by Masaki Yamawaki, Masato Ohnishi, Shenghong Ju, and Junichiro Shiomi

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Presentation transcript:

by Masaki Yamawaki, Masato Ohnishi, Shenghong Ju, and Junichiro Shiomi Multifunctional structural design of graphene thermoelectrics by Bayesian optimization by Masaki Yamawaki, Masato Ohnishi, Shenghong Ju, and Junichiro Shiomi Science Volume 4(6):eaar4192 June 15, 2018 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).

Fig. 1 Nanostructured thermoelectric GNRs. Nanostructured thermoelectric GNRs. (A) Periodically nanostructured GNR (model A) and (B) antidot GNR (model B). The size of the GNR section is determined by the index (Nx, Ny), where Nx and Ny are the numbers of carbon chains along the axial direction and the direction perpendicular to the axis, respectively. Binary flags represent the structural descriptor; 0 and 1, represent, respectively, defective and complete hexagonal lattices for model A and the pristine and antidot GNR sections for model B. Masaki Yamawaki et al. Sci Adv 2018;4:eaar4192 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).

Fig. 2 Multifunctional structural optimization using model A. Multifunctional structural optimization using model A. (A) Maximum (triangle), minimum (inverse triangle), and average (circle) ZT of all the candidates for m = 0 to 10. Dashed lines show the linear fitting in 1 ≤ m ≤ 10. (B) Efficiency of the Bayesian optimization. NBayes/rand is the average number of calculations needed until, for the first time, a structure that belongs to the top k% of all the candidates is found with the Bayesian/random search. (C and D) Optimal geometrical structure for P/Rth and its electron/phonon band structure with that of the pristine GNR. The P- and Rth-optimal structures are GNRs with m = 4 and 7, respectively. Bold lines in the electron and phonon band structures show the edge state and the longitudinal acoustic band, respectively. For the electron band structure, the Fermi level is set to zero. Masaki Yamawaki et al. Sci Adv 2018;4:eaar4192 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).

Fig. 3 Optimization of the antidot GNR structure. Optimization of the antidot GNR structure. (A) Thermoelectric properties—ZT, P, and Rth—of the representative structures: pristine (black), periodic (blue), and optimal (red) structures. The values are normalized by those of the pristine structure. (B) Periodic (top) and optimal aperiodic (bottom) structures. (C and D) Phonon/electron transmission functions, Θph/el(ω), of the representative structures. The Fermi level is set to zero for Θel(E). (E) Θel(E) (orange) and DOS in the nanostructured region (green) near the energy levels corresponding to the peak μ for ZT, μpeak, of the periodic (top) and optimal (bottom) structures; μpeak = −0.140 and −0.105 eV, respectively, as indicated by dashed lines. The band edge of the edge state is located at E = −0.078 eV corresponding to that of the Van Hove singularity, and black arrows and their labels indicate resonant states. (F) LDOS distribution of the resonant states of the periodic (top) and optimal (bottom) structures. The resonant numbers correspond to those in (E). Masaki Yamawaki et al. Sci Adv 2018;4:eaar4192 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).

Fig. 4 Fluctuation of thermoelectric properties. Fluctuation of thermoelectric properties. P (blue), (gray), and Rth (red) of structures with the same numbers of antidots and homogeneous regions as the optimal structure. The thermoelectric properties are normalized by the value for the pristine GNR. The fitting curves of Gaussian distributions are shown as a reference. Masaki Yamawaki et al. Sci Adv 2018;4:eaar4192 Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).