^{1}, De Liu

^{1,a)}, Hongmei Zhang

^{2}and Xiaojun Kong

^{1}

### Abstract

The transport properties and shot noise in Thue-Morse (TM) sequence graphene superlattice are investigated using transfer matrix methods. The results indicate perfect transport with *T* = 1 is always obtained at normal incidence when incident electrons tunnel through different barrier widths and heights. The zero- -gap and other Bragg gap exhibit different behavior as the barrier width or incident angle increases. Furthermore, the changing of the structure parameters and generation of the TM sequence has a great effect on transmission coefficient, conductance, and Fano factor. It is shown that the Fano factor has a maximum close to 1/3 in the vicinity of Dirac point, which result in robust electronic transport properties.

This work was supported by the National Natural Science Foundation of China (Grant No. 10974043), the Natural Science Foundation of Hebei Province (Grant No. A2012205019), Hebei University of Science and Technology Foundation (Grant No. XL200825), and the Doctoral Foundation of Hebei Normal University (Grant No. L2009B02).

I. INTRODUCTION

II. MODEL AND FORMULAS

III. NUMERICAL RESULTS AND DISCUSSIONS

IV. CONCLUSIONS

### Key Topics

- Dirac equation
- 21.0
- Graphene
- 17.0
- Transmission coefficient
- 11.0
- Tunneling
- 9.0
- Lattice constants
- 8.0

## Figures

The schematic potential-energy profile through a TM sequence monolayer GSL.

The schematic potential-energy profile through a TM sequence monolayer GSL.

The transmission coefficient as a function of the incident angle for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{2}= 15 nm, and

*E*= 15 meV.

The transmission coefficient as a function of the incident angle for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{2}= 15 nm, and

*E*= 15 meV.

The transmission coefficient as a function of the incident angle for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *V _{A} * = 40 meV, 50 meV, and 60 meV, respectively. The relevant parameters are

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{1}= 15 nm,

*D*

_{2}= 15 nm, and

*E*= 15 meV.

The transmission coefficient as a function of the incident angle for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *V _{A} * = 40 meV, 50 meV, and 60 meV, respectively. The relevant parameters are

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{1}= 15 nm,

*D*

_{2}= 15 nm, and

*E*= 15 meV.

The transmission coefficient as a function of the incident energy for the TM sequence (N = 5) GSL with different barrier widths (a) and incident angles (b). In (a), , the solid, short dashed, and dotted lines correspond to the TM sequence GSL with *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. In (b), *D* _{1} = 20 nm, the solid, short dashed, and dotted lines correspond to , , and , respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm, and

*D*

_{2}= 15 nm.

The transmission coefficient as a function of the incident energy for the TM sequence (N = 5) GSL with different barrier widths (a) and incident angles (b). In (a), , the solid, short dashed, and dotted lines correspond to the TM sequence GSL with *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. In (b), *D* _{1} = 20 nm, the solid, short dashed, and dotted lines correspond to , , and , respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm, and

*D*

_{2}= 15 nm.

The conductance as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm, and

*D*

_{2}= 15 nm.

The conductance as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm, and

*D*

_{2}= 15 nm.

The conductance as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *V _{A} * = 40 meV, 50 meV, and 60 meV, respectively. The relevant parameters are

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{1}= 15 nm, and

*D*

_{2}= 15 nm.

The conductance as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *V _{A} * = 40 meV, 50 meV, and 60 meV, respectively. The relevant parameters are

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{1}= 15 nm, and

*D*

_{2}= 15 nm.

The Fano factor as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm, and

*D*

_{2}= 15 nm.

The Fano factor as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *D* _{1} = 15 nm, 20 nm, and 25 nm, respectively. The relevant parameters are *V _{A} * =

*V*= 50 meV,

_{B}*L*= 15 nm, and

*D*

_{2}= 15 nm.

The Fano factor as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *V _{A} * = 40 meV, 50 meV, and 60 meV, respectively. The relevant parameters are

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{1}= 15 nm, and

*D*

_{2}= 15 nm.

The Fano factor as a function of the Fermi energy for the TM sequence GSL at growth generations N = 2 (a), N = 3 (b), N = 4 (c), and N = 5 (d), respectively. The solid, short dashed, and dotted lines correspond to *V _{A} * = 40 meV, 50 meV, and 60 meV, respectively. The relevant parameters are

*V*= 50 meV,

_{B}*L*= 15 nm,

*D*

_{1}= 15 nm, and

*D*

_{2}= 15 nm.

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