Quantum Spin Liquids Demonstrate Anisotropic Velocities Of, Advancing Superconductor Understanding

Quantum spin liquids represent a fascinating and elusive state of matter, and understanding their properties is a major challenge in condensed matter physics, with implications for high-temperature superconductivity. Subir Sachdev from Harvard University and the Flatiron Institute, along with colleagues, present a comprehensive review of recent theoretical advances in this field, focusing on how fractionalized Fermi Liquid (FL*) states can explain key observations in cuprate materials. The research addresses long-standing difficulties in existing theories, particularly concerning angle-dependent magnetoresistance and the anisotropic velocities of quasiparticles in superconductors, offering a new framework for understanding these complex phenomena. By exploring both bosonic and fermionic parton theories, the team demonstrates how doping spin liquids can lead to novel metallic states and ultimately, to superconductivity, providing a pathway towards designing and discovering new materials with enhanced properties.

Pseudogap and Fractionalization in Cuprates

The system exhibits both an intermediate temperature pseudogap metal and a lower temperature d-wave superconductor. Numerous theories, following an early suggestion by P. W. Anderson, proposed these phases arise from doped quantum spin liquids, though these theories struggled to account for key observations. Angle-dependent magnetoresistance measurements, including the Yamaji effect, provide compelling evidence for small hole pockets that can tunnel coherently between square lattice layers. Furthermore, velocities of the nodal Bogoliubov quasiparticles in the d-wave superconductor are highly anisotropic, with vF significantly greater than v∆.

Hole Pockets and Anisotropic Superconductivity Revealed

Scientists have achieved a detailed understanding of fractionalized Fermi Liquid (FL*) states, demonstrating how these states resolve long-standing difficulties in describing the behavior of hole-doped cuprate materials. The research focuses on the pseudogap metal and the superconducting phases found in these materials, building upon earlier theories of doped spin liquids. Experiments reveal that these cuprates exhibit small hole pockets capable of coherent tunneling between layers, a finding confirmed by angle-dependent magnetoresistance measurements and the observation of the Yamaji effect. The team measured highly anisotropic velocities of nodal Bogoliubov quasiparticles in the superconducting phase.

This anisotropy is successfully explained by the FL* state, which incorporates gauge-neutral electron-like quasiparticles into the spin liquid framework. The FL* state was initially modeled using a dimer model, then refined with the more realistic Ancilla Layer Model, allowing for a comprehensive theory of both the pseudogap and the superconducting phases. Further investigations involved analyzing visons, topological excitations on the triangular lattice, revealing a stable, real-vortex solution that preserves time-reversal symmetry. Numerical minimization of an energy functional demonstrated that magnitudes of certain parameters are suppressed near the vison core, analogous to Abrikosov vortices.

Analysis of dynamics on the triangular lattice identified bosonic spinons with 2-fold spin and lattice degeneracy, confirming the expected structure of a Z2 spin liquid. By performing a unitary transformation, scientists derived an effective Lagrangian describing the spinons, revealing a relativistic complex scalar field. Measurements confirm the presence of four spinons, consistent with theoretical predictions, and the team established symmetry transformations governing these excitations, including SU(2) spin rotations and a crucial Z2 gauge symmetry. This work delivers a robust theoretical framework for understanding the complex behavior of these materials and opens avenues for exploring novel quantum phenomena.

Fractionalized Fermi Liquid in Cuprate Superconductors

This research establishes a framework for understanding the behavior of electrons in hole-doped cuprates by proposing a “fractionalized Fermi Liquid” state. The team demonstrates how this state successfully addresses longstanding challenges in explaining the properties of these materials, notably the observation of small hole pockets and the highly anisotropic velocities of quasiparticles within the superconducting phase. By building upon theories of fractionalization, where electrons are broken into separate components, they construct a model that accounts for experimental findings previously difficult to reconcile with simpler theories. The work details a progression from initial concepts of spin liquids, through holon and spinon theories, culminating in the development of the fractionalized Fermi Liquid state.

This state is constructed using both a dimer model and a more refined Ancilla Layer Model, allowing for a detailed description of both the pseudogap phase and the superconducting state in cuprates. Importantly, the research reveals that the fluctuations within this model behave like a U(1) gauge field, explaining the observed linear dispersion of spin-singlet states and providing a foundation for understanding the material’s unique electronic properties. The authors acknowledge that the U(1) spin liquid state is ultimately unstable due to monopole tunneling events, a complex phenomenon requiring further investigation, and future research will explore these events and their impact on system stability.