Localized in-gap state in a single-electron doped Mott insulator

Abstract

Motivated by the recent atomic-scale scanning tunneling microscope (STM) observation for a spatially localized in-gap state in an electron doped Mott insulator, we evaluate the local electronic state of the Hubbard model on the square lattice using the cluster perturbation theory. An in-gap state is found to exist below the upper Hubbard band around the dopant lattice site, which is consistent with the STM measurements. The emergence of this local in-gap state is accompanied with a rapid reduction of the double occupancy of electrons. A similar in-gap state is also found to exist on the triangular lattice. These results suggest that the in-gap state is an inherent feature of Mott insulators independent of the lattice structure.PACS numbers: 74.72. Cj, 71.27.+a, 71.10.Fd The mechanism underlying high-T c superconductivity in cuprates remains one of the most challenging and fundamental problems in condensed matter physics [1]. All cuprate superconductors have a layered structure made up of one or more CuO 2 planes. Their parent compounds have one unpaired electron per Cu unit cell, which constitutes a Mott insulating ground state with an antiferromagnetic (AF) long range order [2]. By doping holes or electrons to CuO 2 planes, the AF order is suppressed and a superconducting phase emerges above a critical doping concentration. The evolution from the AF Mott insulating phase to the superconducting phase induced by doping is highly non-trivial [1]. A thorough investigation on the charge and spin dynamics of doped Mott insulators is believed to be the key for the understanding of extraordinary phenomena observed in high-T c superconductors, such as the pseudogap effect.The dynamics of a single hole in an antiferromagnetic Mott insulator has been extensively studied using the self-consistent Born approximation [3][4][5][6][7][8], finite-size exact diagonalization [9][10][11] and quantum Monte Carlo [12,13] methods, based on the t−J-type model. It was predicted that the single-particle spectrum consists of a sharp coherent peak, corresponding to a quasiparticle excitation, and an incoherent background. But this sharp coherent peak was not observed in the spectrum of electrons measured by angle-resolved photoemission spectroscopy on Sr 2 CuO 2 Cl 2 [14] and Ca 2 CuO 2 Cl 2 [15,16]. To reconcile the difference between theory and experiments, two kinds of scenarios were proposed to explain why the sharp quasipartilcle peak is absent. One is to attribute this absence of sharp peak as an extrinsic effect induced by electron-phonon coupling [17]. The other regards this as an intrinsic effect resulting from a selflocalization of doped holes in an AF background which smears out the coherent peak. From the self-consistent mean-field approximation (SCMFA), indeed it was found that the charge excitations are self-localized in a staggered AF ordered state [18][19][20]. This kind of charge self-localization was also predicted to exist in a singlehole Hubbard model by considering the non-perturbative phase string effect [21] or i...

Spectral evolution with doping of an antiferromagnetic Mott state

“…There were also several results reported by using the cluster perturbation theory (CPT). For the electrondoped case [14], an in-gap state was found at the bottom of UHB, which is in agreement with the in-gap states seen by STS on Ca 2 CuO 2 Cl 2 [2] near an impurity. For the hole-doped case [15][16][17][18][19], there were low-energy in-gap states with energy less than 0.2U .…”

Charge dynamics of the antiferromagnetically ordered Mott insulator

“…We begin the discussion of our results for the Mott-insulating state of the square-lattice Hubbard model by considering the averaged double-occupancy parameter, D. For the half-filled system, the average number of doubly occupied sites is equal to the number of empty ones, and is given by The dependence of D on U at zero temperature is shown in figure 2, where our results are compared with calculations by quantum Monte Carlo [18], variational Monte Carlo [60], cluster perturbation theory [86] and DMRG [50]. At the qualitative level, all results lie in the same general range of values and, with the exception of one VMC approach, show a broadly similar functional form.…”

“…, one obtains [86], quantum Monte Carlo (QMC) for a 4×4 lattice at inverse temperature b = 16 (green, down-pointing triangles) [18], variational Monte Carlo with different trial wave functions y ñ (| pow (VMCPow, maroon diamonds) and y ñ | B (VMCB, magenta squares) in the notation of [60]) and DMRG (solid, black line) with extrapolation to the thermodynamic limit [50].…”

Quantum cluster approach to the topological invariants in correlated Chern insulators

“…Yet it does not affect the density of states [25]. CPT has also been successfully applied to the studies of the single-particle spectral functions [26,30,33,34,36,39]. CPT is exact in the non-interacting limit but does not allow for spontaneous symmetry breaking phases.…”

“…Thus, the success of the topological Hamiltonian relies on a credible computation of the interacting single particle Green's functions. In recent years a variety of quantum many-body algorithms gathering under the name of quantum cluster approaches [24,25] have been developed to calculate such single particle Green's functions of a broad range of strongly correlated fermionic systems [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] and bosonic systems [41][42][43]. They share the basic idea of solving a reference system composed of isolated finite-sized clusters that are sometimes embedded in a uncorrelated bath media.…”