t'- and t"-dependence of the bulk-limit superconducting condensation energy of the 2D Hubbard model

TL;DR

This study uses variational Monte Carlo to analyze how the superconducting condensation energy in the 2D Hubbard model depends on t' and t" parameters, revealing conditions under which superconductivity is optimized.

Contribution

It provides the first detailed analysis of the t'- and t"-dependence of the bulk-limit superconducting condensation energy in the 2D Hubbard model.

Findings

Superconducting condensation energy dominates over SDW near optimal doping.

Finite bulk-limit Econd observed at t'=-0.05 and -0.10, matching YBCO.

Econd vanishes at t'=0 and decreases with more negative t'.

Abstract

The 2D Hubbard model having the 2nd- and 3rd-neighbor transfer energies t' and t" is investigated by use of the variational Monte Carlo method. At the nearly optimal doping with on-site Coulomb energy U=6 (energy unit is t) the condensation energy Econd for the d-wave superconductivity (SC) is computed for lattices of sizes from 10x10 to 28x28 with the aim to get its bulk-limit value. t" is fixed at -t'/2. Outside and in the neighborhood of the SDW region of -0.16=<t'=<-0.08 the SC Econd dominates over the SDW Econd. At t'=-0.05 and -0.10 we obtained a definitely finite bulk-limit SC Econd of the order of the experimental value for YBCO. At t'=0 Econd nearly vanishes. For t'=<-0.18, the SC Econd strongly oscillates as a function of the lattice size, when periodic boundary conditions (b.c.'s) are imposed to both axes. In the case of periodic and antiperiodic b.c.'s, a finite bulk-limit value is obtained at t'=-0.22. Econd tends to vanish with further decrease of t'. With our results the SC of LSCO is understandable with t'~ -0.10. The t' values of Hg1201, Tl2201 and Na-CCOC seem close to -0.20 so that they locate in the boundary zone of SC indicated in the present work. Slightly larger U improves the situation by increasing Econd.