  The dispersion of quasiparticles in topological node-line semimetals is
significantly different in different directions. In a certain direction, the
quasiparticles behave like relativistic particles with constant velocity. In
other directions, they act as two-dimensional electron gas. The competition
between relativistic and nonrelativistic dispersions can induce a sign reversal
of Casimir-Lifshitz torque. Three different approaches can be applied to
generate this sign reversal, i.e., tuning the anisotropic parameter or chemical
potential in node-line semimetal, changing the distance between this material
and substrate birefringence. Detailed calculations are illustrated for the
system with topological node-line semimetal Ca$_3$P$_2$ and liquid crystal
material 4-cyano-4-n-pentylcyclohexane-phenyl.
