Formation of Subgap States in Carbon Nanotubes Due to a Local Transverse Electric Field

We introduce two simple models to study the effect of a spatially localized transverse electric field on the lowenergy electronic structure of semiconducting carbon nanotubes. Starting from the Dirac Hamiltonian for the low-energy states of a carbon nanotube, we use scattering theory to show that an arbitrarily weak field leads to the formation of localized electronic states inside the free nanotube band gap. We study the binding energy of these subgap states as a function of the range and strength of the electrostatic potential. When the range of the potential is held constant and the strength is varied, the binding energy shows crossover behavior: the states lie close to the free nanotube band edge until the potential exceeds a threshold value, after which the binding energy increases rapidly. When the potential strength is held constant and the range is varied, we find resonant behavior: the binding energy passes through a maximum as the range of the potential is increased. Large electric fields confined to a small region of the nanotube are required to create localized states far from the band edge. Disciplines Physical Sciences and Mathematics | Physics Comments Suggested Citation: Kinder, J.M. and Mele, E.J. (2007). Formation of subgap states in carbon nanotubes due to a local transverse electric field. Physical Review B. 76, 195438. © 2007 The American Physical Society http://dx.doi.org/10.1103/PhysRevB.76.195438 This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/127 Formation of subgap states in carbon nanotubes due to a local transverse electric field Jesse M. Kinder* and E. J. Mele Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA Received 24 February 2006; revised manuscript received 27 June 2007; published 27 November 2007 We introduce two simple models to study the effect of a spatially localized transverse electric field on the low-energy electronic structure of semiconducting carbon nanotubes. Starting from the Dirac Hamiltonian for the low-energy states of a carbon nanotube, we use scattering theory to show that an arbitrarily weak field leads to the formation of localized electronic states inside the free nanotube band gap. We study the binding energy of these subgap states as a function of the range and strength of the electrostatic potential. When the range of the potential is held constant and the strength is varied, the binding energy shows crossover behavior: the states lie close to the free nanotube band edge until the potential exceeds a threshold value, after which the binding energy increases rapidly. When the potential strength is held constant and the range is varied, we find resonant behavior: the binding energy passes through a maximum as the range of the potential is increased. Large electric fields confined to a small region of the nanotube are required to create localized states far from the