Efficient Chebyshev polynomial approach to quantum conductance calculations: Application to twisted bilayer graphene

TY - JOUR

T1 - Efficient Chebyshev polynomial approach to quantum conductance calculations

T2 - Application to twisted bilayer graphene

AU - De Castro, Santiago Giménez

AU - Ferreira, Aires

AU - Bahamon, D. A.

N1 - Funding Information: A.F. acknowledges support from a Royal Society University Research Fellowship. S.G.d.c. and D.A.B. acknowledge support form the Brazilian Nanocarbon Institute of Science and Technology (INCT/Nanocarbon), CAPES-PROSUC (Grant No. 88887.510399/2020-00, Doctorate degree), FAPESP (Grant 18/07276-5), CAPES-PRINT (Grant No. 88887.575078/2020-00, Sandwich doctorate), CAPES-PRINT (Grant No. 88887.310281/2018-00), CNpQ (309835/2021-6), and Mackpesquisa. The supercomputer time was provided by the high-performance computing cluster of the Mackenzie Presbyterian University. We acknowledge F. M. O. Brito for proofreading the final version of the manuscript. S.G.d.C. also acknowledges the hospitality of the School of Physics, Engineering and Technology at the University of York, U.K., where this work was completed. Publisher Copyright: ©2023 American Physical Society. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2023/1/15

Y1 - 2023/1/15

N2 - In recent years, Chebyshev polynomial expansions of tight-binding Green's functions have been successfully applied to the study of a wide range of spectral and transport properties of materials. However, the application of the Chebyshev approach to the study of quantum transport properties of noninteracting mesoscopic systems with leads has been hampered by the lack of a suitable Chebyshev expansion of Landaeur's formula or one of its equivalent formulations in terms of Green's functions in Keldysh's perturbation theory. Here, we tackle this issue by means of a hybrid approach that combines the efficiency of Chebyshev expansions with the convenience of complex absorbing potentials to calculate the conductance of two-terminal devices in a computationally expedient and accurate fashion. The versatility of the approach is demonstrated for mesoscopic twisted bilayer graphene (TBG) devices with up to 2.3×106 atomic sites. Our results highlight the importance of moiré effects, interlayer scattering events, and twist-angle disorder in determining the conductance curves in devices with a small twist angle near the TBG magic angle θm≈1.1°.

AB - In recent years, Chebyshev polynomial expansions of tight-binding Green's functions have been successfully applied to the study of a wide range of spectral and transport properties of materials. However, the application of the Chebyshev approach to the study of quantum transport properties of noninteracting mesoscopic systems with leads has been hampered by the lack of a suitable Chebyshev expansion of Landaeur's formula or one of its equivalent formulations in terms of Green's functions in Keldysh's perturbation theory. Here, we tackle this issue by means of a hybrid approach that combines the efficiency of Chebyshev expansions with the convenience of complex absorbing potentials to calculate the conductance of two-terminal devices in a computationally expedient and accurate fashion. The versatility of the approach is demonstrated for mesoscopic twisted bilayer graphene (TBG) devices with up to 2.3×106 atomic sites. Our results highlight the importance of moiré effects, interlayer scattering events, and twist-angle disorder in determining the conductance curves in devices with a small twist angle near the TBG magic angle θm≈1.1°.

UR - http://www.scopus.com/inward/record.url?scp=85146860912&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.107.045418

DO - 10.1103/PhysRevB.107.045418

M3 - Article

AN - SCOPUS:85146860912

SN - 2469-9950

VL - 107

JO - Physical Review B

JF - Physical Review B

IS - 4

M1 - 045418

ER -