Charge and Spin Structures of a $d_{x^2 - y^2}$ Superconductor in the Proximity of an Antiferromagnetic Mott Insulator

Details Charge and Spin Structures of a $d_{x^2 - y^2}$ Superconductor in the Proximity of an Antiferromagnetic Mott Insulator Charge and Spin Structures of a $d_{x^2 - y^2}$ Superconductor in the Proximity of an Antiferromagnetic Mott Insulator

1997-06-17

arxiv.org/abs/cond-mat/9706173v1

Physics

Condensed Matter

Strongly Correlated Electrons

46 pages (latex) including 14 figures in encapsulated postscript format. Submitted for publication in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.56.15001

To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(\omega)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $\chi(\vec{q},\omega)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re \chi(\vec{q} = (\pi,\pi), \omega = 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(\omega)$ develops a pseudo-gap feature and below $T_{KT}$ $Im \chi(\vec{q} = (\pi,\pi), \omega)$ shows a peak at finite frequency.

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