Table 1 Violation of the emergent rotational symmetry in hexagonal superconductors

SC order parameter	Symmetry lowering	Emergent rotational symmetry	Refs.
Single-component	None	Preserved	^15,16,18
Single-component	Orthorhombic	Preserved	⁵¹
Single-component	Trigonal	Preserved	¹⁷
Two-component	None	Preserved	^13,14,15,16
Two-component	Orthorhombic^*	Violated	^14,15
Two-component	Trigonal	Violated	^16,17

Predictions based on GL theories are summarized for cases of single- and two-component SC order parameters with or without weak symmetry lowering from the perfect hexagonal lattice. When the emergent rotational symmetry is preserved, the hexagonal H_c2 anisotropy component, \({H}_{{{{{{{{\rm{c2}}}}}}}}}^{(6)}\), should be small and behave as \(\propto {(1-T/{T}_{c})}^{3}\)^13,14,15. This principle holds under the existence of sixfold Fermi-velocity anisotropy¹⁸. In contrast, \({H}_{{{{{{{{\rm{c2}}}}}}}}}^{(6)}\) should behave as \(\propto {(1-T/{T}_{c})}^{1}\) if the emergent rotational symmetry is violated^14,15,16,17, as observed in the present experiment in CsV₃Sb₅.
*Direction of the symmetry-breaking field must follow the magnetic field direction.

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