https://doi.org/10.1140/epjp/i2018-11965-4
Regular Article
Fractional conductivity in 2D and 3D crystals
1
B.M. Birla Science Centre, Adarsh Nagar, 500063, Hyderabad, India
2
Department of Physics and Astronomy, University of Western Ontario, N6A3K7, London, Canada
* e-mail: birlasc@gmail.com
Received:
25
July
2017
Accepted:
1
March
2018
Published online:
12
April
2018
In this work, we show that the phenomenon of fractional quantum Hall effect can be obtained for 2D and 3D crystal structures, using the noncommutative nature of spacetime and the Lambert W function. This fractional conductivity has been shown to be a consequence of the noncommutative geometry underlying the structure of graphene. Also, it has been shown, for graphene, that in the 3D case the conductivity is extremely small and depends on the self-energy that arises due to random fluctuations or zitterbewegung.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
