Hubbard Model Study Reveals Fractionalized Electrons and Prevents Physical Spin Symmetry Breaking

The behaviour of electron spin within materials exhibiting a ‘pseudogap’ state, a precursor to superconductivity, remains a significant puzzle in condensed matter physics, and a team led by Paulo Forni, Pietro M. Bonetti, and Henrik Müller-Groeling at the Max Planck Institute for Solid State Research, alongside Demetrio Vilardi and Walter Metzner, now presents a compelling theoretical framework to address this challenge. Their work investigates how electron spin responds to fluctuating magnetic order within this pseudogap regime, employing a novel approach based on a SU(2) gauge theory. The researchers demonstrate that by treating electrons as fractionalized into chargons and spinons, and accounting for the fluctuations of magnetic order, they can reproduce key experimental observations in cuprate superconductors, including a spin gap, reduced magnetic response at low temperatures, and a vanishing NMR relaxation rate. This theoretical model, which accurately captures the complex interplay between charge, spin, and magnetism, offers valuable insights into the mechanisms driving high-temperature superconductivity and provides a foundation for future investigations into these fascinating materials.

Strongly correlated electron systems exhibit emergent behaviour arising from complex interactions between electrons, often leading to novel magnetic order. Electrons within these systems fractionalize into chargons, particles carrying charge, and spinons, particles carrying spin, effectively separating charge and spin degrees of freedom. This framework links microscopic interactions to macroscopic magnetic properties.

Cuprate Superconductivity, Pseudogap and Magnetic Order

This compilation details research into condensed matter physics, specifically high-temperature superconductivity, the pseudogap phase, and magnetic order in cuprate materials. Research focuses on various types of magnetic order including antiferromagnetism, spiral order, stripe order, and nematic order, investigating the role of magnetic fluctuations in the emergence of superconductivity and the possibility of nematic order in the pseudogap phase. Theoretical methods include Functional Renormalization Group and Dynamical Mean-Field Theory, used to study the flow of interactions and local correlations respectively. Experimental techniques used to probe these materials include neutron scattering, NMR, ARPES, transport measurements, and specific heat measurements.

Key concepts explored include strongly correlated electron systems, the pseudogap, D-wave superconductivity, charge density waves, spin density waves, stripe order, nematic order, and quantum criticality. Research focuses on materials like YBa2Cu3O6+x, HgBa2Cu4O8+δ, and La2CuO4. Overall, the research highlights the complexity of high-temperature superconductivity, the competition between different phases, and the importance of theoretical modeling. This compilation represents a significant body of research into high-temperature superconductivity, aiming to understand the fundamental mechanisms driving this phenomenon and to develop new materials with even higher transition temperatures.

Spinons Stabilize Magnetic Order in Cuprates

Scientists have developed a theoretical framework to understand the pseudogap phase of high-temperature cuprate superconductors, based on a gauge theory that describes fluctuating magnetic order. This approach fractionalizes electrons into chargons and spinons, effectively separating charge and spin degrees of freedom. The team treated the chargons using a sophisticated theoretical method, allowing them to order in either Néel or spiral magnetic states below a specific temperature. Crucially, the spinon fluctuations prevent the breaking of physical spin symmetry at any finite temperature, aligning with experimental observations.

Results demonstrate that this gauge theory accurately reproduces several characteristics of the pseudogap regime. The calculated dynamical spin susceptibility exhibits a spin gap, consistent with experimental findings, and the static uniform spin susceptibility decreases strongly with temperature below a critical value. Furthermore, the calculated nuclear magnetic resonance relaxation rate vanishes exponentially at low temperatures when the ground state is disordered, mirroring experimental data. At low hole doping, the model predicts nematicity, extending across the pseudogap regime at larger doping.

The team’s analysis focuses on regions where the chargons exhibit circular spiral or Néel order, providing a detailed description of the electron spin susceptibility. By deriving general expressions for this susceptibility within the SU(2) gauge theory, they have established a quantitative link between the microscopic model and macroscopic observables. This theoretical framework offers a significant advancement in understanding the complex interplay of charge, spin, and magnetism in high-temperature superconductors, paving the way for future investigations into the mechanisms driving superconductivity.

Spinons and Chargons Explain Pseudogap Behaviour

This research investigates the behaviour of electrons in a two-dimensional Hubbard model, with a focus on understanding the pseudogap phase found in materials like cuprate superconductors. The study introduces a theoretical framework based on a SU(2) gauge theory to describe how electron spin is affected by fluctuating magnetic order. The core idea is to separate the electron into two components, chargons and spinons, allowing researchers to treat charge and spin fluctuations independently. By applying this approach, the team demonstrates that the system exhibits characteristics consistent with experimental observations, including a spin gap, a reduction in spin susceptibility at low temperatures, and a specific type of relaxation behaviour observed in nuclear magnetic resonance experiments.

The results successfully reproduce key features of the pseudogap regime, offering insights into the complex interplay between charge, spin, and magnetic order in these materials. The theoretical framework provides a means to understand how fluctuations in magnetic orientation influence electron behaviour and contribute to the emergence of the pseudogap phase. Future work will extend this framework to investigate how stripe states contribute to the observed pseudogap behaviour, potentially refining the understanding of these complex materials.