Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State

Fig 2*. Published under the Creative Commons Attribution 4.0 International license

High-temperature superconductivity – where electrical current flows with zero resistance at relatively high temperatures – was discovered in 1987 in a class of copper-based crystals known as cuprates. When researchers vary the density of mobile electrons in the cuprates (by doping with impurity ions), these materials transform from magnetic insulators to high-temperature superconductors. A central open question has been the precise relationship between the magnetism and superconductivity. A certain class of magnetism, found in spin liquids with topological order (a material where the electron spins constantly fluctuate and never align), has been viewed as central to understanding the nature of the superconductivity. In particular, a large class of spin-liquid candidates has been proposed as relevant to the physics of cuprates.

In a recent article in Physical Review X, graduate student Alex Thomson and Prof. Subir Sachdev presented a unified theory of spin liquids that are of particular relevance to the cuprates. The authords point out that their main result is a subtle duality between descriptions of these spin liquids using particles with Bose and Fermi statistics. While these spin liquids may appear distinct because their representation uses bosons or fermions, their fully renormalized quasiparticle excitations are shown to be equivalent. A large class of bosonic spin liquids has been proposed using a theory of fluctuating antiferromagnetism, and Thomson and Sachdev show that these liquids are equivalent to fermionic spin liquids proposed from a theory of electrons localizing into Mott insulators.

This unification opens the way to a comprehensive understanding of the disparate physical properties of the doped cuprates in the “pseudogap” regime found at temperatures above the superconducting critical temperature.

* See Alex Thomson and Subir Sachdev, “Fermionic Spinon Theory of Square Lattice Spin Liquids near the Néel State,” Phys. Rev. X 8 (24 January 2018) https://doi.org/10.1103/PhysRevX.8.011012.

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