### Abstract

We calculated the minimal longitudinal conductivity in prefect single-layer and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig in Phys. Rev. B 50, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain σ xx min = (Jπ/2) e2 /h while from the other formula used in the above-mentioned work we find σ̄ xx min = (4J/π) e2 /h, where J=1 for single-layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our two results are in the same order of magnitude as that of experiments and for the single-layer case one of our results agrees with many earlier theoretical predictions. However, for bilayer graphene only two studies are known with predictions for the minimal conductivity different from our calculated values. Similarly to the single-layer case, the physical origin of the minimal conductivity in bilayer graphene is also rooted back to the intrinsic disorder induced by the Zitterbewegung which is related to the trembling motion of the electron.

Original language | English |
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Article number | 033405 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 75 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

**Minimal longitudinal dc conductivity of perfect bilayer graphene.** / Cserti, J.

Research output: Article

}

TY - JOUR

T1 - Minimal longitudinal dc conductivity of perfect bilayer graphene

AU - Cserti, J.

PY - 2007

Y1 - 2007

N2 - We calculated the minimal longitudinal conductivity in prefect single-layer and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig in Phys. Rev. B 50, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain σ xx min = (Jπ/2) e2 /h while from the other formula used in the above-mentioned work we find σ̄ xx min = (4J/π) e2 /h, where J=1 for single-layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our two results are in the same order of magnitude as that of experiments and for the single-layer case one of our results agrees with many earlier theoretical predictions. However, for bilayer graphene only two studies are known with predictions for the minimal conductivity different from our calculated values. Similarly to the single-layer case, the physical origin of the minimal conductivity in bilayer graphene is also rooted back to the intrinsic disorder induced by the Zitterbewegung which is related to the trembling motion of the electron.

AB - We calculated the minimal longitudinal conductivity in prefect single-layer and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig in Phys. Rev. B 50, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain σ xx min = (Jπ/2) e2 /h while from the other formula used in the above-mentioned work we find σ̄ xx min = (4J/π) e2 /h, where J=1 for single-layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our two results are in the same order of magnitude as that of experiments and for the single-layer case one of our results agrees with many earlier theoretical predictions. However, for bilayer graphene only two studies are known with predictions for the minimal conductivity different from our calculated values. Similarly to the single-layer case, the physical origin of the minimal conductivity in bilayer graphene is also rooted back to the intrinsic disorder induced by the Zitterbewegung which is related to the trembling motion of the electron.

UR - http://www.scopus.com/inward/record.url?scp=33846386851&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846386851&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.75.033405

DO - 10.1103/PhysRevB.75.033405

M3 - Article

AN - SCOPUS:33846386851

VL - 75

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 3

M1 - 033405

ER -