Abstract

The effect of next-nearest-neighbor (nnn) hopping on the spin and charge structures around vortices in underdoped high-temperature superconductors is studied at finite temperature by numerically solving the Bogoliubov-de Gennes equations based on a model Hamiltonian with competing antiferromagnetic spin density wave (SDW) and d-wave superconductivity orders. We show that one-dimensional (1D) y- or x-axis–oriented stripes for the SDW and the associated charge density wave (CDW) exist for small nnn hopping strengths. A coexistence of both y- and x-axis–oriented stripes may occur for a relatively large nnn hopping strength. The two-dimensional (2D) spatial modulations with fourfold symmetry can be obtained with further enlarging nnn hopping strength, implying the possible existence of 2D checkerboard-like SDW and CDW orders. In addition, a transition of “1D stripe to 2D checkerboard-like pattern” can take place with increasing temperature.

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