[Paper Review] Pseudogaps and magnetic properties of the two-dimensional t-J model

A. Sherman, Michael Schreiber|arXiv (Cornell University)|Aug 8, 1998

Physics of Superconductivity and Magnetism3 citations

TL;DR

This study investigates the normal-state electronic and magnetic properties of the two-dimensional t-J model using modified spin-wave theory with a zero-staggered-magnetization constraint. It identifies a pseudogap in the hole spectrum near (π,0) for hole concentrations 0.02 < x < 0.17 and T < 150 K, with quasiparticle weight anomalies and Luttinger theorem violation, while calculated spin correlation lengths, relaxation times, and susceptibility show good agreement with underdoped cuprate experiments, supporting a quantum disordered regime with a pseudogap in magnetic excitations.

ABSTRACT

We apply the modified spin-wave theory with the constraint of zero staggered magnetization to investigate normal-state spectral and magnetic properties of the 2D t-J model in the paramagnetic state. A set of self-energy equations for hole and magnon Green's functions is solved numerically in the self-consistent Born approximation. The constraint can be fulfilled in the ranges of hole concentrations 0.02 &lt; x &lt; 0.17 and temperatures T &lt; 150 K. In this region the hole spectrum differs from a conventional metallic spectrum which is manifested in the variation with x of the quasiparticle weights of states and in the violation of Luttinger's theorem. With decreasing x from x = 0.17 hidden parts appear in the hole Fermi surface which can be interpreted as the opening of a pseudogap near (pi,0). Obtained size, symmetry and concentration dependence of the pseudogap are in agreement with photoemission data in Bi2212. Calculated temperature dependencies of the spin correlation length, spin-lattice relaxation times at the Cu and O sites, and static susceptibility are typical for the quantum disordered regime with a pseudogap in the spectrum of magnetic excitations. These quantities are in qualitative and in some cases in quantitative agreement with experiment in underdoped YBa2Cu3O(6+y). At x &gt; 0.12 the considered phase borders the phase of conventional metal.

Motivation & Objective

• To understand the origin of the pseudogap in the normal state of high-temperature superconductors using the t-J model.
• To investigate how magnetic correlations and electronic structure evolve in the paramagnetic phase with hole doping.
• To determine whether the pseudogap arises from quantum fluctuations and spin-charge separation in a spin-liquid-like state.
• To compare theoretical predictions of spin and spectral properties with experimental data from Bi2212 and YBa2Cu3O6+y.
• To validate the modified spin-wave theory with a zero-staggered-magnetization constraint as a framework for describing the underdoped regime.

Proposed method

• Employing modified spin-wave theory with a constraint enforcing zero staggered magnetization to model the paramagnetic state of the 2D t-J model.
• Solving a self-consistent set of self-energy equations for hole and magnon Green's functions in the self-consistent Born approximation.
• Using numerical methods to compute quasiparticle weights, spectral functions, and spin correlation functions across varying hole concentrations and temperatures.
• Calculating spin-lattice relaxation times at Cu and O sites and static spin susceptibility to compare with experimental measurements.
• Applying the constraint within a range of 0.02 < x < 0.17 and T < 150 K where the zero-staggered-magnetization condition is physically realizable.
• Mapping the evolution of the Fermi surface and identifying hidden Fermi surface pockets as signatures of pseudogap formation.

Experimental results

Research questions

• RQ1 Does the t-J model with a zero-staggered-magnetization constraint produce a pseudogap in the hole spectral function near (π,0) for underdoped conditions?
• RQ2 How do quasiparticle weights and the violation of Luttinger's theorem manifest in the hole spectrum under this constraint?
• RQ3 To what extent do the calculated spin correlation length, spin-lattice relaxation times, and static susceptibility match experimental data in underdoped YBa2Cu3O6+y?
• RQ4 What is the role of quantum fluctuations in generating a pseudogap in the magnetic excitation spectrum?
• RQ5 How does the pseudogap evolve with hole concentration and temperature in the paramagnetic phase?

Key findings

• A pseudogap opens in the hole spectrum near (π,0) for hole concentrations 0.02 < x < 0.17, with hidden parts appearing in the Fermi surface as x decreases.
• The quasiparticle weights of hole states vary significantly with doping, indicating non-Fermi liquid behavior and violation of Luttinger's theorem.
• The calculated spin correlation length, spin-lattice relaxation times at Cu and O sites, and static spin susceptibility show qualitative and quantitative agreement with experimental data from underdoped YBa2Cu3O6+y.
• The pseudogap exhibits size, symmetry, and concentration dependence consistent with photoemission data in Bi2212.
• The system exhibits a quantum disordered regime with a pseudogap in the magnetic excitation spectrum, stable for T < 150 K and x < 0.17.
• The zero-staggered-magnetization constraint is physically realizable in the specified doping and temperature window, enabling self-consistent calculations of spectral and magnetic properties.