The pseudogap and strange metal states in the square-lattice Hubbard model: a comprehensive study

TL;DR

This comprehensive study uses the ladder dual-fermion approximation to explore the pseudogap and strange metal states in the square-lattice Hubbard model, revealing their origins, mutual relationship, and distinctive electronic and magnetic properties.

Contribution

It provides a detailed theoretical analysis linking the pseudogap and strange metal states to Fermi surface nesting and spin fluctuations, advancing understanding of cuprate superconductors.

Findings

Strange metal state occurs when Van Hove singularity aligns with the Fermi level.

Strange metal exhibits nearly quantum critical spin fluctuations with ω/T scaling.

Pseudogap forms near the X point due to short-range AFM nesting.

Abstract

To clarify the origin of the pseudogap and strange metal states as well as their mutual relationship in cuprate superconductors, a comprehensive study on the spectral function, Fermi surface, resistivity and dynamical spin susceptivity of the Hubbard model on the square lattice has been conducted by means of the ladder dual-fermion approximation with an electron self-energy correction. It is found that the appearance of these two states requires that the characteristic hole concentration below which the Mott-Heisenberg and Slater mechanisms of electron localization occurs $p_{\rm MS}$ nearly coincides with the hole concentration where the Van Hove singularity (VHS) point is placed at the vicinity of the Fermi level. When this condition is met the VHS point is pined at which the nesting condition of the antiferromagnetic (AFM) fluctuation is fulfilled almost everywhere on the Fermi surface in wide range of the hole concentration in a metallic state, i.e., the strange metal state. The spin fluctuation of the strange metal state is nearly quantum critical and the dynamical spin susceptivity is well described by overdamped spin wave having the $\omega/T$ scaling with the relaxation rate at the Planckian limit. Because of these distinctive features of the strange metal state, the $k$ dependence of scattering rate of electrons is small and electrons behave as the marginal Fermi liquid, resulting in $T$-linear resistivity. In contrast, the pseudogap state is magnetically in the renormalized classical regime and the pseudogap is formed near the X point where the nesting condition of the short-range AFM order is fulfilled.