Superconductivity in a single-layer alkali-doped FeSe: A weakly coupled two-leg ladder system

We prepare single-layer potassium-doped iron selenide (110) film by molecular-beam expitaxy. Such a single-layer film can be viewed as a two-dimensional system composed of weakly coupled two-leg iron ladders. Scanning tunneling spectroscopy reveals that superconductivity is developed in this two-leg ladder system. The superconducting gap is similar to that of the multilayer films. However, the Fermi-surface topology in this quasi-one-dimensional system is remarkably different from that of the bulk materials. Our results suggest that superconducting pairing is very short ranged or takes place rather locally in iron chalcogenides. The superconductivity is most likely driven by electron-electron correlation effect and is insensitive to the change of Fermi surfaces.

Figure 1

Single-layer K${}_x$Fe${}_{2-y}$Se${}_2$ (110). (a) Two-leg ladder system composed of weakly coupled iron atom chains. The same convention for Miller indices is used throughout. In the single layer two-leg ladder system (schematic on right), each FeSe(001) layer contributes one ladder (the shaded area in the schematic on left, dashed lines marked the Fe ladder), which is along the [$\overline{1}$10] direction. A layer of K atoms is sandwiched between two ladders. (b) STM topographic image (150 $\mathrm{nm}\times 150$ nm, 3.9 V, 0.02 nA) of a single layer K${}_x$Fe${}_{2-y}$Se${}_2$(110) island. Two distinct regions are marked by 346 phase and 245 phase. The apparent height of island is insensitive to bias voltage from 0.5 to 4.0 V and estimated to be $5.5\pm 0.3$ Å. The substrate is bilayer graphene characterized by 6$\times$6 hexagonal superstructure (c). (d) STM image of 245 phase (1.35 V, 0.03 nA). The periodic stripe pattern is attributed to the $\sqrt{5}\times \sqrt{5}$ Fe vacancy order seen along the [110] direction. (e) STM image of 122 phase (8 nm $\times$ 8 nm, 10 mV, 0.02 nA). The locations of iron ladders are marked by dashed lines. The locations of K and Se atoms are marked by red and white dots, respectively.

Figure 2

Superconductivity in single layer 346 phase. (a) The superconducting gap (solid curve) of single layer 346 phase. Set point: 14 mV and 0.1 nA. Temperature: 0.4 K. The modulation amplitude and frequency for lock-in measurement are 0.3 mV and 931 Hz. For comparison, the spectrum for multilayer 122 phase (dashed curve) is shown. (b) A 5 nm $\times$ 25 nm topography image (14 mV, 0.1 nA) of the superconducting region. The area shown here is part of the region in Fig. 1b. Inhomogeneity in electronic structure is revealed. (c) A series of $dI/dV$ spectra measured at 16 points indicated in (b). Set point: 14 mV and 0.1 nA. The spectra are offset for clarity.

Figure 3

Magnetic field splitting of the quasiparticle states. $dI/dV$ spectra show density of states for single-layer 346 phase at 0 and 10 T, respectively. Set point: 14 mV, 0.1 nA. The coherence peaks are split into spin-up and spin-down components under magnetic field.

Figure 4

First-principles calculation of single-layer K${}_3$Fe${}_4$Se${}_6$. A 500-eV cutoff in the plane-wave expansion ensures the calculations converge to ${10}^{-5}$ eV. For each magnetic configuration, all atomic positions and the lattice constants were optimized until the largest force on each atom is 0.01 eV/Å. A 12$\times$12$\times$1 Monkhorst-Pack $k$-grid Brillouin zone is sampled throughout all calculations while the Gaussian smearing technique is used in the case of metallic states. To model the thin film, a supercell of slab is used with periodic boundary conditions in all three dimensions with a 10-Å-thick vacuum layer between two slabs in order to eliminate the interslab interactions. (a) The band structure. There are two bands crossing the Fermi surface. (b) Fermi-surface sheets. The electron and hole pockets are located at $N$ and $M$ points respectively. The Fermi energy sets to zero.