  In this article, we investigate the existence of nematic-superconducting
states in the Ginzburg-Landau regime, both analytically and numerically. From
the configurations considered, a slab and a cylinder with a circular
cross-section, we demonstrate the existence of geometrical thresholds for the
obtention of non-zero nematic order parameters. Within the frame of this
constraint, the numerical calculations on the slab reveal that the competition
or collaboration between nematicity and superconductivity is a complex energy
minimization problem, requiring the accommodation of the Ginzburg-Landau
parameters of the decoupled individual systems, the sign of the bi-quadratic
potential energy relating both order parameters and the magnitude of the
applied magnetic field. Specifically, the numerical results show the existence
of a parameter regime for which it is possible to find mixed
nematic-superconducting states. These regimes depend strongly on both the
applied magnetic field and the potential coupling parameter. Since the proposed
model corresponds to the weak coupling regime, and since it is a condition on
these parameters, we design a test to decide whether this condition is
fulfilled.
