Superconducting state properties of a d-wave superconductor with mass anisotropy

TL;DR

This paper develops a Ginzburg-Landau theory for anisotropic d-wave superconductors, revealing how mass anisotropy affects vortex structures, order parameters, and symmetry properties, with specific application to YBa2Cu3O7.

Contribution

It introduces an anisotropic GL framework incorporating effective mass anisotropy, analyzing its impact on vortex states and order parameter symmetries in d-wave superconductors.

Findings

Both s- and d-wave order parameters can coexist with the same transition temperature when anisotropy is present.

Vortex states exhibit two-fold symmetry in order parameters, contrasting with the four-fold symmetry expected in pure d-wave cases.

Vortex lattice adopts an oblique structure influenced by anisotropy across a wide temperature range.

Abstract

YBa$_2$Cu$_3$O$_7$ (YBCO) exhibits a large anisotropy between the $a$ and $b$ axes in the CuO$_2$ planes because of the presence of CuO chains. In order to account for such an anisotropy we develop a Ginzburg-Landau (GL) theory for an anisotropic d-wave superconductor in an external magnetic field, based on an anisotropic effective mass approximation within CuO$_2$ planes. The anisotropic parameter $\lambda=m_x/m_y$, where $m_x$ ($m_y$) is the effective mass in the $x$ ($y$) direction, is found to have significant physical consequences: In the bulk case, there exist both the $s$- and $d$-wave order parameters with the same transition temperature, as long as $\lambda\ne 1$. The GL equations are also solved both analytically and numerically for the vortex state, and it is shown that both the $s$- and $d$-wave components show a two-fold symmetry, in contrast to the four-fold symmetry around the vortex, as expected for the purely $d$-wave vortex. With the deviation of $\lambda$ from unity, the opposite winding between the $s$- and $d$-wave components observed in the purely $d$-wave case is gradually taken over by the same winding number. The vortex lattice is found to have oblique structure in a wide temperature range with the precise shape depending on the anisotropy.