Direct observation of vortex liquid droplets in the iron pnictide superconductor CaKAs$_4$Fe$_4$ at $0.5T$_c$

TL;DR

This study uses scanning tunneling microscopy to image vortices in the iron-based superconductor CaKAs4Fe4 across temperature and field, revealing that vortex liquid droplets form locally well below the macroscopic melting temperature (as low as $0.5 T_c$). The authors quantify thermally activated vortex motion, show strong correlations between droplet formation and the local pinning landscape (including linear intergrowth defects), and demonstrate that vortex mobility follows a universal field-dependent trend consistent with the Dew-Hughes pinning model ($f_n \propto h^{p}(1-h)^{q}$ with $H_{c2}\approx 50$ T, $p\approx 0.95$, $q=3$). Their observations indicate that dissipation at the local scale can arise far below $T_c$, and that macroscopic measurements may mask a broad inhomogeneous melting region governed by pinning. The work underscores the importance of nanoscale pinning engineering for superconducting devices and provides a framework for understanding percolative dissipation in type-II superconductors.

Abstract

Type-II superconductors under magnetic fields are in a quantum coherent non-dissipative state as long as vortices remain pinned. Dissipation appears when vortices depin, eventually driven by thermal fluctuations. This can be associated to a melting transition between a vortex solid and a vortex liquid. This transition is almost always observed very close to T$_c$ when probed by macroscopic experiments. However, it remains unclear how the vortex solid responds to thermal fluctuations at the scale of individual vortices far from the melting transition. Here we use scanning tunneling microscopy (STM) to visualize vortices in CaKAs$_4$Fe$_4$ (T$_c \approx$ 35 K). We find vortex liquid droplets-localized regions in space where vortices strongly fluctuate due to thermal exctiation-at temperatures as low as 0.5\,T$_c$. Our results show that the onset of dissipation at the local scale occurs at temperatures considerably below T$_c$ in type-II superconductors.

Figures (15)

• Figure 1: Schematic representation of vortex solid and liquid phases. (a) At low temperatures, the vortices are pinned and eventually form a disordered solid. The superconducting state (dark blue) is clearly distinguished with respect to the normal state at the center of the vortex core (white). (b) As the temperature rises, vortices begin to move, hopping between different positions. Vortex motion leads to fluctuations in the vortex positions which are much faster than our measurement time, resulting in an apparent increase in the vortex core size (the time-averaged density of states is represented by the green halo). (c) In certain areas we eventually observe "vortex liquid droplets" (large yellow area marked by the red line). These droplets coexist with a vortex solid. (d) Close to the critical temperature, $T_c$, of the superconductor, we observe a vortex liquid spanning large fractions of the field of view. The vortex liquid phase consists of large areas with a spatially uniform tunneling conductance which is below the tunneling conductance at high values, evidencing the presence of a superconducting gap.
• Figure 1: Comparison of topography and zero bias conductance maps. (a,b,c) STM topography corresponding to the zero bias tunneling conductance map acquired simultaneously and shown in (g-i). White bars correspond to 40 nm. The color scale corresponds to height changes of about 0.4 nm. (d-f) Height profile as a function of position along the line scan shown as a green arrow in (a-c), respectively. Red dashed lines mark the largest defects identified from the STM topography. We mark the position of linear defects with black arrows in both topography and height profiles. (g-i) The zero bias tunneling conductance map acquired simultaneously as topographies in (a-c). The color scale corresponds to conductance changes of about 0.8 times the tunneling conductance normalized to its normal state value (i.e. in many yellow areas, the superconducting gap is very weak but remains generally open). Red dashed lines mark the largest defects identified in the STM topography. Maps taken at 10 K and 6 T for a,g; at 10 K and 10 T for b,h; and at 15 K and 14 T for c,i.
• Figure 2: Direct observation of vortex liquid droplets well below T$_c$ in CaKAs$_{4}$Fe$_4$. In (a-e) we show maps of the zero bias tunneling conductance for different temperatures and at 10 T, in approximately the same field of view. Linear defects found in the surface of the sample lead to the roughly diagonal yellow lines shown in the maps (more information in the Supplementary Information Section I and Supplementary Figures 1. and 2; maps at other temperatures and magnetic fields are commented and provided in the Supplementary Information Section III and in the Supplementary Figure 4). At higher temperatures we mark with red contours the areas where we do no longer identify isolated vortices in the tunneling conductance maps. In these areas, the tunneling conductance is still well below that of the normal phase. The white scale bar in panel (a) corresponds to 40 nm. The color scale corresponds to slightly different conductance values in each figure, to maximize contrast. To discuss the value of the conductance in (a-e) we show in (f) the tunneling conductance at zero bias normalized to its high bias value versus temperature, taken at different positions. Lines connect points and are guides to the eye. We show the tunneling conductance taken in between vortices (blue areas in (a-e)) as blue circles. The change induced by the temperature smearing in the zero bias tunneling conductance is shown as an orange line. We also show as yellow triangles the tunneling conductance inside the vortex liquid droplets (average over areas within the red lines in a-e).
• Figure 2: Possible role of defects and intergrowth in vortex pinning of CaKAs$_{4}$Fe$_4$. Schematic representation of the CaKFe$_4$As$_4$ crystal lattice with an interstitial single layers of CaFe$_2$As$_2$ or KFe$_2$As$_2$ marked with an blue planes. We represent the vortices as yellow cylinders that become pinned on the borders of these interstitial layers.
• Figure 3: Thermal fluctuations of vortices. In (a-c) and in (e-g) we show zero bias tunneling conductance maps acquired sequentally at, respectively, 2 T and 10 T. Each map has been taken in half an hour, and the field of view remains the same at each magnetic field. Vortex positions are marked by red circles. The black lines join nearest neighbour vortices, obtained by triangulation. In (d,h) we superimpose red circles united by a red line for each magnetic field ((d) for 2 T and (h) for 10 T) on the first zero bias tunneling conductance map of the sequence. These circles and red lines mark the trajectory of each vortex in the sequence. We see that most vortices remain at the same position. However, a few vortices have moved. For example, the vortices marked in white in the top central part of (d), or at the bottom center in (h), are the vortices in each case that present the largest displacement in the field of view. Note that the largest displacement is much larger at 2 T than at 10 T. In total, we acquired six consecutive images at each magnetic field. White bars in (a) and (e) correspond to 40 nm.