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Related Experiment Video

Updated: May 14, 2026

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

Published on: July 24, 2015

Impurity state and variable range hopping conduction in graphene.

Sang-Zi Liang¹, Jorge O Sofo

¹Department of Physics and Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.

Physical Review Letters

|February 2, 2013

Summary

This summary is machine-generated.

Variable range hopping theory does not apply to covalently attached impurities in graphene. Impurity state wave function decay follows a power law, leading to conductivity dependent on temperature, aligning with experimental data.

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Mechanics

Background:

Variable range hopping theory describes electron transport in disordered materials.
Exponential localization of impurity states is a key assumption in this theory.
Graphene with covalently attached impurities presents a different scenario.

Purpose of the Study:

To analyze impurity state localization in graphene with covalently attached impurities.
To determine the applicability of variable range hopping theory in this system.
To investigate the temperature dependence of conductivity.

Main Methods:

Nearest-neighbor, tight-binding model for adatom-graphene system.
Green's function perturbation methods.
Analysis of impurity state wave function decay.

Main Results:

Impurity state wave function amplitude decays as a power law.
Exponents of decay depend on sublattice, direction, and impurity species.
Conductivity exhibits a power-law dependence on temperature.

Conclusions:

Variable range hopping theory, as formulated for exponential localization, is not directly applicable.
The power-law decay of wave functions leads to a distinct temperature dependence of conductivity.
The findings are consistent with experimental observations in graphene systems.