Abstract
We investigate chiral superconductivity which occurs in the electronic nematic state. A vortex state in a $c\ensuremath{-}\text{axis}$ magnetic field is studied on the basis of the two-component Ginzburg-Landau model for nematic-chiral superconductors. It is shown that various vortex lattice structures are stabilized by nontrivial cooperation of nematicity and chirality in superconductors. In particular, the vortex lattice structural transition occurs when a square anisotropy parameter $\ensuremath{\nu}$ is positive (negative) and the nematicity is induced along the [110] axis ([100] axis). We discuss nematic-chiral superconductivity in ${\text{URu}}_{2}{\text{Si}}_{2}$, ${\text{Sr}}_{2}{\text{RuO}}_{4}$, and ${\text{UPt}}_{3}$. An experimental test for the examination of nematic order and chiral superconductivity is proposed.
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