Observation of Distinct Spatial Distributions of the Zero and Nonzero Energy Vortex Modes in $({\mathrm{Li}}_{0.84}{\mathrm{Fe}}_{0.16})\mathrm{OHFeSe}$

The energy and spatial distributions of vortex bound state in superconductors carry important information about superconducting pairing and the electronic structure. Although discrete vortex states, and sometimes a zero energy mode, had been observed in several iron-based superconductors, their spatial properties are rarely explored. In this study, we used low-temperature scanning tunneling microscopy to measure the vortex state of (Li,Fe)OHFeSe with high spatial resolution. We found that the nonzero energy states display clear spatial oscillations with a period corresponding to bulk Fermi wavelength; while in contrast, the zero energy mode does not show such oscillation, which suggests its distinct electronic origin. Furthermore, the oscillations of positive and negative energy states near $E_F$ are found to be clearly out of phase. Based on a two-band model calculation, we show that our observation is more consistent with an $s_{++}$ wave pairing in the bulk of (Li, Fe)OHFeSe, and superconducting topological states on the surface.

Figure 1

(a) STM image of $({\mathrm{Li}}_{0.84}{\mathrm{Fe}}_{0.16})\mathrm{OHFeSe}$ ($34\times 34{\mathrm{nm}}^2$). (b) Averaged superconducting gap spectrum along the arrow in (a). Setpoint: $V_b=6\mathrm{mV}$, $I=100\mathrm{pA}$, $\mathrm{\Delta }V=0.15\mathrm{mV}$. (c) Summed $dI/dV$ spectra over a $4.5\times 4.5{\mathrm{nm}}^2$ region at the center of the vortex core (marked in the inset image). Setpoint: $V_b=6\mathrm{mV}$, $I=80\mathrm{pA}$, $\mathrm{\Delta }V=50\mu \mathrm{V}$. Red curve is the multi-Gaussian fit and the dashed curves are individual peaks. Numbered arrows near the peaks indicate the energy position where the $dI/dV$ maps in panels (d)–(l) are taken. (d)–(p) High spatial resolution $dI/dV$ maps of the vortex in panel (c) inset (size: $21\times 21{\mathrm{nm}}^2$), taken at various energies (setpoint: $V_b=6\mathrm{mV}$, $I=100\mathrm{pA}$, $\mathrm{\Delta }V=50\mu \mathrm{V}$). The mapping area is the square region marked in panel (a) [some DOS modulation at the top-left corner of panels (k)–(p) is from a surface defect, as seen in panel (a)].

Figure 2

Spatial distributions of the vortex states. (a)–(c) Fourfold symmetrized $dI/dV$ maps of the $E_{-1}$, $E_1$, $E_0$ states, respectively. (d) Line profiles along the Fe-Fe direction of the (symmetrized) $dI/dV$ maps of $E_1$, $E_0$, $E_{-1}$ states. (e) Color plot of the symmetrized $dI/dV$ line profile taken at various energies. (f),(g) Fourfold symmetrized FFT of the $dI/dV$ maps of $E_{-1}$ and $E_1$ states. (h) “Phase referenced” FFT of the $E_{\pm 1}$ states (focused on center ring). (i) FFT line profiles taken along the $\mathrm{\Gamma }\text{−}M$ direction at various energies, shown in the color plot. (j) The bulk Fermi surface sketch of (Li,Fe)OHFeSe, different orbital components are indicated by different colors. (k) Normal state QPI taken at $E=20\mathrm{meV}$ (adapted from Ref. [35]).

Figure 3

Vortex state simulations. (a) Analytic solutions of the zero energy vortex mode from the topological surface state [15, 16], and conventional $\mu =\pm 1/2$ CdGM states [10], assuming they have a $k_F$ of $\sim 0.03{\AA }^{-1}$ and $0.175{\AA }^{-1}$, respectively. (b)–(d) Two-band model calculations of the vortex states distribution under $s_{++}$, bonding-antibonding $s_{\pm }$, and nodeless $d$-wave pairing of the bulk state of (Li,Fe)OHFeSe (line cut across the vortex center, $\xi$ is the coherence length).