TY - JOUR

T1 - Collective resonances near zero energy induced by a point defect in bilayer graphene

AU - You, Jhih Shih

AU - Tang, Jian Ming

AU - Huang, Wen Min

N1 - Funding Information:
We thank Hsiu-Hau Lin for useful discussions. JSY is supported by the Ministry of Science and Technology, Taiwan through grant MOST 104-2917-I-564-054. WMH acknowledge supports from the National Science Council in Taiwan through grant MOST 104-2112-M-005-006-MY3. Financial supports and friendly environment provided by the National Center for Theoretical Sciences in Taiwan are also greatly appreciated.
Publisher Copyright:
© 2018, The Author(s).

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Intrinsic defects give rise to scattering processes governing the transport properties of mesoscopic systems. We investigate analytically and numerically the local density of states in Bernal stacking bilayer graphene with a point defect. With Bernal stacking structure, there are two types of lattice sites. One corresponds to connected sites, where carbon atoms from each layer stack on top of each other, and the other corresponds to disconnected sites. From our theoretical study, a picture emerges in which the pronounced zero-energy peak in the local density of states does not attribute to zero-energy impurity states associated to two different types of defects but to a collective phenomenon of the low-energy resonant states induced by the defect. To corroborate this description, we numerically show that at small system size N, where N is the number of unit cells, the zero-energy peak near the defect scales as 1/lnN for the quasi-localized zero-energy state and as 1/N for the delocalized zero-energy state. As the system size approaches to the thermodynamic limit, the former zero-energy peak becomes a power-law singularity 1/|E| in low energies, while the latter is broadened into a Lorentzian shape. A striking point is that both types of zero-energy peaks decay as 1/r2 away from the defect, manifesting the quasi-localized character. Based on our results, we propose a general formula for the local density of states in low-energy and in real space. Our study sheds light on this fundamental problem of defects.

AB - Intrinsic defects give rise to scattering processes governing the transport properties of mesoscopic systems. We investigate analytically and numerically the local density of states in Bernal stacking bilayer graphene with a point defect. With Bernal stacking structure, there are two types of lattice sites. One corresponds to connected sites, where carbon atoms from each layer stack on top of each other, and the other corresponds to disconnected sites. From our theoretical study, a picture emerges in which the pronounced zero-energy peak in the local density of states does not attribute to zero-energy impurity states associated to two different types of defects but to a collective phenomenon of the low-energy resonant states induced by the defect. To corroborate this description, we numerically show that at small system size N, where N is the number of unit cells, the zero-energy peak near the defect scales as 1/lnN for the quasi-localized zero-energy state and as 1/N for the delocalized zero-energy state. As the system size approaches to the thermodynamic limit, the former zero-energy peak becomes a power-law singularity 1/|E| in low energies, while the latter is broadened into a Lorentzian shape. A striking point is that both types of zero-energy peaks decay as 1/r2 away from the defect, manifesting the quasi-localized character. Based on our results, we propose a general formula for the local density of states in low-energy and in real space. Our study sheds light on this fundamental problem of defects.

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U2 - 10.1038/s41598-018-29213-z

DO - 10.1038/s41598-018-29213-z

M3 - Article

C2 - 30026578

AN - SCOPUS:85050611177

VL - 8

JO - Scientific Reports

JF - Scientific Reports

SN - 2045-2322

IS - 1

M1 - 10938

ER -