On the existence of nematic-superconducting states in the Ginzburg-Landau regime

Abstract

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.

Figures (4)

• Figure 1: (Color online) For $B_e=1$ and $v=0.5$, continuous transition from the superconducting state ($f\equiv f_{\text{sc}}$ and $g\equiv 0$) to the nematic state ($g\equiv g_{\text{an}}$ and $f\equiv 0$), as $\beta$ varies from $\beta\sim 0.015$ to $\beta \sim 1.76$.
• Figure 2: (Color online) Magnetic field $B(x)$ (solid blue line), superconductor order parameter $f(x)$ (solid red line), and nematic order parameter $g(x)$ (solid yellow line) as a function of the distance in the strip with respect to the origin for $B_e=1$ and $v=0.5$, in the situations a) $\beta=0.015$ (near-to-superconducting response), b) $\beta=1.76$ (near-to-nematic state) and c) $\beta=0.8$ (nematic-superconducting state). As a reference, we add the corresponding superconducting profiles $B_{\text{sc}}(x)$ and $f_{\text{sc}}(x)$, and the anharmonic solution to the nematic order parameter $g_{\text{an}}(x)$ in dashed lines, whenever is needed.
• Figure 3: (Color online) Magnetic field $B(x)$ (solid blue line), superconductor order parameter $f(x)$ (solid red line), and nematic order parameter $g(x)$ (solid yellow line) as a function of the distance in the strip with respect to the origin for $B_e=1$ and $v=-0.02$, in the situations a) $\beta=0.1$, b) $\beta=1.4$ and c) $\beta=0.6$. As a reference, we add the corresponding superconducting profiles $B_{\text{sc}}(x)$ and $f_{\text{sc}}(x)$, and the anharmonic solution to the nematic order parameter $g_{\text{an}}(x)$ in dashed lines, whenever is needed.
• Figure 4: (Color online) Magnetic field $B(x)$ (blue line), superconducting order parameter $f(x)$ (red line), and nematic order parameter $g(x)$ (yellow line) as a function of the distance in the strip with respect to the origin. We fix the parameters as $v=0.5$ and $\beta=0.8$ for the applied magnetic fields a) $B_e=0$ (dashed lines) $B_e=0.1$ (solid lines) and (b) $B_e=3$.