### Abstract

We demonstrate that the quasi-one-dimensional (1D) current transport, experimentally observed in graphene as measured by a collinear four-point probe in two electrode configurations A and B, can be interpreted using the sensitivity functions of the two electrode configurations (configurations A and B represents different pairs of electrodes chosen for current sources and potential measurements). The measured sheet resistance in a four-point probe measurement is averaged over an area determined by the sensitivity function. For a two-dimensional conductor, the sensitivity functions for electrode configurations A and B are different. But when the current is forced to flow through a percolation network, e.g., graphene with high density of extended defects, the two sensitivity functions become identical. This is equivalent to a four-point measurement on a line resistor, hence quasi-1D transport. The sensitivity analysis presents a formal definition of quasi-1D current transport, which was recently observed experimentally in chemical-vapor-deposition graphene. Our numerical model for calculating sensitivity is verified by comparing the model to analytical calculations based on conformal mapping of a single extended defect.

Original language | English |
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Journal | Physical Review B |

Volume | 90 |

Issue number | 24 |

Pages (from-to) | 245432 |

Number of pages | 5 |

ISSN | 0163-1829 |

DOIs | |

Publication status | Published - 2014 |

### Bibliographical note

©2014 American Physical Society## Cite this

Boll, M., Lotz, M. R., Hansen, O., Wang, F., Kjær, D., Bøggild, P., & Petersen, D. H. (2014). Sensitivity analysis explains quasi-one-dimensional current transport in two-dimensional materials.

*Physical Review B*,*90*(24), 245432. https://doi.org/10.1103/PhysRevB.90.245432