Analytical study of the energy levels in bilayer graphene quantum dots

D. R. Da Costa; M. Zarenia; Andrey Chaves; G. A. Farias; F. M. Peeters

doi:10.1016/j.carbon.2014.06.078

Analytical study of the energy levels in bilayer graphene quantum dots

D. R. Da Costa, M. Zarenia, Andrey Chaves, G. A. Farias, F. M. Peeters

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

38 Scopus citations

Abstract

Using the four-band continuum model we derive a general expression for the infinite-mass boundary condition in bilayer graphene. Applying this new boundary condition we analytically calculate the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our results for the energy spectrum show an energy gap between the electron and hole states at small magnetic fields. Furthermore the electron (e) and hole (h) energy levels corresponding to the K and K' valleys exhibit the E_K^e(h)(m)=-E_K' ^h(e)(m) symmetry, where m is the angular momentum quantum number.

Original language	English (US)
Pages (from-to)	392-400
Number of pages	9
Journal	Carbon
Volume	78
DOIs	https://doi.org/10.1016/j.carbon.2014.06.078
State	Published - Nov 2014

Bibliographical note

Funding Information:
This work was financially supported by CNPq , under contract NanoBioEstruturas 555183/2005-0, PRONEX/FUNCAP , CAPES Foundation under the process number BEX 7178/13-1, the Flemish Science Foundation (FWO-Vl), the European Science Foundation (ESF) under the EUROCORES program EuroGRAPHENE (project CONGRAN), the Bilateral programme between CNPq and FWO-Vl, and the Brazilian Program Science Without Borders (CsF). We thank M. Ramezani Masir and M. Grujić for helpful comments and discussions.

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title = "Analytical study of the energy levels in bilayer graphene quantum dots",

abstract = "Using the four-band continuum model we derive a general expression for the infinite-mass boundary condition in bilayer graphene. Applying this new boundary condition we analytically calculate the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our results for the energy spectrum show an energy gap between the electron and hole states at small magnetic fields. Furthermore the electron (e) and hole (h) energy levels corresponding to the K and K' valleys exhibit the EKe(h)(m)=-EK' h(e)(m) symmetry, where m is the angular momentum quantum number.",

author = "{Da Costa}, {D. R.} and M. Zarenia and Andrey Chaves and Farias, {G. A.} and Peeters, {F. M.}",

note = "Funding Information: This work was financially supported by CNPq , under contract NanoBioEstruturas 555183/2005-0, PRONEX/FUNCAP , CAPES Foundation under the process number BEX 7178/13-1, the Flemish Science Foundation (FWO-Vl), the European Science Foundation (ESF) under the EUROCORES program EuroGRAPHENE (project CONGRAN), the Bilateral programme between CNPq and FWO-Vl, and the Brazilian Program Science Without Borders (CsF). We thank M. Ramezani Masir and M. Gruji{\'c} for helpful comments and discussions.",

year = "2014",

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doi = "10.1016/j.carbon.2014.06.078",

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AU - Da Costa, D. R.

AU - Zarenia, M.

AU - Chaves, Andrey

AU - Farias, G. A.

AU - Peeters, F. M.

N1 - Funding Information: This work was financially supported by CNPq , under contract NanoBioEstruturas 555183/2005-0, PRONEX/FUNCAP , CAPES Foundation under the process number BEX 7178/13-1, the Flemish Science Foundation (FWO-Vl), the European Science Foundation (ESF) under the EUROCORES program EuroGRAPHENE (project CONGRAN), the Bilateral programme between CNPq and FWO-Vl, and the Brazilian Program Science Without Borders (CsF). We thank M. Ramezani Masir and M. Grujić for helpful comments and discussions.

PY - 2014/11

Y1 - 2014/11

N2 - Using the four-band continuum model we derive a general expression for the infinite-mass boundary condition in bilayer graphene. Applying this new boundary condition we analytically calculate the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our results for the energy spectrum show an energy gap between the electron and hole states at small magnetic fields. Furthermore the electron (e) and hole (h) energy levels corresponding to the K and K' valleys exhibit the EKe(h)(m)=-EK' h(e)(m) symmetry, where m is the angular momentum quantum number.

AB - Using the four-band continuum model we derive a general expression for the infinite-mass boundary condition in bilayer graphene. Applying this new boundary condition we analytically calculate the confined states and the corresponding wave functions in a bilayer graphene quantum dot in the absence and presence of a perpendicular magnetic field. Our results for the energy spectrum show an energy gap between the electron and hole states at small magnetic fields. Furthermore the electron (e) and hole (h) energy levels corresponding to the K and K' valleys exhibit the EKe(h)(m)=-EK' h(e)(m) symmetry, where m is the angular momentum quantum number.

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DO - 10.1016/j.carbon.2014.06.078

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SN - 0008-6223

VL - 78

SP - 392

EP - 400

JO - Carbon

JF - Carbon

ER -

Analytical study of the energy levels in bilayer graphene quantum dots

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