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

Weng-Hang Leong, Shun-Li Yu, T. Xiang, and Jian-Xin Li

Phys. Rev. B 90, 245102 – Published 1 December 2014

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.

Received 11 February 2014
Revised 30 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.245102

Authors & Affiliations

Weng-Hang Leong¹, Shun-Li Yu¹, T. Xiang^2,3, and Jian-Xin Li^1,4

¹Department of Physics and National Laboratory of Solid State Microstructure, Nanjing University, Nanjing 210093, China
²Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100190, China
³Collaborative Innovation Center of Quantum Matter, Beijing, China
⁴Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China

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Vol. 90, Iss. 24 — 15 December 2014

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Images

Figure 1
Tilings of the square lattice with (a) 9-site and (b) 13-site clusters. The triangles on the sites schematically illustrate the antiferromagnetic spin configuration.
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Figure 2
(a) A 12-site cluster, as enclosed by the red dashed lines, on the square lattice. The black and gray lines denote the intra- and intercluster hoppings, respectively. (b) and (c) The LDOS within the clusters without electron doping (i.e., at half-filling) and with one electron doping, respectively. The color lines indicate the results on the sites with the same colors in (a). The LDOS on the red sites in the undoped system is also shown with a gray line in (c) for comparison. (d) The difference $Δ$ between the LDOS with and without electron doping on the corresponding color sites. (e) $Δ$ on sites indicated by color dots in the inset with an on-site attractive potential $v = - 0.08$ on the red site. The gray arrows in (d) and (e) indicate the peak positions of the LDOS for the lower and upper Hubbard bands on the red site at half-filling.
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Figure 3
Left panel: Tilings of clusters with different sizes and shapes. (a), (c), (e), and (g) have respectively 8, 9, 12, and 13 sites in each cluster, as enclosed by the red dashed lines, on the square lattice. Right panel: Difference in the LDOS $Δ$ on the corresponding colored sites in the left panel. The gray arrows indicate the peak positions in the LDOS for the lower and upper Hubbard bands without doping.
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Figure 4
(a) Maximal height of the in-gap LDOS as a function of the distance $R$ from the center of the doped cluster. The symbols with different colors represent the results obtained from different cluster tilings (the symbols denoted by 12c represent the results obtained with the 12-site cross cluster). The solid lines are the Gaussian fittings to the results. (b) Schematic diagram illustrating the spectral weight transfer in the localized limit in a single-electron doped three-band model. The green part between the lower (LHB) and upper (UHB) Hubbard bands represents the spectrum from the oxygen charge transfer band.
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Figure 5
(a) Difference in the LDOS $Δ$ on one of the red sites shown in Fig. 2 for different $U$ . The peak positions of the LDOS for the lower and upper Hubbard bands at half-filling are indicated by the gray triangles. (b) $U$ dependence of the double occupation number $D$ (red line with squares) and the local spectral weight of the in-gap state $W_{loc}$ (blue line with triangles). (c) and (d) $W_{loc}$ and $D$ as a function of $U$ for several different cluster sizes and tilings (the symbols denoted by 12c represent the results obtained with the 12-site cross cluster).
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Figure 6
(a) A 13-site cluster, as enclosed by the red dash lines, on the triangular lattice. (b) The difference in the LDOS $Δ$ on the sites with the same colors shown in (a). The peak positions in the LDOS for the lower and upper Hubbard bands at half-filling are indicated by the gray arrows.
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