triplet superconductor under sufficient field $H\gtrsim $20kOe. In this case, there are many proposals for $f({\bf k})$. However, again, the specific form is not needed for our results.

For chiral order parameter symmetry expected of the Sr$_2$RuO$_4$, with $\bf{d}$ in the basal plane and no spin-orbit coupling, the order parameter has four complex degrees of freedom: $$\hat{\Delta}({\bf k})=
\sum_{\sigma=\pm}\tilde{f}(k_\sigma,k_z)\left[
 \begin{array}{cc}
  \Delta_{\uparrow\uparrow,\sigma}& 0 \\
  0 & \Delta_{\downarrow\downarrow,\sigma}
  \end{array}
\right], \label{EQ:OP-chiral}$$ where the function $\tilde{f}$, like the non-chiral case discussed above, depends on the specific odd angular momentum channel and $k_\sigma = k_x + i\sigma k_y$. This is equivalent to $${\bf d} ({\bf k}) = \Delta_+ {\bf {\hat d}}_+ \exp (i
n\varphi_{\bf{\hat k}})+\Delta_- {\bf {\hat d}}_- \exp (-i
n\varphi_{\bf{\hat k}}), \label{EQ:OPp+ip}$$ where $n$ is an integer ($n=1$ for $p$-wave, $n=3$ for $f$-wave) and $\varphi_{\bf{\hat k}}$ is the azimuthal angle associated with a unit vector $\hat{\bf k}$ in the 2D plane (assuming quasi-2D setting with the angular momentum along the $c$-axis: ${\bf \hat
l} = {\bf \hat z}$). Although $\Delta_- = 0$ for homogeneous chiral superconductor, we will show that $\Delta_- \neq 0$ often plays an important role in describing the vortex lattice structure of chiral superconductor.

Eqs.(\[EQ:OP-nonchiral\]) and (\[EQ:OPp+ip\]) clearly shows that 