Abstract
The surfaces of PtCoO2 and PdCoO2 support states with properties very different from those of the bulk, as discussed in the Introduction (Sect. 1.2.1), and shown in Sect. 2.6.5 on the example of PdCoO2. The surface states found on their CoO2-terminated surfaces are the topic of this chapter, which I will start by describing the experimental observations, and the conclusions that can be drawn based on the experiments and symmetry arguments alone (Sect. 6.1). I will go on to introduce the density functional theory (DFT) calculations of these surface states performed by Helge Rosner, compare them to the experiment, and show how this comparison was necessary to correctly interpret the calculations, but also to motivate further measurements (Sect. 6.2). Both the experiment and the first principles calculations show that the surface states exhibit a spin-splitting that is unusually large for a system based on 3d orbitals, motivating a careful examination of the basic principles underlying the appearance of spin-split band structures in solids (Sects. 6.3–6.5). This analysis, although motivated by our measurements, in not at all specific to delafossites. In contrast, it outlines a general framework which can be used to think about systems exhibiting spin-splitting. In Sect. 6.4 I work with a didactic model based on p-orbitals, as originally introduced by Petersen and Hedegård [1], which is very useful for establishing and illustrating the main principles behind spin-splitting. In Sect. 6.5 I discuss the generality of the conclusions drawn from the p-orbital model, and finally, in Sect. 6.6 I extend the analysis to a tight binding model whose ingredients are directly relevant to the CoO2 layer of the delafossites. I show how this model gives a new perspective on the density functional theory calculations, and how its predictions were confirmed by measurements on a new compound, PdRhO2 (Sect. 6.7). A reader more interested in the results specifically relevant for the delafossite surface states than in the general analysis of the development of spin splitting and orbital angular momentum in solids may prefer to jump directly from Sects. 6.2 to 6.6, and back-refer to Sects. 6.3–6.5 as necessary.
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Notes
- 1.
The synchrotron radiation is not continuous, but arrives in pulses, as determined by electron bunches in the synchrotron ring (see Sect. 2.6.1). The relevant parameter for space charge is actually the number of photons per pulse, rather than the average intensity. However, from the point of view of the user, tuning the number of photons per pulse is equivalent to tuning the intensity.
- 2.
This is actually half the value that would be obtained by simply combining the Coulomb field (Eq. 6.9) and the general expression for the coupling of a moving spin and static electric field (Eq. 6.8). The additional factor of 1/2 is a consequence of a relativistic kinematic effect called the Thomas correction, which is related to the fact the energy is evaluated in a rotating coordinate system [11, 12].
- 3.
This is in fact the origin of the term ‘fine structure constant’; while atomic spectra are dominantly governed by the Coloumb interaction, making Rydberg (\(1 \,\mathrm {Ry}=13.6 \,\mathrm {eV}\)) the relevant energy scale, the spin-orbit interaction gives rise to their fine structure, with level splittings reduced by the factor of \(\alpha ^{2}\).
- 4.
The simplified notation in this section is slightly different from the one used in Sect. 3.1, which is consistent with Reference [18]. They are related by: \(t_{\alpha \beta }\left( \vartheta _{ij}\right) =E_{\alpha ,\beta }\left( \cos \left( \vartheta _{ij}\right) ,\sin \left( \vartheta _{ij}\right) ,0\right) \).
- 5.
These can be obtained from the more standard form in the basis of spherical harmonics by the coordinate transformation given in Appendix E.1.
- 6.
See Sect. D.3 for a comparison of the numerical values extracted from all the compounds.
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Sunko, V. (2019). Rashba-Like Spin-Split Surface States. In: Angle Resolved Photoemission Spectroscopy of Delafossite Metals. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-31087-5_6
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