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Chinese Physics Letters

Effect of Impurity on the Doping-Induced in-Gap States in a Mott Insulator

Cheng-Ping He, Shun-Li Yu, Tao Xiang, Jian-Xin Li

Published May 1, 2022• 5 citations
Publisher

Abstract

Motivated by the recent measurements of the spatial distribution of single particle excitation states in a hole-doped Mott insulator, we study the effects of impurity on the in-gap states, induced by the doped holes, in the Hubbard model on the square lattice by the cluster perturbation theory. We find that a repulsive impurity potential can move the in-gap state from the lower Hubbard band towards the upper Hubbard band, providing a good account for the experimental observation. The distribution of the spectral function in the momentum space can be used to discriminate the in-gap state induced by doped holes and that by the impurity. The spatial characters of the in-gap states in the presence of two impurities are also discussed and compared to the experiment.

DOI
10.1088/0256-307x/39/5/057401

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Motivated by the recent measurements of the spatial distribution of single particle excitation states in a hole-doped Mott insulator, we study the effects of impurity on the in-gap states, induced by the doped holes, in the Hubbard model on the square lattice by the cluster perturbation theory. We find that a repulsive impurity potential can move the in-gap state from the lower Hubbard band towards the upper Hubbard band, providing a good account for the experimental observation. The distribution of the spectral function in the momentum space can be used to discriminate the in-gap state induced by doped holes and that by the impurity. The spatial characters of the in-gap states in the presence of two impurities are also discussed and compared to the experiment.
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.
The local density of states near dopants or impurities has recently been probed by scanning tunneling microscopy in both the parent and very lightly doped compounds of the high-Tc{T}_{c}Tc​ cuprate superconductors. We use a slave-rotor representation of the Hubbard model to compute the local density of states on impurities in a Mott insulator. Our calculation accounts for the following key features of the experimental observation: (i) positions and amplitudes of the in-gap spectral weights of a single impurity; (ii) the spectral weight transfer from the upper Hubbard band to the lower Hubbard band; (iii) the difference between the cases of single and multiple impurities. For multiple impurities, our study explains the complete suppression of spectral weight observed at precisely the Fermi energy and links this property to zeros of the underlying bulk Green's function of the Mott insulating phase.
We study the nature of electronic states induced by the non-magnetic impurities in a hole-doped Mott insulator. We further examine the consequences of doping on the transport and spectral properties. By employing exact diagonalizaton + Monte-Carlo simulation based on the many-body computational techniques, which allows for the thermal and spatial fluctuations besides a fine resolution in the momentum-space spectral function, the current investigation unravels the degree of localization of the electronic states induced by the impurity atoms as a function of temperature. The major consequences of doping impurity, which introduces holes in the systems, include the appearance of impurity states just above the Fermi level and only in the vicinity of momenta where the gap opens along the normal state Fermi surface in the insulating state. The electronic state at the impurity site is split because of the antiferromagnetic background. The pseudogap-like behavior of the density of states is weakened as reflected by the enhanced charge fluctuations even away from the impurity site at an elevated temperature. Our study also reflects on the degree of improvement in conductivity as well as particle-hole asymmetry introduced in the momentum-resolved spectral function, which maximizes towards the high-symmetry points like ([Formula: see text].
Since the discovery of half-filled cuprate to be a Mott insulator, the excitation spectra above the chemical potential for the unoccupied states has attracted much research attention. There were many theoretical works using different numerical techniques to study this problem, but many have reached different conclusions. One of the reasons is the lack of very detailed high-resolution experimental results for the theories to be compared with. Recently, the scanning tunneling spectroscopy [P. Cai et al., Nat. Phys. 12, 1047 (2016); C. Ye et al., Nat. Commun. 4, 1365 (2013)] on lightly doped Mott insulator with an antiferromagnetic order found the presence of in-gap states with energy of order half an eV above the chemical potential. The measured spectral properties with doping are not quite consistent with earlier theoretical works. Although the experiment has disorder and localization effect, but for the energy scale we will study here, a model without disorder is sufficed to illustrate the underlying physics. We perform a diagonalization method on top of the variational Monte Carlo calculation to study the evolution of antiferromagnetic Mott state with doped hole concentration in the Hubbard model. Our results found in-gap states that behave similarly with ones reported by STS. These in-gap states acquire a substantial amount of dynamical spectral weight transferred from the upper Hubbard band. The in-gap states move toward chemical potential with increasing spectral weight as doping increases. Our result also provides information about the energy scale of these in-gap states in relation with the Coulomb coupling strength UUU.
Calculations of the single-particle spectral function for the two-band Hubbard model as a function of doping and nearest-neighbor Coulomb repulsion are performed on finite-size clusters. It is shown that for hole doping the effect of the nearest-neighbor Coulomb repulsion leads to the effective pinning of the Fermi energy, and to the creation of new states in the charge-transfer gap. For electron doping, however, the model behaves as a one-band Hubbard model with the Fermi energy moving into the conduction band. The results of this calculation are in qualitative agreement with some of the spectroscopic studies of the electronic structure at the Fermi energy of the high-temperature cuprate superconductors.
In strongly correlated electron systems, the emergence of states in the Mott gap in the single-particle spectrum following the doping of the Mott insulator is a remarkable feature that cannot be explained in a conventional rigid-band picture. Here, based on an analysis of the quantum numbers and the overlaps of relevant states, as well as through a demonstration using the ladder and bilayer $t\text{\ensuremath{-}}J$ models, it is shown that in a continuous Mott transition due to hole doping, the magnetically excited states of the Mott insulator generally emerge in the electron-addition spectrum with the dispersion relation shifted by the Fermi momentum in the momentum region where the lower Hubbard band is not completely filled. This implies that the dispersion relation of a free-electron-like mode in the electron-addition spectrum eventually transforms into essentially the momentum-shifted magnetic dispersion relation of the Mott insulator, while its spectral weight gradually disappears toward the Mott transition. This feature reflects the spin-charge separation of the Mott insulator.