Magnetic properties and superconductivity in the two-dimensional repulsive Hubbard model

Abstract

A new method for estimating the parameter ensuring the fulfillment of the Mermin-Wagner theorem in the strong coupling diagram technique (SCDT) for the two-dimensional Hubbard model is suggested. With the precise parameter value, calculated magnetic quantities are in good agreement with the results of numeric and optical-lattice experiments. Obtained spin and charge vertices are used for investigating superconductivity in the $t$-$U$ and $t$-$t^{\prime }$-$t"$-$U$ Hubbard models in the regime of strong correlations. We found no superconducting transition in the $t$-$U$ model. In the $t$-$t^{\prime }$-$t"$-$U$ model, the transition occurs for the singlet $d_{x^2-y^2}$ pairing at $T_c\approx 0.016t$. The difference between the two models is in the renormalized hopping describing electron motion in SCDT. In the $t$-$U$ model, it vanishes for momenta $(\pi ,0)$, $(0,\pi )$ of extrema of the $d$-wave order parameter, while the hopping is finite in the $t$-$t^{\prime }$-$t"$-$U$ model. In the one-band model, there are optimal values of $t^{\prime }$ and $t"$ ensuring the highest $T_c$.

10 pages, 11 figures

References in corpus (5)

• Competition between d-wave superconductivity and antiferromagnetism in the 2D Hubbard model
• Does Simple Two-Dimensional Hubbard Model Account for High-Tc Superconductivity in Copper Oxides?
• Superconductivity, antiferromagnetism and phase separation in the two-dimensional Hubbard model: A dual-fermion approach
• Superconductivity and antiferromagnetism in the two-dimensional Hubbard model: a variational study
• Phase separation and competition of superconductivity and magnetism in the two-dimensional Hubbard model: From strong to weak coupling