We revisit the holon-doublon binding problem in two-dimensional (2D) photoexcited Mott insulators. Low-energy photoexcited states in Mott insulators are described as a pair state of a doublon and a holon. The most basic question is whether its bound state is formed in the lowest-energy state, and negative and positive responses have been discussed in the past. In this study we begin with the 2D Hubbard model, and transform it into the first effective model, which is based on the
t/U expansion, with
U and
t being the Hubbard
U and the electron hopping energy, respectively. We find that quantitative reliability is assured for $U/t\ensuremath{\gtrsim}10$. Furthermore, we transform it into a second effective model that selects essential states in the low-energy region. In both effective models we distinguish two magnetic terms, namely, the spin-exchange interaction and the three-site transfer, and parametrize the two terms with the parameters
Jex and
J3site. By changing the parameters apart from the restriction given by the Hubbard model, any positive
Jex value with
J3site=0 yields a finite amount of binding, whereas a finite value of
J3site suppresses the binding significantly, still leaving the Hubbard case of
U=10t in the vicinity of the bound-unbound boundary.
We study the evolution of metals from Mott insulators in the carrier-doped 2D Hubbard model using a cluster extension of the dynamical mean-field theory. While the conventional metal is simply characterized by the Fermi surface (pole of the Green function G), interference of the zero surfaces of G with the pole surfaces becomes crucial in the doped Mott insulators. Mutually interfering pole and zero surfaces are dramatically transferred over the Mott gap, when lightly doped holes synergetically loosen the doublon-holon binding. The heart of the Mott physics such as the pseudogap, hole pockets, Fermi arcs, in-gap states, Lifshitz transitions, and non-Fermi liquids appears as natural consequences of this global interference in the frequency space.