We theoretically investigate the properties of multiphoton excited states in strongly correlated one-dimensional (1D) and two-dimensional (2D) electron systems at half filling using the extended Hubbard model. In the 2D case, we find the photoexcited states where two or more than two holons and doublons are strongly bound, and the cluster of bound holons and doublons coexists with the surrounding antiferromagnetic (AF) spin order, for the realistic Coulomb interaction parameters. The holon-doublon cluster (HDC) states have a unique charge aggregation mechanism originating from the spin-spin interaction in the AF spin background as well as from the direct Coulomb interaction. In the 1D case, the HDC states are destabilized by the spin-spin interaction in contrast to the 2D case. These charge aggregation mechanisms are the outcomes of exotic natures of holons and doublons, and the difference in the mechanism between the 1D and 2D cases is due to the difference in the coupling between spin and charge degrees of freedom. We also calculate the light-induced absorption that enables us to experimentally observe the predicted HDC states.
The effective Hamiltonian of the Hubbard model for multiphoton excited states is derived assuming a strong Coulomb repulsion. Diagonalizing the effective Hamiltonian exactly, the lowest energy one-photon excited state is calculated in the two-dimensional Hubbard model at half-filling, and its physical properties are investigated. For
t/U< 0.0165, where t is the magnitude of the transfer integral between the nearest-neighbor sites and U is an on-site Coulomb repulsion energy, ferromagnetic spin order is photogenerated from the antiferromagnetic ground state, and, for
t/U> 0.0166, antiferromagnetic spin order survives one-photon excitation. Photoinjected opposite charges are unbound because of strong electron correlation for
t/U< 0.08, and bound for
t/U> 0.08. The probability that the photoinjected opposite charges are on nearest-neighbor sites is strongly suppressed through all the correlation regions including this charge-bound region. We see a tendency toward spin-charge separation, but the coupling is not small in the one-photon excited state. The local spin structure around the bound positive and negative charges injected by photoexcitation is quite different from that induced by two-hole doping; this result suggests that multiphoton excitation will generate an electronic order which differs from that generated by doping.
We theoretically investigate the light absorption spectrum of two-dimensional (2D) Mott insulators. We employ the numerical diagonalization method to calculate the light absorption spectrum with using the effective Hamiltonian for the extended Hubbard model, which is valid when the on-site Coulomb interaction energy
U is much larger than the nearest-neighbor transfer integral
t and the nearest-neighbor Coulomb interaction energy
V. For
V=0, the absorption spectrum consists of a broad band with a width of about
16t and a sharp central peak, and the energy eigenstates contributing to the absorption spectrum do not have the antiferromagnetic (AF) spin order, when
U is sufficiently larger than
t. These features result from the spin-charge interplay inherent in the very strong correlation region where charge transfer term is dominant. With decreasing
U∕t, the peak structure in absorption spectrum becomes unclear and some low energy eigenstates have the AF spin order, as a result of the spin-spin interaction term. For large
V∕t, the dominant peak arises in the lower energy region of the spectrum. A large number of holon-doublon bound states, which have nearly the same charge but different spin structures, are responsible for this peak, in contrast to the conventional exciton state. This is also in contrast to the charge bound states in one-dimensional (1D) Mott insulators, where a single energy eigenstate dominates the optical transition moment as a result of the spin-charge separation. The essentially different absorption spectra between the 1D and 2D Mott insulators originate from the difference in the coupling between spin and charge degrees of freedom.
We theoretically investigate the dynamics of the photoexcited state in the strongly correlated low-dimensional electron systems. In the two-dimensional case, the ultrafast relaxation originating from the transfer of photogenerated charges in the antiferromagnetic background is followed by the slower one originating from the spin structure rearrangement with the new charge distributions. This clearly shows the difference in the relaxation between charge and spin degrees of freedom. In the one-dimensional case, spin-charge separation holds and the mechanical coherence is preserved.
We theoretically investigate the dynamics of photoexcited states in one-dimensional Mott insulators. We adopt the Pariser–Parr–Pople model, and numerically calculate the time development of the nonequilibrium state excited by a light pulse. In the weaker light excitation case where the maximum photoexcitation density is below about 18%, the charge carriers in the photoexcited states are holons and doublons, and the geminate recombination of bound doublon–holon pairs, namely, the Auger recombination process dominates the decay of the photogenerated holons and doublons with the realistic Coulomb parameters. In the stronger light excitation case where the density is above the value, the charge carriers of the photoexcited states cannot be described by holons and doublons. As a result, the Auger recombination process of doublon–holon pairs is not the main decay route of the photogenerated charges. Furthermore, the spin and the charge degrees of freedom are coupled, and spin relaxation occurs in the photoexcited states. As the density of the photogenerated charge carriers becomes larger, the decay time decreases. This tendency is consistent with experiments.
We theoretically investigate the properties of multiphoton excited states in strongly correlated two-dimensional electron systems. The effective Hamiltonian of the Hubbard model for the multiphoton excited states is derived assuming strong Coulomb repulsion. Diagonalizing the effective Hamiltonian exactly, the lowest energy state in two-photon excited manifold is calculated in the 20 site two-dimensional square lattice at half filling. Analysis of correlation functions suggests that the antiferromagnetic spin order characteristic of the half filled ground state is destroyed by two-photon excitation, and two different d-wave superconducting states and a spiral spin state are photogenerated.
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.