Recent experimental evidence suggests the presence of an unconventional, nodal surface-superconducting state in trigonal ${\mathrm{PtBi}}_2$. We construct a Ginzburg-Landau theory for the three superconducting order parameters, which correspond to the three irreducible representations of the point group $C_{3v}$. The irreducible representations $A_1$ and $A_2$ are the most likely. We develop a systematic method to determine the symmetry-allowed terms and apply it to derive all terms up to fourth order in the three order parameters. The Ginzburg-Landau functional also includes coupling to the magnetic field. The functional is employed to determine the effect of an applied uniform magnetic field on the nodal structure for $A_1$ and $A_2$ pairing. The results facilitate clear-cut experimental differentiation between these symmetries. We also predict field-induced helical superconductivity.

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• Superconductivity
• Topological superconductors
• Unconventional superconductors
• Weyl semimetal
• Landau-Ginzburg theory