Visualization of vortex sheets and half quantum vortices in the chiral odd-parity superconductor UPt$_{3}$

Abstract

Superconductivity is characterized by vanishing electrical resistance and magnetic flux expulsion. For conventional type II superconductors, the magnetic flux expulsion is incomplete in an applied magnetic field above a critical value and magnetic flux penetrates the bulk of the superconductor in discrete quantized magnetic flux tubes (vortices), each carrying a single quantum of flux (h/2e). Investigating the unconventional superconductor UPt$_{3}$ with a scanning superconducting quantum interference device (SQUID) microscope, we observed mobile half-quantum vortices together with one quantum vortices. Cooling the material under a higher magnetic field revealed the presence of lines of magnetic contrast resembling domain walls. These observations agree with theoretical predictions for chiral superconductivity with a two dimensional complex order-parameter with sheets of half-quantum vortices separating domains of opposite order-parameter chirality.

Figures (15)

• Figure 1: Temperature dependence of magnetic induction of a single vortex in UPt$_{3}$ (A) Consecutive magnetic images of the same vortex as temperature is increased step-wise. (B) Profiles through this vortex for temperatures from 0.3 to 0.5K. (C) The temperature dependence of the maximum field at the center of the vortex.
• Figure 2: Vortices, antivortices and half-quantum vortices in the B-phase of UPt${}_3$ . (A) An image of the local magnetic field over a sample surface of UPt$_3$ following cooling from above $T_c^+$ to 0.3 K in close to zero applied magnetic field. Several vortices, two anti-vortices and a half-quantum vortex are visible. The lines labeled A and B pass through the center of a vortex and a half-quantum vortex respectively. (B) The field profiles along the lines shown in panel (A). The solid curves are fits (see text) to these profiles with flux $\phi_0$ and $\phi_0/2$ (and the same SQUID to sample surface distance). (C) is a frequency histogram of local field maxima values from 7 such images captured in 7 consecutive cool downs from above $T_{c^+}$ to 0.3 K in the B-phase. The vertical dashed lines show the field maximum values corresponding to 0.5 $\phi_0$ and $\phi_0$ vortices. (D) The same procedure was followed as in (C) except that the sample was cooled instead to 0.475 K in the A-phase. The vertical dashed line shows the $B_\text{max}$ value for full quantum $\phi_0$ vortices at this temperature; no half quantum vortices were seen.
• Figure 3: Emergence and merging of half-quantum vortices in the B-phase of UPt$_3$. (A) A magnetic image obtained after cooling from abouve $T_c^+$ in close to zero field to 0.3 K, then (B) after subsequently increasing the temperature to 0.35 K and (C) after further increasing the temperature to 0.375 K. In panel (B) the single 1$\Phi_{0}$ vortex situated close to the center of the image in panel (A) has split into two half-quantum vortices and four other half-quantum vortices have entered the imaged region in the lower right quadrant forming an arc of half-quantum vortices. In panel (C) the half quantum vortices have combined to leave only full quantum vortices. Further details are discussed in the main text.
• Figure 4: Domain walls in the B-phase of UPt${}_3$. The images were acquired when decreasing the temperature (from the A-phase to the B-phase) in a -0.4 mT/$\mu_{0}$ applied magnetic field. In the B-phase, between 0.45 K and 0.44 K, an extended domain wall first starts to become discernible. The contrast across the domain wall becomes very intense at 0.25 K and single vortices are visible on either side of the domain wall (a cut through the data in panel D is shown in Fig. S5).
• Figure 5: Temperature evolution of domain structure. The figure compares consecutive magnetic images for warming and cooling in a small applied field. (A) is the magnetic image following cooling from above $T_c^+$ to 0.35 K in an applied field 0.37 mT/$\mu_{0}$. (B) is the image after subsequently warming the sample to 0.4 K. (C) Is the image following cooling from above $T_c^+$ to 0.35 K in 0.36 mT/$\mu_{0}$. (D) is the image following subsequently cooling the sample further to 0.30 K. Circular domains are found in images (A) and (D). A region of reduced flux density is observed in (D) at the position occupied by the domain wall in (C).