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Updated: May 30, 2026

Precision Milling of Carbon Nanotube Forests Using Low Pressure Scanning Electron Microscopy

Precision Milling of Carbon Nanotube Forests Using Low Pressure Scanning Electron Microscopy

Published on: February 5, 2017

Bloch oscillations in carbon nanotubes.

Esther Jódar¹, Antonio Pérez-Garrido, Fernando Rojas

¹Departamento Física Aplicada, Antiguo Hospital de Marina Campus Muralla del Mar, UPCT, Cartagena 30202 Murcia, Spain.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|August 10, 2011

Summary

Electrons in carbon nanotubes exhibit Bloch oscillations under electric fields. Numerical simulations reveal frequencies proportional to the field strength, consistent with theoretical predictions for atomic chains.

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Area of Science:

Condensed Matter Physics
Materials Science
Nanotechnology

Background:

Bloch oscillations are a quantum mechanical phenomenon observed in electrons within periodic potentials subjected to external forces.
Carbon nanotubes (CNTs) possess unique one-dimensional structures with potential for novel electronic behaviors.

Purpose of the Study:

To numerically investigate the occurrence and characteristics of Bloch oscillations in electrons within various carbon nanotube structures.
To determine the relationship between applied electric field strength and Bloch oscillation frequency in CNTs.

Main Methods:

Numerical simulations were employed to model electron behavior in different types of carbon nanotubes.
The quadratic displacement of electrons was calculated as a function of applied electric field strength along the nanotube axis.
Observed oscillation frequencies were analyzed and compared to theoretical predictions.

Main Results:

Electrons in carbon nanotubes demonstrate Bloch oscillations when subjected to a constant electric field parallel to the nanotube axis.
The Bloch frequency is directly proportional to the applied electric field strength.
Due to the double periodicity of CNT geometry, two distinct oscillation frequencies emerge, one being twice the other.
These observed frequencies align with theoretical predictions for linear atomic chains, considering the specific periodicities of CNTs.

Conclusions:

Carbon nanotubes exhibit Bloch oscillations, confirming their potential as systems for studying this quantum phenomenon.
The observed double frequencies are a direct consequence of the unique geometric periodicity of carbon nanotubes.
The findings validate theoretical models of Bloch oscillations in one-dimensional periodic structures and highlight the relevance of CNTs in this context.