^{1,a)}and Hiroshi Mizuta

^{1,2}

### Abstract

We investigate extraordinary magnetoresistance (EMR) of inhomogeneous graphene-metal hybrids using finite element modelling. Inhomogeneous graphene is a binary system made of electron and hole puddles. Two geometries of the embedded metallic structure were considered: circular and fishbone geometries. We found that the breaking of graphene into charge puddles weakens the magnetoresistance of the hybrid system compared to a homogeneous graphene-metal system. For a fixed value of the magnetic field, the magnetoresistance increases with decreasing area fraction occupied by electrons puddles. Fishbone geometry showed an enhanced magnetoresistance compared to circular geometry. The EMR is also investigated as a function of the contact resistance for the fishbone geometry where it was found that a minimal contact resistance is essential to obtain enhanced EMR in graphene-metal hybrid devices.

I. INTRODUCTION

II. EFFECTIVE CONDUCTIVITY IN INHOMOGENEOUS GRAPHENE

III. FINITE ELEMENT CALCULATIONS

IV. RESULTS AND DISCUSSION

A. Circular geometry

B. Fishbone geometry

V. EFFECT OF CONTACT RESISTANCE

VI. CONCLUSION

### Key Topics

- Magnetoresistance
- 44.0
- Graphene
- 43.0
- Magnetic fields
- 33.0
- Contact resistance
- 12.0
- Tensor methods
- 9.0

## Figures

Plot of the calculated as a function of the area fraction *f _{n} * for different values of the magnetic field, i.e., B = 0.5 T, 1 T, 1.5 T, and 2 T.

Plot of the calculated as a function of the area fraction *f _{n} * for different values of the magnetic field, i.e., B = 0.5 T, 1 T, 1.5 T, and 2 T.

Plot of the calculated as a function of the area fraction *f _{n} * for different values of the magnetic field, i.e., B = 0.5 T, 1 T, 1.5 T, and 2 T.

*f _{n} * for different values of the magnetic field, i.e., B = 0.5 T, 1 T, 1.5 T, and 2 T.

Calculated as a function of the magnetic field for different values of the area fraction , 0.5, and 0.7.

Calculated as a function of the magnetic field for different values of the area fraction , 0.5, and 0.7.

Calculated as a function of the magnetic field for different values of the area fraction , 0.5, and 0.7.

Plot of the magnetoresistance versus magnetic field for homogenous and non-homogenous graphene, for three values of the fill factor , 0.65, and 0.8. For non-homogeneous graphene, the value of was used. The structure is shown on the inset where a circular gold shunt is embedded in a circular sheet of graphene. Simulations were performed using a Van der Pauw geometry as indicated.

Plot of the magnetoresistance versus magnetic field for homogenous and non-homogenous graphene, for three values of the fill factor , 0.65, and 0.8. For non-homogeneous graphene, the value of was used. The structure is shown on the inset where a circular gold shunt is embedded in a circular sheet of graphene. Simulations were performed using a Van der Pauw geometry as indicated.

Magnetoresistance as a function of the applied magnetic field *B*, of a shunted graphene structure, for three values of the area fraction of electron puddles. The inset shows the Hall coefficient as a function of the puddles area fraction for *B* = 0.5 T.

Magnetoresistance as a function of the applied magnetic field *B*, of a shunted graphene structure, for three values of the area fraction of electron puddles. The inset shows the Hall coefficient as a function of the puddles area fraction for *B* = 0.5 T.

Dependence of the magnetoresistance on the area fraction *f _{n} * for a shunted circular graphene structure, for several values of the fill factor and at a magnetic field value of

*B*= 5 T.

Dependence of the magnetoresistance on the area fraction *f _{n} * for a shunted circular graphene structure, for several values of the fill factor and at a magnetic field value of

*B*= 5 T.

Dependence of the magnetoresistance on the magnetic field for several values of the area fraction of electron puddles, i.e., 0.15, 0.25, 0.35, and 0.45. The inset shows the metallic fishbone structure embedded in a circular graphene sheet, used in the simulation.

Dependence of the magnetoresistance on the magnetic field for several values of the area fraction of electron puddles, i.e., 0.15, 0.25, 0.35, and 0.45. The inset shows the metallic fishbone structure embedded in a circular graphene sheet, used in the simulation.

Dependence of the magnetoresistance on the magnetic field for several values of the ratio *n*/*p*, i.e., 1, 1.2, 1.4, 1.6, and 2. The inset shows the Hall resistivity for the same values of *n*/*p*.

Dependence of the magnetoresistance on the magnetic field for several values of the ratio *n*/*p*, i.e., 1, 1.2, 1.4, 1.6, and 2. The inset shows the Hall resistivity for the same values of *n*/*p*.

Dependence of the magnetoresistance on the magnetic field for several values of the contact conductivity , 3 × 10^{−4}, 6 × 10^{−4}, 1 × 10^{−3}, 1 × 10^{−2}, and 1 × 10^{−1} ( ). The simulation was performed for the fishbone geometry.

Dependence of the magnetoresistance on the magnetic field for several values of the contact conductivity , 3 × 10^{−4}, 6 × 10^{−4}, 1 × 10^{−3}, 1 × 10^{−2}, and 1 × 10^{−1} ( ). The simulation was performed for the fishbone geometry.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content