Vortex lattice and vortex bound states in ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ investigated by scanning tunneling microscopy/spectroscopy

We investigate the vortex lattice and vortex bound states in ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ single crystals by scanning tunneling microscopy/spectroscopy (STM/STS) under various magnetic fields. A possible structural transition or crossover of vortex lattice is observed with the increase of magnetic field, i.e., the vortex lattice changes from a distorted hexagonal lattice to a distorted tetragonal one at the magnetic field near 0.5 T. It is found that a mixture of stripelike hexagonal and square vortex lattices emerges in the crossover region. The vortex bound state is also observed in the vortex center. The tunneling spectra crossing a vortex show that the bound-state peak position holds near zero bias with the STM tip moving away from the vortex core center. The Fermi energy estimated from the vortex bound state energy is very small. Our investigations provide experimental information to both the vortex lattice and the vortex bound states in this iron-based superconductor.

Figure 1

(a) A typical topographic image of the Cs-terminated surface on ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ measured with bias voltage of $V_{\mathrm{bias}}=170$ mV and tunneling current of $I_t=50$ pA. The inset shows the atomically resolved image ($V_{\mathrm{bias}}=20$ mV and $I_t=200$ pA). (b) Typical tunneling spectra measured at some defect-free position on ${\mathrm{CsFe}}_2{\mathrm{As}}_2$ at different temperatures. The spectra are offset for clarity. (c) Normalized tunneling spectrum measured at 0.4 K by the one measured at 3 K, and the Dynes model fitting curves by an $s$-wave and a $d$-wave gap. (d) A series of tunneling spectra across a defect signatured by a dark spot. The spectra are offset for clarity.

Figure 2

(a)–(c) Images of vortex lattices measured at 0.4 K under various magnetic fields. The scanning areas are all $380\times 380 {\mathrm{nm}}^2$. Delaunay triangulation plots are used to indicate the lattice structures in the figures. (d)–(f) Self-correlation mapping to the real-space vortex lattice image measured at different fields in (a)–(c), respectively. The inset in (f) shows the atomically resolved surface which is a part of the vortex image region, and the main axes of the surface Cs atoms are marked by black arrows. (g)–(i) The spatial evolution of intensity along the arrowed lines in (d)–(f), respectively. The spatial period $a_0$ is also presented for each figure.

Figure 3

(a)–(c) Statistics on the angle values of all the Delaunay triangles in Figs. 2–2. (d) The ratio of vortex interaction energy per unit length in the ideal hexagonal lattice over that in the tetragonal lattice (see text).

Figure 4

(a) Experimental result of stripelike vortex lattice mixed by hexagonal and square lattice. The data are the same as those in Fig. 2, while the intervortex plots are a bit different to show the strip features. (b) The schematic image of the possible stripelike vortex lattice structure in the crossover region. (c) Self-correlation image of (b).

Figure 5

(a) Vortex image by mapping of differential conductance at zero bias. (b) Spatial evolution of the tunneling spectra at 0.4 K crossing a vortex core center along the arrowed line in (a). The spectra are offset for clarity. The red curve is measured at the vortex center, while the green one is measured far away with a distance of 40.5 nm from the vortex center. (c) The subtracted results $\mathrm{\Delta }G$ of the tunneling spectra with the green curve in (b). The bound-state peak location is very close to zero bias (the red vertical dashed line). (d) Spatial evolution of $\mathrm{\Delta }G$ taken at 0.05 mV from the difference spectra in (c) and fitting curve of the exponential decay formula.