# Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots

## Abstract

Koopmans’ theorem implies that the Hartree-Fock quasiparticle gap in a closed-shell system is equal to its single-particle energy gap. In this work, the theorem is generalized to optical transitions in the Hubbard model of graphene nanodots. Based on systematic configuration interaction calculations, it is proposed that the optical gap of a closed-shell graphene system within the Hubbard model is equal to its tight-binding single-particle energy gap in the absence of electron correlation. In these systems, the quasiparticle energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interaction, and thus, both become small when only on-site Hubbard interactions are present. Moreover, the contributions of the quasiparticle and excitonic effects to the optical gap are revealed to nearly cancel each other, which results in an unexpected overlap of the optical and single-particle gaps of the graphene systems.

- Authors:

- State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai (China)
- (China)
- (Canada)
- Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167 (China)

- Publication Date:

- OSTI Identifier:
- 22415816

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 77 NANOSCIENCE AND NANOTECHNOLOGY; BINDING ENERGY; CONFIGURATION INTERACTION; COULOMB FIELD; ELECTRON CORRELATION; ENERGY GAP; GRAPHENE; HARTREE-FOCK METHOD; HUBBARD MODEL; QUANTUM DOTS

### Citation Formats

```
Sheng, Weidong, E-mail: shengw@fudan.edu.cn, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Luo, Kaikai, and Zhou, Aiping.
```*Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots*. United States: N. p., 2015.
Web. doi:10.1063/1.4905789.

```
Sheng, Weidong, E-mail: shengw@fudan.edu.cn, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Luo, Kaikai, & Zhou, Aiping.
```*Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots*. United States. doi:10.1063/1.4905789.

```
Sheng, Weidong, E-mail: shengw@fudan.edu.cn, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5, Luo, Kaikai, and Zhou, Aiping. Wed .
"Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots". United States.
doi:10.1063/1.4905789.
```

```
@article{osti_22415816,
```

title = {Communication: Generalization of Koopmans’ theorem to optical transitions in the Hubbard model of graphene nanodots},

author = {Sheng, Weidong, E-mail: shengw@fudan.edu.cn and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 and Department of Physics, University of Ottawa, Ottawa, Ontario K1N 6N5 and Luo, Kaikai and Zhou, Aiping},

abstractNote = {Koopmans’ theorem implies that the Hartree-Fock quasiparticle gap in a closed-shell system is equal to its single-particle energy gap. In this work, the theorem is generalized to optical transitions in the Hubbard model of graphene nanodots. Based on systematic configuration interaction calculations, it is proposed that the optical gap of a closed-shell graphene system within the Hubbard model is equal to its tight-binding single-particle energy gap in the absence of electron correlation. In these systems, the quasiparticle energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interaction, and thus, both become small when only on-site Hubbard interactions are present. Moreover, the contributions of the quasiparticle and excitonic effects to the optical gap are revealed to nearly cancel each other, which results in an unexpected overlap of the optical and single-particle gaps of the graphene systems.},

doi = {10.1063/1.4905789},

journal = {Journal of Chemical Physics},

number = 2,

volume = 142,

place = {United States},

year = {Wed Jan 14 00:00:00 EST 2015},

month = {Wed Jan 14 00:00:00 EST 2015}

}