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### Abstract

The tight-binding method is employed to investigate the single-electron electronic structure of triangular graphene quantum dots subject to non-uniform electric fields. The specially designed non-uniform electric fields can provide the equal or opposite electrostatic potentials for all edge carbon atoms. The low-energy eigenstates do not vary significantly with the non-uniform electric fields, which allows electrical linear control of the low-energy states. Moreover, the levels of degenerate zero-energy states can be adjusted electrically independently while the levels of nonzero-energy states almost do not vary. This linear control by non-uniform electric fields can be a more efficient way to tune the degenerate zero-energy states. Our findings may be useful for the application of graphene quantum dots to electronic and photovoltaic devices.

This work was supported by the National Natural Science Foundation of China under Grant No. 11274205.

I. INTRODUCTION

II. THE ELECTRIC FIELDS AND THE TIGHT BINDING MODEL

III. RESULTS AND DISCUSSIONS

IV. SUMMARY

### Key Topics

- Quantum dots
- 36.0
- Electric fields
- 35.0
- Graphene
- 26.0
- Electrostatics
- 13.0
- Carbon
- 4.0

## Figures

Two non-uniform electric fields applied to a triangular zigzag graphene quantum dot ( ). (a) Two gates with electrostatic potentials are applied inside and outside the quantum dot. The width of the gate electrode with the negative voltage can be considered as zero. (b) The contour of the electrostatic potential by the electric field shown in (a). (c) Two gates with electrostatic potentials are applied to the left and right of the quantum dot. (d) The contour of the electrostatic potential by the electric field shown in (c). (e) The graphene quantum dot is labelled with the number of the site n.

Two non-uniform electric fields applied to a triangular zigzag graphene quantum dot ( ). (a) Two gates with electrostatic potentials are applied inside and outside the quantum dot. The width of the gate electrode with the negative voltage can be considered as zero. (b) The contour of the electrostatic potential by the electric field shown in (a). (c) Two gates with electrostatic potentials are applied to the left and right of the quantum dot. (d) The contour of the electrostatic potential by the electric field shown in (c). (e) The graphene quantum dot is labelled with the number of the site n.

The low-energy spectra of the quantum dots subjected to the non-uniform electric field as shown in Fig. 1(a) . (a) , (b) , and (c) .

The low-energy spectra of the quantum dots subjected to the non-uniform electric field as shown in Fig. 1(a) . (a) , (b) , and (c) .

The density of the eigenstates of the graphene quantum dot ( ). (a) and (b) correspond, respectively, to the top branch and the central branch of the zero-energy splitting with in Fig. 2 ; (c)–(e) correspond, respectively, to the top branch, the central branch, and the bottom branch of the zero-energy splitting with in Fig. 5 . The value of the corresponding site n is indicated in the top of each peak.

The density of the eigenstates of the graphene quantum dot ( ). (a) and (b) correspond, respectively, to the top branch and the central branch of the zero-energy splitting with in Fig. 2 ; (c)–(e) correspond, respectively, to the top branch, the central branch, and the bottom branch of the zero-energy splitting with in Fig. 5 . The value of the corresponding site n is indicated in the top of each peak.

The density plot of the eigenstates of the graphene quantum dot ( ). (a)–(e) correspond, respectively, to Fig. 3(a) – 3(e) . Here, the size of each shaded circle is roughly proportional to the corresponding density.

The low-energy spectra of the graphene quantum dots subjected to the non-uniform electric field as shown in Fig. 1(c) . (a) , (b) , and (c) .

The low-energy spectra of the graphene quantum dots subjected to the non-uniform electric field as shown in Fig. 1(c) . (a) , (b) , and (c) .

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