The economic sustainability of individual farming operations and the area’s berry industry in total will ultimately be impacted by and continue to evolve with the ever changing business environment, and by an array of risks and challenges.Angle-resolved photo emission spectroscopy is used to directly measure the band structure of solids and is an essential experimental tool for solid state physics research. In addition to the band structure, ARPES provides information on other aspects of the electronic structure. For example, ARPES with a spin detector can be used to obtain spin information of the initial states. Polarization dependent experiments can provide symmetry information on the initial states; initial states from, for example, px and py orbitals can show dramatically different ARPES intensities depending on the polarization of the incident light. In recent years, there has been much interest in using circular dichroism in ARPES as a way to measure some aspects of initial states, such as the orbital angular momentum or the Berry curvature. It is well understood that OAM plays an important role in spin-split phenomena in systems without inversion symmetry, such as surfaces of solids and monolayer transition metal dichalcogenides. CD-ARPES has been utilized to obtain the crucial information on the electronic structures of such systems. While the final state of the photoemission process certainly has an effect on the CD-ARPES intensities, plastic grow bag experimental results show that CD-ARPES is a rough measure of the OAM of the initial state if the photon energy is not too low.
Exploiting this feature in CD-ARPES measurements, information on the OAM and hidden Berry curvature of 2H-WSe2 was recently obtained using CD-ARPES. An important aspect of this research was that the Berry curvature contribution to the CD-ARPES intensity could be isolated by decomposing the CD-ARPES intensity map into symmetric and anti-symmetric components about the experimental mirror plane, which is perpendicular with respect to the crystal mirror plane of 2H-WSe2. The symmetric component was attributed to the OAM or Berry curvature contribution, since the electronic structure should be symmetric about the chosen experimental mirror plane set along K–Ŵ–K′ in momentum space.Experimental geometry, including single crystal orientation, is especially important in this experiment. The crystal structure of the top atomic layer or ML of 2H-WSe2 is a hexagonal lattice, as shown in Fig. 1a; there is a unique mirror plane in the crystal structure, as indicated in the figure. The experimental mirror plane is defined by the plane defined by the normal of the sample surface and the direction of incident light. Two experimental geometries are possible, according to the direction of incident light, as indicated by blue and red arrows in Fig. 1a. The experimental geometries using incident light described by blue and red arrows are regarded as geometry-A and geometry-B for convention, respectively. Notably, the signals from the top layer of bulk 2H-WSe2 dominate the CD-ARPES data due to the surface sensitivity of ARPES; the corresponding momentum space view is shown in Fig. 1b.
The mirror plane is oriented along the M–Ŵ–M direction, and the direction of incident light is indicated by blue and red arrows on the mirror plane in Fig. 1b. This experimental geometry differs from that used in previous work, in which the experimental mirror plane was rotated by 30° with respect to the crystal mirror plane, such that the experimental mirror plane is oriented along the K–Ŵ–K′ direction. We expanded on our previous CD-ARPES work on 2H-WSe2 by focusing on a different mirror plane. Here, we report our CD-ARPES studies on 2H-WSe2 with the experimental mirror plane parallel to the crystal mirror plane or along the M–Ŵ–M direction in momentum space . 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 anti-symmetric function of the CD map for the experimental mirror plane is expected for this experimental geometry, given that the Berry curvature is also anti-symmetric 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, 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′ . Te 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. Te 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, pe grow bag 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 anti-symmetric 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. It is important to isolate the Berry curvature contribution to INCD A from other contributions. 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. Ten, 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 model. 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-ARPES. 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, 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.