Quantum Vortex Core and Missing Pseudogap in the Multiband BCS-BEC Crossover Superconductor FeSe

FeSe is argued as a superconductor in the Bardeen-Cooper-Schrieffer Bose-Einstein condensation crossover regime where the superconducting gap size and the superconducting transition temperature $T_c$ are comparable to the Fermi energy. In this regime, vortex bound states should be well quantized and the preformed pairs above $T_c$ may yield a pseudogap in the quasiparticle-excitation spectrum. We performed spectroscopic-imaging scanning tunneling microscopy to search for these features. We found Friedel-like oscillations near the vortex, which manifest the quantized levels, whereas the pseudogap was not detected. These apparently conflicting observations may be related to the multiband nature of FeSe.

Figure 1

(a)–(e) Tunneling-conductance maps showing a single vortex at different $E$. Data were taken at 0.4 K in a magnetic field of 0.25 T along the $\mathbf{c}$ axis. The tip was stabilized at tunneling current $I=100\mathrm{pA}$ at $V=10\mathrm{mV}$. Modulation amplitude for the lock-in detection $V_{\text{mod}}=0.07{\mathrm{mV}}_{\mathrm{rms}}$. (f) Tunneling spectra taken at the vortex center (red) and away from vortices (blue). $V_{\text{mod}}=0.05{\mathrm{mV}}_{\mathrm{rms}}$. Inset: Magnified spectrum at the vortex center.

Figure 2

Spatial variations of the tunneling conductance (a) and the bound-state energy (b) along the $\mathbf{a}$ axis showing the oscillatory behaviors. (c) Energy-dependent line profile of the Fourier-transformed QPI pattern along the ${\mathbf{q}}_a$ direction. (Data adopted from Ref. [6].) Yellow solid line denotes the dispersion of the electron-band branch obtained by fitting the peak positions of the constant-energy line profile (red circles) to the polynomial function with even powers up to 6. (d) Fourier transforms from (b). Smooth background was subtracted before the Fourier transformation. As indicated by the vertical gray bar, the wave vector of the bound-state oscillation coincides with $\pi /k_F$ obtained in (c). Spatial variations of the tunneling conductance and the bound-state energy along the $\mathbf{b}$ axis are shown in (e) and (f), respectively.

Figure 3

(a) Tunneling spectra taken at different temperatures. Measurement conditions were $I=100\mathrm{pA}$, $V=95\mathrm{mV}$, and $V_{\text{mod}}=0.7{\mathrm{mV}}_{\mathrm{rms}}$. Each curve is shifted by 1 nS for clarity. Inset: Topography showing the position (red cross) where the spectra were taken. Scale bar corresponds to 5 nm. (b) Low-energy tunneling spectra taken at different temperatures. Measurement conditions were $I=100\mathrm{pA}$, $V=20\mathrm{mV}$, and $V_{\text{mod}}=0.07{\mathrm{mV}}_{\mathrm{rms}}$. Each curve is shifted by 5 nS for clarity.

Figure 4

(a) Temperature dependence of the gap amplitude assumed in the analysis. (b)–(d) Low-energy tunneling spectra normalized by the spectrum at 25 K (filled black circles) and their comparisons with the simulated spectra (solid lines). For the simulated spectra in (b)–(d), assumed $T_v$’s are $\infty$, 20 K, and 9 K, respectively. Each curve is shifted by 1 for clarity. (e) Calculated evolution of the $T_{\mathrm{ins}}$ and $T_c$ with increasing intraband $d$-wave interaction. The vertical gray bar refers to the parameter region relevant for FeSe. Inset: The two-band electronic structure adopted in this model.