Within the experimental constraint, there are two possible experimental geometries based on the incident beam directions, as shown by the blue and red arrows in Fig. 1a,b. The CD-ARPES values for the two geometries are nearly opposite to each other near the Brillouin zone corner, whereas they are almost identical near the Ŵ point. These observations are well explained by accounting for the Berry curvature contribution to CD-ARPES. Our results thus indicate that the deviation from the median value between the two experimental geometries can be interpreted as the Berry curvature or OAM. Figure 1c,d present the constant energy ARPES maps taken by RCP and by LCP incident light in geometry-A, respectively. The binding energy of all maps shown in Fig. 1 is 0.5 eV lower than the valence band maximum energy . CD signals, in which the intensity corresponds to the difference in the intensity taken by RCP and that taken by LCP , are mapped in the momentum space . The antisymmetric function of the CD map for the experimental mirror plane is expected for this experimental geometry, given that the Berry curvature is also antisymmetric with regard to the experimental geometry. Figure 1f–h present the ARPES maps taken with RCP and LCP incident light in geometry-B and the corresponding CD map, respectively; the upper left corner corresponds to the K′ point in Fig. 1f–h and the K point in Fig. 1c–e. Remarkably, vertical vegetable tower the CD signals at each corner of the BZ in Fig. 1h are almost opposite to those in Fig. 1e, whereas the CD signals near the center of the BZ are nearly the same.
This can be explained by taking the Berry curvatures into account, given that the Berry curvatures are opposite at the K point and K′ point, whereas the Berry curvatures are nearly zero around the Ŵ point. A detailed analysis of CD data was performed for ARPES cut data along the K–M–K′ and K′ –Ŵ–K directions in geometry-A and along the K′ –M–K and K–Ŵ–K′ directions in geometry-B . Figure 2a,b present ARPES spectra taken by RCP and LCP light, respectively, in geometry-A along K–M–K′ , as indicated by the dotted line in Fig. 1e. Figure 2d,e present ARPES spectra taken by RCP and LCP light, respectively, in geometry-B along the K′ –M–K direction, as indicated by the dotted line in Fig. 1h. Two parallel dispersive bands are evident in the spectra, of which the maxima are located at K and K′ . The energy difference between the upper and lower bands originates from atomic spin–orbit coupling of the W atom. The spin directions of the two bands are opposite, but the Berry curvature and OAM are the same, as expected from the massive Dirac–Fermion model. ARPES intensity clearly depends on the polarization of the incident light. Figure 2c,f present CD-ARPES intensity distributions for geometry-A along K–M–K′ and for geometry-B along K′ –M–K, respectively. The CD intensities of the two bands are similar at each momentum point, but the intensities are almost opposite between the CD for geometry-A and that for geometry-B; this is consistent with the constant energy maps shown in Fig. 1e,h.Normalized CD intensities as a function of momentum are shown in Fig. 3a for the upper band and in Fig. 3b for the lower band.
INCD is obtained by /, where IR and IL correspond to the ARPES intensity taken with RCP and LCP, respectively. INCD for the upper band along K–M–K′ in geometry-A, as indicated by the filled squares in Fig. 3a, has a positive value toward the K point from the M point. INCD exhibits a slight sign change beyond K and K′ points, although it is difficulty to catch the fact in Fig. 2c due to very weak ARPES intensities. INCD for the upper band along K′ –M–K , indicated by the empty squares in Fig. 3a, exhibits a negative value toward the K′ point from the M point and a positive value toward the K point from the M point, except very close to the M point, as we can also notice in Fig. 2f; sign changes beyond K′ and K were also evident in the data. The INCDs in geometry-A and -B are roughly opposite, but not exactly. The INCD for the lower band in geometry-A and geometry-B are also similar to those of the upper band, but they are slightly weaker. INCD consists of symmetric and antisymmetric functions about the experimental mirror plane . Figure 3c,d present the INCD S s for the upper and lower bands from two geometries, respectively. Figure 3e,f present the INCD A s for the upper and lower bands from two geometries, respectively. As shown in the figures, the INCD S s were close to zero, and INCD A s were dominant components, regardless of the geometry or band. An asymmetric CD-ARPES distribution about the experimental mirror plane is a usual feature from solids, as the inversion symmetry along the surface normal direction is lifted on the surface of solids, which is similar to an oriented CO molecule system. The CD-ARPES contribution caused by the inversion symmetry breaking in the material surface can be called surface effects.
However, it is surprising that the CD was nearly opposite between geometry-A and -B. Based on this finding, we believe that a substantial portion of INCD A originates from the Berry curvature , given that the CD signs follow the Berry curvature direction, as shown in Figs. 1e,h and 2c,f. The Berry curvature contribution to CD-ARPES should be exactly opposite between the normalized CD-intensities along K–M–K′ in geometry-A and along K′ –M–K in geometry-B, because the Berry curvatures themselves are exactly opposite for K and K′ points. We assume that other contributions, mainly the surface effects, are the same, regardless of the geometry. Then, the median values of INCD A s from geometry-A and -B can be considered from the other contributions to INCD A s. Additionally, this assumption is experimentally justified by CD-ARPES data near the Ŵ point, as shown in Figs. 4 and 5. The difference in INCD A with respect to the median value is exactly opposite between the K–M–K′ cut in geometry-A and the K′ –M–K cut in geometry-B; this difference can be interpreted as the Berry curvature contribution to INCD A . Figure 3g presents the differences, along with the theoretical values of the Berry curvature and OAM. The differences are similar to the Berry curvature and OAM, except for the crossing at zero and the changing signs near 0.7 Å−1 . The sign change of the difference of INCD A from the median value is mainly due to the change in the final state character as the momentum of the photoelectron varies. We know that the wave function characters of the initial states near the K point change gradually and depend on the distance from the K point in the massive Dirac–Fermion model17–19. The sign of CD-ARPES data can be reversed for the same initial states by only changing the final states, as indicated in the photon energy dependence of CD-ARPES22,23. Figure 4 presents the ARPES cuts and CD-ARPES data along the K′ –Ŵ–K in geometry-A, and along K–Ŵ–K′ in geometry-B, as indicated in Fig. 1. These cuts are special, in terms of the Berry curvature and OAM of the electronic states near the Ŵ point being almost negligible, vertical farm tower compared with those of states near the K point. Therefore, the Berry curvature contribution to CD-ARPES data is expected to be almost zero near the Ŵ point. The CD-ARPES signals in both geometries are quite strong near the Ŵ point and exhibit a clear node at Ŵ, indicating no symmetric component of the CD intensity. Te CD-ARPES intensities near the K point from both geometries are much weaker than those near the Ŵ point, and the CD-ARPES intensities near the K point from geometry-A are even weaker than those from geometry-B. Figure 5a–c present INCDs, INCD S s, and INCD A s, respectively. The symmetric components are negligible; the asymmetric components make up the majority of the INCDs . Remarkably, INCDs along K′ –Ŵ–K in geometry-A and along K–Ŵ–K′ in geometry-B are the same near the Ŵ point , and INCD A s are, in turn, the same near the Ŵ point . Figure 5d presents the deviations of INCD A s from the median value, along with the theoretical values of the Berry curvature and the OAM. The deviation is almost zero near Ŵ point and begin to have large value at the momentum at which the Berry curvature and the OAM are also about to increase from almost zero value. This provides experimental evidence that the deviation from the median value of INCDs in geometry-A and -B can be interpreted as the Berry curvature contribution. Although the Berry curvature and the OAM continually increase as they approach the K point, the deviation from the median value from CD-ARPES data seems to be almost constant away from the Ŵ point.Let us briefly touch upon the possible incident photon energy dependence in CD-ARPES or the final state effect.
This is because one can wonder if the CD-ARPES pattern we obtained is seen only with the particular photon energy and a different photon energy may give us a different result. In such case, changing the photon energy will also change the CD-ARPES pattern and the CD-ARPES may not be related to OAM or the local Berry curvature. We would like to point out that incident photon energy dependent CD-ARPES has been performed on the same material. The results showed that CD-ARPES features related to the local Berry curvature are the same regardless of the photon energy. Even though it was for a different plane of incidence compared to the current one, the photon energy independence of the pattern provides a good reason to believe that the CD-ARPES pattern is proportional to OAM or the local Berry curvature. In some the other systems such as Bi2Te3 , PtCoO2 and Au, CD-ARPES results show a sign change. Yet, those results still show that node lines in CD-ARPES mapremain the same except a special resonant channel is involved. In addition, characteristic patterns of CD-ARPES map cannot be explained without consideration of OAM. Therefore, we argue that the interpretation of the CD-ARPES intensity in this work should be robust although the data was taken only with a single photon energy. CD-ARPES data on 2H-WSe2were taken with the crystal mirror plane set as the experimental mirror plane. Within the experimental constraint, there are two possible experimental geometries. We found that CD-ARPES data for the two geometries are almost opposite to each other near the BZ corners, and nearly the same near the Ŵ point. The experimental observations are well explained by accounting for the Berry curvature contribution to CD-ARPES. The Berry curvature contribution to the INCDs can be quantitatively extracted through an analysis that compares INCDs for the two geometries. Our results provide experimental evidence that the deviation from the median value between the two experimental geometries can be interpreted as the Berry curvature or the OAM. Our work may be applicable to observations of the Berry curvature or the OAM in topological materials, such as Weyl semimetals and Berry curvature dipole materials.Successful biliary cannulation was first achieved by the obstetrician William McCune and the surgical team at George Washington University, using an Eder fiberoptic duodenoscope equipped with a forward and side lens. At that time, McCune recorded a 50% success rate, and wrote, “Anyone who looks through one of these instruments has to have 2 personality characteristics. First, he has to be honest, and second, must have an undying, blind, day and night, uncompromising persistence.” Rapid improvement in success rates came one year later in Japan, when Oi developed a side-viewing fiberoptic duodenoscope with the ability to manipulate the cannula. The investigators reported a 77% success rate, without significant morbidity. Five years later, the improvement in endoscopic retrograde cholangiopancreatography methodologies led to additional techniques; some researcher in Erlangen, Germany and Kawai in Japan were independently working on therapeutic uses of ERCP, documenting the first cases of biliary sphincterotomy.