极速快3

Observation of topological superconductivity on the surface

2019-12-29

Dirac-cone–type spin-helical surface band and s-wave superconducting gap

To experimentally prove that FeTexSe1–x (x ~ 0.5) is a topological superconductor with intrinsic topological surface states and s-wave superconductivity on the surface, one needs to observe the following three phenomena in spectroscopic measurements: (i) Dirac-cone–type surface states; (ii) helical spin polarization of the surface states, which locks the spin direction perpendicular to the momentum direction; and (iii) an s-wave superconducting gap of the surface states when T < Tc. Previously, we obtained some experimental evidence for the band inversion of the bulk pz and dxz bands (, ). However, the topological surface band was never directly observed, owing to the small energy and momentum scales. The SOC gap is estimated to be about 10 meV in the calculations, which makes it extremely difficult to resolve the Dirac-cone–type surface states in angle-resolved photoelectron spectroscopy (ARPES). In the previous ARPES experiments, only the three t2g (dxy, dyz, and dxz) and the pz bulk bands were observed at Γ (, , ). In the experiment that we present below, by using ARPES with high energy and momentum resolution (HR-ARPES; energy resolution ~ 1.4 meV) () and spin-resolved ARPES (SARPES; energy resolution ~ 5.5 meV) (), we were able to observe the three necessary phenomena required for the proof of topological superconductivity in high-quality single crystals of FeTe0.55Se0.45.

We first demonstrated the observation of the Dirac-cone–type surface states. High-resolution cuts of the band structure around Γ with p- and s-polarized photons are shown in , respectively. According to the matrix element effect [part I of ()], both the surface and the bulk bands (pz and dxz) should be visible for p-polarized photons, whereas only the bulk valence band (dxz) is visible for s-polarized photons. The momentum distribution curve (MDC) curvature plot (an improved version of the second derivative method) () of the data with p-polarized photons shows a clear Dirac-cone–type band (). We obtained a parabola-like band by extracting the energy distribution curve (EDC) peaks of the data with s-polarized photons (). Combining the bands observed in , we conclude that the Dirac-cone–type band (blue lines in ) is the topological surface band, and the parabolic band (white curve in or red curve in ) is the bulk valence band. Further, we directly separated the bulk valence band from the Dirac-cone–type surface band with the data at very low temperature (2.4 K) when the spectral features were narrower (). We overlapped the Dirac-cone–type surface band in and the parabolic bulk band in onto the EDC curvature plot in . The extracted bands overlap well with the curvature intensity plot, confirming the existence of the parabolic bulk band and the Dirac-cone–type surface band. The overall band structure is summarized in , demonstrating a Dirac surface band very close to EF.

Fig. 2 Dirac-cone–type surface band.

(A) Band dispersion along ΓM, recorded with a p-polarized 7-eV laser. (B) MDC curvature plot of the data from (A), which enhances vertical bands (or the vertical part of one band) but suppresses horizontal bands (or the horizontal part of one band) (). The red dots trace the points where the intensity of the MDC curvature exceeds the red bar in the color-scale indicator, and the blue lines are guides to the eye indicating the band dispersion. (C) Same as (A), but recorded with s-polarized light. The red line comes from the Lorentzian fitting of the EDC peaks. The red line is reproduced in (B) as a white line. (D and E) Zoomed-in view of the dashed box area in (A). The data are recorded at 2.4 K to reduce the thermal broadening. (D) EDCs of the zoomed-in area. The black and blue markers respectively trace the EDC peaks from two bands. arb., arbitrary. (E) EDC curvature plot of the zoomed-in area. The blue lines are the same as the ones in (B), and the red line is the same as the one in (C). (F) Summary of the overall band structure. The background image is a mix of raw intensity and EDC curvature (the area in the dashed box). The bottom hole-like band is the bulk valence band, whereas the Dirac-cone–type band is the surface band.

Next, we carried out high-resolution spin-resolved experiments to check the spin polarization of the Dirac-cone–type band. Two EDCs at the cuts indicated in were measured. If the Dirac-cone–type band comes from the spin-polarized surface states, the EDCs at cuts 1 and 2 should show reversed spin polarizations. Indeed, the spin-resolved EDCs in , show that the spin polarizations are reversed for cuts 1 and 2, whereas the background shows no spin polarization (). These data are consistent with the spin-helical texture, which is the direct consequence of “spin-momentum locking” of topological surface states. We also measured an additional two EDCs at different positions on the FS [part III of ()]. The spin polarizations of all four EDCs are consistent with the spin-helical texture predicted by theory (). The small magnitude of the spin polarizations in , may partly be explained by the large broadening of the SARPES data, originating from the lower resolution of that technique ().

Fig. 3 Spin-helical texture of the surface band.
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