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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 1:28 |
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Conference: Bucharest University Faculty of Physics 2015 Meeting
Section: Solid State Physics and Materials Science
Title:
p/n/p Graphene Nanoribbons: Spectral Properties and Quantum Charge Transport
Authors:
Tudor E. PAHOMI
Affiliation:
Faculty of Physics, University of Bucharest, RO-077125, Măgurele - Bucharest, Romania, EU
E-mail
tudor.pahomi@gmail.com
Keywords:
Zigzag Nanoribbon, Surface State, Energy Spectrum, Green's Function, Landau Level
Abstract:
The energy spectra of graphene zigzag nanoribbons are studied theoretically within a tight-binding approximation in the second quantization formalism (considering only the hopping to the nearest neighbors) after a brief presentation of the electronic properties of infinite graphene and the identification of characteristic massless Dirac-like quasi-particles. Starting with bare nanoribbons, either an external perpendicular magnetic field is switched on or a gate voltage is applied such that a p/n/p structure is obtained, and afterwards the spectra are discussed with simultaneous magnetic field and gate voltage. The topological zero-energy modes localized on the zigzag terminations of the nanoribbons are compared to the “interface” states, found at the p/n or n/p interfaces of the p/n/p structure. The magnetic field is introduced by a Peierls substitution of the hopping matrix elements and the gate voltage induces on-site energies. Green's functions technique is used to compute the local and total densities of states in the system, which are congruent with the spectra discussed. Several inherited features from the infinite graphene are emphasized, like the two-fold valley-degeneracy, specific for graphene (resulting in the characteristic room-temperature relativistic quantum Hall effect), or the formation of bulk Landau levels in magnetic field. The simulations are entirely numerical, but the results are supported by matching portions of the spectra with analytical expressions valid for infinite graphene, especially the position of Landau plateaus. Finally, the quantum transmittances between the two zigzag edges are computed, by finding the Green's function of the nanoribbon Hamiltonian coupled to two semi-infinite metallic wires.
References:
[1] K. S. Novoselov et al. “Electric Field Effect in Atomically Thin Carbon Films”, Science 306.5696 (2004), pp. 666–669.
[2] B. A. Bernevig with T. L. Hughes. Topological Insulators and Topological Superconductors. Princeton University Press, 2013.
[3] L. Brey and H. A. Fertig. “Electronic states of graphene nanoribbons studied with the Dirac equation”, Phys. Rev. B 73.23 (2006), p. 235411.
[4] M. O. Goerbig. “Electronic properties of graphene in a strong magnetic field”, Rev. Mod. Phys. 83.4 (2011), pp. 1193–1243.
[5] M. Zarenia et al. “Snake states in graphene quantum dots in the presence of a p-n junction”, Phys. Rev. B 87.3 (2013), p. 35426.
Acknowledgement:
The author is grateful to Alexandru Aldea, senior researcher at the National Institute for Materials Physics, who supervised the present work. Thanks go also to Bogdan Ostahie, PhD student and research assistant at the same institute, for useful advice and discussions.
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