Non-minimally Coupled Quintom Model Inspired by String Theory
  In this paper we consider a quintom model of dark energy with a single scalar field $T$ given by a Lagrangian which inspired by tachyonic Lagrangian in string theory. We consider non-minimal coupling of tachyon field to the scalar curvature, then we obtain the equation of state (EoS), and the condition required for the model parameters when $\omega$ crosses over -1. 
J. Sadeghi, M. R. Setare, A. Banijamali, F. Milani