Kagome Lattices Advance Quantum Spin Liquids and Unconventional Superconductivity Research

Kagome lattices, distinguished by their unique geometric arrangement, represent a promising frontier in condensed matter physics, particularly for understanding exotic states of matter like quantum spin liquids and unconventional superconductivity. Li-Wei He, Shun-Li Yu, and Jian-Xin Li comprehensively review recent progress in this rapidly evolving field, detailing investigations into quantum spin liquids, the emergence of fractional magnetization plateaus in kagome antiferromagnets, and the surprising discovery of unconventional superconductivity in vanadium-based kagome materials. Their work clarifies the theoretical underpinnings of these phenomena, employing advanced computational methods to model quantum states and predict material behaviour, while also synthesising the latest experimental findings. This review establishes a crucial connection between theoretical predictions and observed properties, paving the way for the design of novel materials exhibiting these fascinating quantum behaviours.

Kagome Superconductivity and Charge Density Wave Interplay

Research into kagome materials has revealed a fascinating interplay between superconductivity and charge density waves, challenging conventional understandings of these electronic phases. Scientists are actively investigating materials like AV3Sb5, where A represents alkali metals such as cesium, rubidium, and potassium, to understand how these two phenomena coexist and influence each other. The properties of both superconductivity and charge order are sensitive to the specific alkali metal present, influencing transition temperatures and the characteristics of the superconducting gap, and researchers are exploring how these properties can be tuned by altering the material’s composition. Advanced experimental techniques are crucial to probing these materials.

Angle-resolved photoemission spectroscopy maps the electronic band structure, identifying features like Dirac or Van Hove singularities thought to be important for superconductivity. Scanning tunneling microscopy and spectroscopy provide real-space images of electronic density, revealing the superconducting gap and charge density wave patterns. Muon spin rotation and relaxation detects time-reversal symmetry breaking, a signature of unconventional superconductivity, while transport measurements study electrical conductivity and related properties. Recent discoveries include evidence for unconventional pairing symmetry through flux quantization measurements and non-reciprocal charge transport, indicating broken time-reversal symmetry.

Theoretical and computational studies complement these experimental efforts. Researchers employ models to understand the observed phenomena, building upon foundational work in superconductivity and applying them to the unique kagome lattice structure. Simulations explore the electronic structure and spin-lattice relaxation in superconducting vortex states, and investigate phenomena such as the superconducting diode effect, where critical current depends on current direction, and the behaviour of superconducting vortices. Researchers are also exploring the effects of disorder and impurities on the superconducting properties, and utilizing optical manipulation to control the charge-density-wave state.

Kagome Antiferromagnetism and Quantum Spin Liquids

The kagome lattice, with its unique arrangement of corner-sharing triangles, has become a central focus for research into quantum spin liquids and unconventional superconductivity. Scientists are investigating the nearest-neighbor kagome antiferromagnetic Heisenberg model to understand its classical ground-state properties and guide investigations into these exotic quantum states. This work builds upon Anderson’s pioneering theory of resonating valence bonds, laying the theoretical foundation for understanding these complex systems, and researchers employ this model to predict the existence of quantum spin liquids characterized by long-range entanglement and fractional excitations, even at absolute zero temperature. To explore these theoretical predictions, scientists focus on materials exhibiting strong geometric frustration, such as Herbertsmithite.

Detailed investigations of this material reveal properties consistent with a quantum spin liquid ground state, confirming the potential of the kagome lattice to host such phases. Furthermore, studying kagome antiferromagnets under external magnetic fields reveals novel quantum states, including magnetization plateau phases, representing distinct arrangements of magnetic moments. Researchers analyze these phases through careful measurements of magnetic susceptibility and neutron scattering, providing insights into the underlying quantum mechanisms. Parallel to these investigations of quantum magnetism, scientists explore the potential for unconventional superconductivity within the kagome lattice structure.

The unique electronic structure of these materials, particularly the presence of van Hove singularities, is believed to play a crucial role in promoting unconventional pairing mechanisms. Recent breakthroughs involve the discovery of superconductivity in a family of compounds, AV3Sb5, where A represents potassium, rubidium, or cesium. Scientists analyze the electronic band structure of these compounds to understand how the filling of the van Hove singularity contributes to the emergence of superconductivity, and detailed measurements of specific heat and magnetic penetration depth characterize the superconducting state and search for evidence of unconventional pairing symmetries.

Kagome Lattices Reveal Quantum Spin Liquid Phases

Researchers have made significant advances in understanding quantum spin liquids (QSLs) and unconventional superconductivity through detailed investigations of kagome lattice materials. This work centers on exploring the unique properties arising from the kagome lattice’s geometric structure, a platform for studying exotic quantum phenomena. The team employs a combination of theoretical modeling and computational techniques to characterize these states of matter. A key achievement involves classifying QSLs based on their underlying gauge symmetries. By constructing mean-field Hamiltonians and analyzing their symmetries, scientists can identify different types of QSLs distinguished by their gauge-inequivalent configurations.

This approach allows for the construction of microscopic wave functions used as starting points for calculations, a powerful technique for studying QSL states. Furthermore, the research demonstrates a method for calculating the ground state degeneracy (GSD), a crucial indicator of topological order. For a Z2 QSL state on a torus, inserting a global Z2 flux into either hole incurs no energy cost, leading to four degenerate ground states. The team constructed mean-field ground states with different boundary conditions and, after applying projections, determined the number of non-vanishing states to identify the GSD. Measurements of the topological entanglement entropy (TEE) were also performed, revealing its connection to the quantum dimensions of topological excitations and the GSD.

Kagome Lattice Supports Dirac Spin Liquid State

Recent research has significantly advanced understanding of quantum spin liquids (QSLs) and unconventional superconductivity, particularly within the context of the kagome lattice, a structure exhibiting strong geometric frustration. Investigations into the nearest-neighbor kagome antiferromagnetic Heisenberg model demonstrate extensive ground state degeneracy, a crucial factor enabling the potential formation of QSLs.