The origin of the large T c variation in FeSe thin films probed by dual-beam pulsed laser deposition

Abstract

FeSe is one of the most enigmatic superconductors. Among the family of iron-based compounds, it has the simplest chemical makeup and structure, and yet it displays superconducting transition temperature ( $T_{\text{c}}$ ) spanning 0 to 15 K for thin films, while it is typically 8 K for single crystals. This large variation of $T_{\text{c}}$ within one family underscores a key challenge associated with understanding superconductivity in iron chalcogenides. Here, using a dual-beam pulsed laser deposition (PLD) approach, we have fabricated a unique lattice-constant gradient thin film of FeSe which has revealed a clear relationship between the atomic structure and the superconducting transition temperature for the first time. The dual-beam PLD that generates laser fluence gradient inside the plasma plume has resulted in a continuous variation in distribution of edge dislocations within a single film, and a precise correlation between the lattice constant and $T_{\text{c}}$ has been observed here, namely, $T_{\text{c}}\propto \sqrt{c-c_0}$ , where c is the c-axis lattice constant (and $c_0$ is a constant). This explicit relation in conjunction with a theoretical investigation indicates that it is the shifting of the $d_{\text{xy}}$ orbital of Fe which plays a governing role in the interplay between nematicity and superconductivity in FeSe.

Supplementary information: The online version contains supplementary material available at 10.1007/s44214-024-00058-0.

Keywords: High-temperature superconductivity; High-throughput technique; Iron chalcogenide superconductors; Pulsed laser deposition.

Figure 1

Comparison of conventional single-beam (a–d) and dual-beam (e–h) pulsed laser deposition (PLD) methods and resulting lattice constant – $T_{\text{c}}$ variation in FeSe films. (a) Schematics of the single-laser PLD method. (b) The XRD patterns for the out-of-plane (002) peak taken at equally spaced positions along the x-direction from a single representative film with $T_{\text{c}}$ of $\approx 8\text{ K}$. (c) The temperature dependence of the normalized resistance [$R(T)$] curves at different positions on the same film as in panel (b) along the x-direction. In panels (b) and (c), the curves are vertically shifted for clarity. The characterized region moves from the center ($x=0\text{ mm}$) to the edge ($x=10\text{ mm}$) of the substrate from the bottom to the top curves, as indicated by the black arrow on the right side. The XRD peak position in 2θ and $T_{\text{c}}$ do not change across the sample as in any typical film made by conventional PLD, as marked by the straight red dotted lines. (d) The out-of-plane lattice constant (c-axis) versus the superconducting transition temperature ($T_{\text{c}}$) for FeSe films made by conventional PLD. 200 sample data points plotted are selected randomly from more than 1500 samples. (e) Schematics of the dual-beam PLD method. (f) The XRD patterns for the out-of-plane (002) peak of the dual-beam FeSe film along the x-direction from −15 to +15 mm, encompassing the entire length of the substrate. A clear continuous shifting of the FeSe (002) peak is observed, first to lower angle approaching the middle position (0 mm), and then the shifting is reversed in a symmetrical manner. (g) The corresponding normalized $R(T)$ curves at different locations along the x-direction, with the highest $T_{\text{c}}$ in the middle, corresponding to the position on the film with the largest c-axis as well as the shortest a-axis. The curves are shifted vertically for ease of comparison. The red lines in panels (f) and (g), track the variations of the FeSe (002) peak and $T_{\text{c}}$, respectively. The arrow on the right side indicates the x coordinate positions on the film from bottom to top with 0.5 mm increment. (h) The c-axis lattice vs $T_{\text{c}}$ for FeSe extracted from two dual-beam PLD thin films (filled circles are extracted from panels (f) and (g)). The red dashed line is the best fit using the expression $T_{\text{c}}\propto \sqrt{c-c_0}$, with $c_0=5.51$ Å

Figure 2

HAADF STEM images taken along the [100] zone axis for two superconducting FeSe films with different $T_{\text{c}}$’s. (a–b) Typical STEM images for samples with (a) $T_{\text{c}}=9\text{ K}$ (SC09) and (b) $T_{\text{c}}=3\text{ K}$ (SC03). The white dashed line in panel (b) highlights the region where the lattice is distorted, with typical dimensions of several nanometers. The bottom images show the magnifications of the red rectangles in the top images, and the blue curves indicate the contrast change across the top row of Se atoms. The grey dashed lines represent the period of the in-plane lattice. For SC09, the atoms well match the periodicity. For SC03, the left side is normal while approaching the right side the periodicity gradually becomes half, indicating lattice distortion around this region. (c) The bottom image is the magnified view of the distorted region in panel (b). The schematic picture above it reconstructs the Fe and Se atom configurations in the bottom image, and the top two pictures together illustrate that the observed lattice distortion is an overlap of a standard FeSe region (top plane) and a stretched region (second plane)

Figure 3

The density distribution and the morphology of atomic clusters of the plasma plume due to dual-beam laser ablation. (a) (Bottom) The density distribution of plasma above the surface of FeSe target computed by the fluid model; (Top) Cross-sectional SEM image at the center and edge of the resulted FeSe film, with their thicknesses labeled respectively. $z=0\text{ mm}$ corresponds to the top surface of FeSe target, and the substrate are 50–70 mm above the target. (b) Integration of the plasma density at the top of the mushroom cloud in panel (a), indicated by the dashed box. The plasma density exhibits no significant change along x-direction, corroborating the uniform thickness of the FeSe film deposited on the substrate. (c) The intensity distribution of the dual-beam laser on the FeSe target. The inset white-blue images show distributions of mesoscopic atomic clusters evaporated from the FeSe target near the laser-material interaction zone ($z<0.2\mu \text{m}$ in panel (a)) obtained by the molecule dynamic simulation at three x locations with different laser intensities (indicated by the red arrows). The image dimensions are roughly 0.05 μm in the x-direction and 0.2 μm in the z-direction (limited by the number of unit cells which can be treated by the molecular dynamic simulation). Each colored pixel represents one unit cell (molecule). Particle clusters (dark blue areas) and voids (light areas) can be clearly discerned indicating that higher energy intensity leads to more uniform cluster distribution in the micrometer range near the interaction zone. If $t=0\text{ s}$ denotes the moment the laser pulse hits the target surface, the time scale is approximately $t=1\text{ ns}$ for panel (c) and $t=5\mu \text{s}$ for panel (b)

Figure 4

Transport properties of five representative uniform FeSe thin films with different $T_{\text{c}}$’s (samples denoted as SC03, SC08, SC11, SC12, and SC14 have $T_{\text{c}}=3,8,11,12,\text{and }14\text{ K}$, respectively). (a) X-ray rocking curves of the FeSe (003) peak. (b) The temperature dependence of the normalized in-plane resistivity. Inset: The mapping of the c-axis lattice and $T_{\text{c}}$ relation of the uniform FeSe thin films (colored dots) to the lattice constant – $T_{\text{c}}$ relation (grey line) we uncovered here (i.e. $T_{\text{c}}\propto \sqrt{c-c_0}$). (c–d) The Hall resistivity ${\rho }_{\text{xy}}(B)$ at 10 K intervals for two samples: SC03 (c) and SC14 (d). Here, the symbols are experimental data and the solid lines are the linear fits. (e) The corresponding temperature dependence of the Hall coefficients [$R_{\text{H}}(T)$] for different samples. All the $R_{\text{H}}$ (T) curves overlap above $T^{\ast }\sim 120\pm 10\text{ K}$, indicated by the orange shadow area, but diverge considerably below $T^{\ast }$