Impurity-induced configuration-transition in the Fulde-Ferrell-Larkin-Ovchinnikov state of a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-wave superconductor

Abstract

The effect of impurities on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a layered superconductor with $d$-wave pairing symmetry is investigated using the tight-binding model and the Bogoliubov--de Gennes equations. At low temperature and a strong exchange or Zeeman field applied parallel to its conducting plane, a two-dimensional (2D) square lattice-like Larkin-Ovchinnikov state is more energetically favorable in a clean system. In the presence of impurities, the spatial profile of the order parameter remains as a 2D square lattice, and it is distorted only near the impurities when the impurity concentration is low. As impurity concentration is increased to a certain level, a quasi-one-dimensional (1D)-like FFLO state becomes more energetically favorable. Increasing temperature with fixed impurity concentration can also induce a 2D to 1D FFLO state transition. Within the present finite-size calculation, we did not find the existence of the Fulde and Ferrell state before the system becomes normal as the impurity concentration is raised.