases, a hexagonal structure emerges, where fractionalized vortices and suppressed order parameters are observed on each of the three sublattices.

When examining the current loops surrounding each sublattice reveals a unique pattern of circulating currents, indicating a complex interaction of electronic states. When considering the implications for experimental observation. In turn, the predicted quasi-particle interference patterns are directionally dependent when an external magnetic field is applied below the critical temperature — the chiral d±id phase can mimic characteristics of conventional s-wave pairing. Such as a weak suppression of Tc with disorder and the potential presence of a Hebel-Slichter peak in NMR spin-lattice relaxation.

Fractionalised vortices reveal complex superconductivity in kagome metals

Scientists are beginning to map the subtle internal structure of superconductivity, moving beyond simple pictures of how electrons flow without resistance — recent theoretical work concerning kagome metals reveals a surprising complexity within superconducting vortices. Tiny whirlpools that form when these materials are exposed to magnetic fields. Calculations indicate these vortices are not singular points. But rather composed of fractional components, each carrying a diminished superconducting flux.

Instead of a single vortex, the material hosts a collection of smaller, interconnected swirls tied to the geometry of the kagome lattice itself. Meanwhile, understanding these fractional vortices addresses a long-standing puzzle: the emergence of time-reversal symmetry breaking observed in some kagome superconductors. For years, physicists have struggled to reconcile theoretical predictions with experimental observations of unusual electronic behaviour in these materials. With many seeking explanations beyond conventional superconductivity.

This project offers a potential mechanism for this symmetry breaking. Linking it directly to the arrangement of these fractional vortices and their interaction with the material’s underlying structure. By interpreting these findings requires caution, as the modelling relies on approximations and initial assumptions. Better computational methods may reveal a more complete picture.

Such outcomes could influence the design of future superconducting devices, potentially allowing for greater control over magnetic fields at the nanoscale. The challenge remains translating these theoretical insights into tangible improvements in materials science and engineering. Unlike previous models that treated vortices as uniform entities. This effort highlights the importance of considering the interaction between superconductivity and the material’s atomic structure.

Future investigations should focus on experimentally verifying the existence of these fractional vortices, perhaps through advanced imaging techniques. Since the kagome lattice is found in a variety of materials, this understanding could extend to other systems exhibiting similar unconventional superconducting properties, opening new avenues for exploration in the quest for room-temperature superconductivity.