Application of iterative phase-retrieval algorithms to ARPES orbital tomography

Abstract

Electronic wave functions of planar molecules can be reconstructed via inverse Fourier transform of angle-resolved photoelectron spectroscopy (ARPES) data, provided the phase of the electron wave in the detector plane is known. Since the recorded intensity is proportional to the absolute square of the Fourier transform of the initial state wave function, information about the phase distribution is lost in the measurement. It was shown that the phase can be retrieved in some cases by iterative algorithms using a priori information about the object such as its size and symmetry. We suggest a more generalized and robust approach for the reconstruction of molecular orbitals based on state-of-the-art phase-retrieval algorithms currently used in coherent diffraction imaging (CDI). We draw an analogy between the phase problem in molecular orbital imaging by ARPES and of that in optical CDI by performing an optical analogue experiment on micrometer-sized structures. We successfully reconstruct amplitude and phase of both the micrometer-sized objects and a molecular orbital from the optical and photoelectron far-field intensity distributions, respectively, without any prior information about the shape of the objects.

k-space imaging of anisotropic 2D electron gas in GaN/GaAlN high-electron-mobility transistor heterostructures

“…Therefore, the ( K x , K y )-dependent ARPES maps in Fig. 2a–c visualize essentially the 2D Fourier expansion of 30 , 31 .…”

“…Neglecting the experimental geometry and polarization effects, this expression simplifies to the scalar product . For sufficiently high photon energies, approximates a plane wave periodic in the in-plane xy direction and damped in the out-of-plane direction z , and the ARPES intensity appears 30 , 31 as . We will now apply this formalism to the QWS wavefunctions .…”

Photoemission response of 2D electron states

“…of the (final-state damping weighted) z-dependent coefficient A(z) for this K xy in 2D expansion of the |i〉-wavefunction. This property of the ARPES response can in principle be used to reconstruct the wavefunctions of 2D states using iterative algorithms similar to those used in molecular wavefunction reconstruction (Puschnig et al 2009, Weiss et al 2015, Bradshaw & Woodruff 2015, Kliuiev et al 2016. If λ is much larger than the |i〉-wavefunction localization region, a likely situation for sufficiently high hv, the above FT simplifies to…”

Efficient orbital imaging based on ultrafast momentum microscopy and sparsity-driven phase retrieval

“…For sufficiently thin molecules, |ψ(k z )| 2 can be assumed to be unity. This approximation works well for the orbitals of planar aromatic molecules at low binding energy, and 2D orbital imaging has been demonstrated in for example pentacene [1,2,5,19], sexiphenyl [1] and PTCDA [2].…”