Description
We discuss an extension of the standard effective model of d-
wave superconductivity of a single band tight-binding
Hamiltonian with nearest neighbor attraction to include finite
range periodically modulated pair-hopping. The pair-hopping
is characterized by a fixed wave number $\vec{Q}$ breaking
lattice rotational but not translational symmetry, assuming an
underlying nematic order. Within self-consistent BCS theory
we study the general variational state consisting of two
incommensurate singlet pair amplitude order parameters
$\Delta_{\vec{Q}_1}$ and $\Delta_{\vec{Q}_2}$. We find
two types of near degenerate ground states; of the Larkin-
Ovchnnikov (LO) type with
$\Delta_{\vec{Q}_1}=\Delta_{\vec{Q}_2}$ and
$\vec{Q}_1=-\vec{Q}_2\approx \vec{Q}$ or of the Fulde-
Ferrell (FF) type with $\Delta_{\vec{Q}_2}=0$ and
$\vec{Q}_1\approx \pm\vec{Q}$. An anomalous term in the
current operator arising from the pair-hopping ensures that
Blochs's theorem on zero current in the ground state is
enforced also for the FF ground state, despite the
spontaneously broken time-reversal symmetry. We also
discuss states with a uniform current by exploring the space
of pair-momenta $\vec{Q}_1$ and $\vec{Q}_2$. We find a
rich phenomenology including the possibility of
inhomogeneous current densities due to phase separation
and unconventional directional dependence of the depairing
current.