In physics and chemistry, photoemission orbital tomography (POT; sometimes called photoemission tomography) is a combined experimental / theoretical approach which was initially developed to reveal information about the spatial distribution of individual one-electron surface-state wave functions and later extended to study molecular orbitals. Experimentally, it uses angle-resolved photoemission spectroscopy (ARPES) to obtain constant binding energy photoemission angular distribution maps. In their pioneering work, Mugarza et al. in 2003 used a phase-retrieval method to obtain the wave function of electron surface states based on ARPES data acquired from stepped gold crystalline surfaces; they obtained the respective wave functions and, upon insertion into the Schrödinger equation, also the binding potential. More recently, photoemission maps, also known as tomograms (also known as momentum maps or k {\displaystyle k} -maps), have been shown to reveal information about the electron probability distribution in molecular orbitals. Theoretically, one rationalizes these tomograms as hemispherical cuts through the molecular orbital in momentum space. This interpretation relies on the assumption of a plane wave final state, i.e., the idea that the outgoing electron can be treated as a free electron, which can be further exploited to reconstruct real-space images of molecular orbitals on a sub-Ångström length scale in two or three dimensions. Presently, POT has been applied to various organic molecules forming well-oriented monolayers on single crystal surfaces or to two-dimensional materials.
Theory
Within the framework of POT, the photo-excitation is treated as a single coherent process from an initial (molecular) orbital Ψ i {\displaystyle \Psi _{i}} to the final state Ψ f {\displaystyle \Psi _{f}} , which is referred to as the one-step-model of photoemission. The intensity distribution in the tomograms, I ( k x , k y ; E k i n ) {\displaystyle I(k_{x},k_{y};E_{\mathrm {kin} })} , is then given from Fermi's golden rule as
I ( k x , k y ; E k i n ) ∝ | ⟨ Ψ f ( k x , k y ; E k i n ) | A → ⋅ p → | Ψ i ⟩ | 2 × δ ( E i + Φ + E k i n − ℏ ω ) . {\displaystyle I(k_{x},k_{y};E_{\mathrm {kin} })\propto \left|\langle \Psi _{f}(k_{x},k_{y};E_{\mathrm {kin} })|{\vec {A}}\cdot {\vec {p}}|\Psi _{i}\rangle \right|^{2}\times \delta \left(E_{i}+\Phi +E_{\mathrm {kin} }-\hbar \omega \right).}
Here, k x {\displaystyle k_{x}} and k y {\displaystyle k_{y}} are the components of the emitted electron's wave vector parallel to the surface, which are related to the polar and azimuthal emission angles θ {\displaystyle \theta } and ϕ {\displaystyle \phi } defined in the figure as follows,
k x = k sin θ cos ϕ {\displaystyle k_{x}=k\sin \theta \cos \phi }
k y = k sin θ sin ϕ {\displaystyle k_{y}=k\sin \theta \sin \phi }
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