Hidden-fermion representation of self-energy in pseudogap and superconducting states of the two-dimensional Hubbard model

We study the frequency-dependent structure of electronic self-energy in the pseudogap and superconducting states of the two-dimensional Hubbard model. We present the self-energy calculated with the cellular dynamical mean-field theory systematically in the space of temperature, electron density, and interaction strength. We show that the low-frequency part of the self-energy is well represented by a simple equation, which describes the transitions of an electron to and from a hidden-fermionic state. By fitting the numerical data with this simple equation, we determine the parameters characterizing the hidden fermion and discuss its identity. The simple expression of the self-energy offers a way to organize numerical data of these uncomprehended superconducting and pseudogap states, as well as a useful tool to analyze spectroscopic experimental results. The successful description by the simple two-component fermion model supports the idea of "dark" and "bright" fermions emerging from a bare electron as bistable excitations in doped Mott insulators.