Doping-induced States in the Single-particle Spectrum Originating from Magnetic Excitation of a Mott Insulator

By infinitesimal doping of a Mott insulator, states are induced in the Mott gap in the single- particle spectrum. To clarify the nature of these states, their relationships with the magnetically excited states of the Mott insulator are investigated. By using the commutator between the Hamiltonian and an electron creation operator of the t-J model, it is shown that the doping- induced states generally have considerable overlaps with the magnetically excited states of the Mott insulator. In addition, the electron-addition spectral weight of spin-1 states from the spin- 1/2 ground state is shown to be three times as large as that of spin-0 states in the t-J model. These results imply that the doping-induced states in the small-doping limit of a continuous Mott transition can generally be interpreted as essentially the magnetically excited states of the Mott insulator which exhibit the momentum-shifted magnetic dispersion relation primarily outside the free-electron Fermi surface in the electron-addition spectrum following the doping. This picture is supported by numerical results for the one- and two-dimensional t-J models.