Bare electron dispersion from experiment: Self-consistent self-energy analysis of photoemission data

Abstract

Performing an in-depth analysis of the photoemission spectra along the nodal direction of the high temperature superconductor Bi-2212 we have developed a procedure to determine the underlying electronic structure and established a precise relation of the measured quantities to the real and imaginary parts of the self-energy of electronic excitations. The self-consistency of the procedure with respect to the Kramers-Kronig transformation allows us to draw conclusions on the applicability of the spectral function analysis and on the existence of well defined quasiparticles along the nodal direction even for the underdoped Bi-2212 in the pseudogap state.PACS numbers: 74.25.Jb, 74.72.Hs, 71.18.+y With modern angle-resolved photoemission spectroscopy (ARPES) [1,2] one gets a direct snapshot of the density of low energy electronic excited states in the momentum-energy space of 2D solids [3,4,5,6]. All the interactions of the electrons which are responsible for the unusual normal and superconducting properties of cuprates are encapsulated in such pictures, but are still hard to decipher. One way to take into account these interactions is to consider electronic excitations as quasiparticles which, compared to the non-interacting electrons, are characterized by an additional complex selfenergy [7]. Extraction of the self-energy from experiment is thus of great importance to check the validity of the quasiparticle concept and understand the nature of interactions involved, but appears to be problematic since the underlying band structure of the bare electrons is a priori unknown.One can evaluate the interaction parameters taking the bare band dispersion from band structure calculations [4], however this unavoidably increases the uncertainty of any conclusions on the strength and nature of the interactions involved. A direct determination of the bare band structure from experiment would be much more attractive in this sense. Previously, the bare band dispersion has been assigned to the high binding energy part of the experimental dispersion [8]. In Refs. 9, 10 we have discussed that the bare Fermi velocity estimated from the nodal ARPES spectra using the Kramers-Kronig (KK) transformation is in reasonable agreement with band structure calculations [11,12] and with an analysis of the anisotropic plasmon dispersion [13], although it has been pointed out that in order to quantify interaction parameters such as coupling strength [14] or self-energy [15] a precise and reliable approach of bare band determination is needed.In this Letter we introduce an approach to directly extract the bare band dispersion and the self-energy functions from ARPES spectra. We show that the approach is self-consistent within the highest experimental accuracy available today, and, applying the procedure to the spectra from the underdoped Bi-2212, we demonstrate the validity of the quasiparticle concept even in the underdoped regime and in the pseudogap state. The detailed description of the procedure as well as its application to other samples o...

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