Type-1.5 Superconductivity

We demonstrate the existence of a novel superconducting state in high quality two-component ${\mathrm{MgB}}_2$ single crystalline superconductors where a unique combination of both type-1 (${\lambda }_1/{\xi }_1<1/\sqrt{2}$) and type-2 (${\lambda }_2/{\xi }_2>1/\sqrt{2}$) superconductor conditions is realized for the two components of the order parameter. This condition leads to a vortex-vortex interaction attractive at long distances and repulsive at short distances, which stabilizes unconventional stripe- and gossamerlike vortex patterns that we have visualized in this type-1.5 superconductor using Bitter decoration and also reproduced in numerical simulations.

Figure 1

Magnetic decoration images of the vortex structure at $T=4.2\mathrm{K}$ and $H=1\mathrm{Oe}$ in (a) ${\mathrm{MgB}}_2$ and (b) ${\mathrm{NbSe}}_2$ single crystals. The scale bars in the images correspond to $10\mu \mathrm{m}$. Notice that the density of vortices in the decoration experiments represents the internal field $B$ rather than the applied field $H$. This leads to a different number of decorated vortices for ${\mathrm{NbSe}}_2$ and ${\mathrm{MgB}}_2$, even at the same applied field.

Figure 2

(a) Experimental vortex locations in a selected part of the image shown in Fig. 1a. The vortex configuration resulting from the numerical simulations in a two-component superconductor at low density is shown in (b) evidencing an inhomogeneous spatial distribution of vortices. In both cases, the regions enclosed by the dashed white line indicate voids of vortices caused by the inhomogeneous distribution. In (c) the vortex pattern obtained by a magnetic decoration of the ${\mathrm{NbSe}}_2$ crystal at 1 Oe is shown and (d) corresponds to the vortex pattern obtained by a numerical simulation of a type-2 superconductor. The white scale bars correspond to $10\mu \mathrm{m}$. (e) and (f) display the distribution of first neighbor distance, $P_a$, of the experimental and theoretical vortex structures, respectively. In the case of ${\mathrm{MgB}}_2$, $P_a$ shows additional peaks at distances shorter and longer than the most probable separation (see the red and green arrows). The pair of vortices separated at the distances where the additional peaks are located are highlighted in (a) and (b) by red and green circles. The light blue circles correspond to pair of vortices separated by the most probable distance.

Figure 3

(a) Magnetic decoration image in the ${\mathrm{MgB}}_2$ single crystal at $H=5\mathrm{Oe}$. (b) Disordered Abrikosov lattice obtained at $H=5\mathrm{Oe}$ in the ${\mathrm{NbSe}}_2$ sample. The formation of vortex stripes is also reproduced in numerical simulations of a two-component type-1.5 superconductor (c) in contrast to a homogeneous vortex distribution in a type-2 superconductor at the same vortex density (d). The scale bars in the images correspond to $10\mu \mathrm{m}$. Inset of (b): Vortex density along lines parallel to the vortex stripe direction [yellow dashed lines in (a)] for ${\mathrm{MgB}}_2$ and ${\mathrm{NbSe}}_2$ vortex structures. The variation of the vortex density is calculated as a function of the distance measured along the direction perpendicular to the stripes [yellow arrows in (a) and (b)]. The curves are normalized by their respective average density. The results of a similar calculation performed on the simulated vortex structures are shown in the inset of (d).