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Chiral superconductivity in nematic states

We investigate chiral superconductivity which occurs in the electronic nematic state. A vortex state in a $c$-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 $ν$ is positive (negative) and the nematicity is induced along the [110] axis ([100] axis). We discuss nematic-chiral superconductivity in URu$_2$Si$_2$, Sr$_2$RuO$_4$, and UPt$_3$. An experimental test for the examination of nematic order and chiral superconductivity is proposed.