Scanning tunneling microscopy/spectroscopy of vortices in LiFeAs

We investigate vortices in LiFeAs using scanning tunneling microscopy/spectroscopy. Zero-field tunneling spectra show two superconducting gaps without detectable spectral weight near the Fermi energy, evidencing fully gapped multiband superconductivity. We image vortices in a wide field range from 0.1 T to 11 T by mapping the tunneling conductance at the Fermi energy. A quasihexagonal vortex lattice at low field contains domain boundaries which consist of alternating vortices with unusual coordination numbers of 5 and 7. With increasing field, the domain boundaries become ill defined, resulting in a uniformly disordered vortex matter. Tunneling spectra taken at the vortex center are characterized by a sharp peak just below the Fermi energy, apparently violating particle-hole symmetry. The image of each vortex shows energy-dependent 4-fold anisotropy which may be associated with the anisotropy of the Fermi surface. The vortex radius shrinks with decreasing temperature and becomes smaller than the coherence length estimated from the upper critical field. This is direct evidence of the Kramer-Pesch effect expected in a clean superconductor.

Figure 1

(a) STM topograph of cleaved (001) surface of LiFeAs at 0.54 K. The setup conditions for imaging were sample-bias voltage $V_s=+20$ mV and tunneling current $I_t=10$ pA. The inset shows a magnified topography with atomic resolution ($V_s=+20$ mV, $I_t=100$ pA). (b) Tunneling spectrum taken away from defects. Tip stabilization condition was $V_s=+98.9$ mV and $I_t=100$ pA. Measurement was done with a bias modulation amplitude $V_{\mathrm{mod}}=1$ mV${}_{\mathrm{rms}}$. Data were taken at 1.5 K. (c) Low-energy tunneling spectra at different temperatures. Two gaps are identified in the spectra and both gaps disappear above 18 K which corresponds to bulk $T_c$. Tip was stabilized at $V_s=+25$ mV and $I_t=125$ pA. $V_{\mathrm{mod}}=0.1$ mV${}_{\mathrm{rms}}$.

Figure 2

(a)–(c) Images of vortices at 1.5 K obtained by mapping tunneling conductance at $E_F$. Tip was stabilized at $V_s=+20$ mV and $I_t=100$ pA. $V_{\mathrm{mod}}=0.7$ mV${}_{\mathrm{rms}}$. Arrows denote the nearest Fe-Fe direction. (d)–(f) Delaunay triangulation diagrams obtained from vortex images shown in (a)–(c). Vertices with symbols denote vortices with coordination numbers different from conventional value of 6 (blue triangle, 5; red square, 7; green star, others). Dashed black square is drawn separately from the edge of the field of view (black solid square) by the mean value of intervortex distance at each field. Defect fraction [Fig. 3b] was calculated using vortices within this dashed black square to avoid the effect of the edge. (g)–(i) Two-dimensional autocorrelation function calculated from vortex images shown in (a)–(c). (j)–(l) Two-dimensional Fourier transformations from vortex images shown in (a)–(c).

Figure 3

(a) Applied-field dependence of vortex density in LiFeAs. Solid black line denotes the behavior expected in the case that the single vortex carries the single vortex quantum of 2.07$\times {10}^{-15}$ T m${}^2$. (b) Applied-field dependence of fraction of defect vortices with coordination numbers different from conventional value of 6. (c) and (d) Delaunay triangulation diagrams at 2 T and 8 T in the fields of view which contain equal number of vortices. Symbols have the same meanings as in Figs. 2d, 2e, 2f.

Figure 4

(a)–(d) Tunneling-conductance images around a single vortex at different energies. Arrows denote the nearest Fe-Fe direction. Tip was stabilized at $V_s=+25$ mV and $I_t=250$ pA. $V_{\mathrm{mod}}=0.2$ mV${}_{\mathrm{rms}}$. Data were taken at 0.54 K. (e) Tunneling spectra taken at the center of vortex (red) and away from vortices (blue). $V_{\mathrm{mod}}=0.10$ mV${}_{\mathrm{rms}}$. Line profiles of tunneling conductance across the vortex center. (f) Along the nearest Fe-Fe direction. (g) Along the nearest As-As direction. $V_{\mathrm{mod}}=0.15$ mV${}_{\mathrm{rms}}$.

Figure 5

Temperature dependence of the tunneling spectra at the vortex center (a) and away from vortices (b). Tip was stabilized at $V_s=+25$ mV and $I_t=250$ pA. $V_{\mathrm{mod}}=0.1$ mV${}_{\mathrm{rms}}$. Each curve (except at 7.5 K) is shifted vertically for clarity. Thin black lines denote the convoluted 0.54 K spectra by Fermi-Dirac distribution function.

Figure 6

Tunneling-conductance images at $E_F$ at different temperatures. Tip was stabilized at $V_s=+25$ mV and $I_t=250$ pA. $V_{\mathrm{mod}}=0.2$ mV${}_{\mathrm{rms}}$. Note that color scale is different from that for Figs. 4a, 4b, 4c, 4d.

Figure 7

Line profiles of tunneling-conductance at $E_F$ at different temperatures. (a) Along the nearest Fe-Fe direction. (b) Along the nearest As-As direction. Solid lines denote results of Gaussian fitting. (c) Temperature dependence of half-width at half maximum of the fitted Gaussian peak, which represents the vortex-core size.