(a) The schematic picture of the system described by the NEGF formalism. The system is divided into three regions: one conductor connected with two semi-infinite leads. (b) Structure of a 3 × 3 supercell of graphyne. Unit cell is highlighted by the red dashed line. PL is for principal layer and k ‖ is for the parallel k vectors to reduce the two-dimensional system to one-dimensional described in the text. For each k ‖, graphyne can be considered as an infinite one-dimensional chain of principal layers. (c) Band structure of graphyne. The red solid line and blue dashed line stand for the results from DFT calculations and Wannier interpolations, respectively. Inset illustrates the band structure of graphene around the Dirac point. (d) Phonon dispersion relations of graphyne. The phonon spectra of graphene is depicted in the inset for comparison.
Spatial decay of the matrix elements of Hamiltonian H( R ) and interaction force constant (IFC) K( R ). (a) and (b) are the H( R ) and K( R ) for graphyne, respectively, (c) and (d) for graphene. R is the distance between the matrix element and the unit cell. The dashed lines in the figure mark the distance beyond which the matrix elements are truncated. The red circle and blue triangle symbols represent the matrix elements of IFC without and with corrections.
(a) Electron transmittance as a function of energy for graphyne. Inset illustrates the scaled transmittance of graphyne (red solid line) and graphene (blue dashed line). The scaled transmittance is the transmittance divided by the cross section length. (b) The chemical potential dependent electronic conductance of graphyne and graphene at typical temperatures. Inset is the enlargement of low chemical potential part. G 0 is the normalized conductance quanta as 2e 2/h divided by the cross section length in Å.
Phonon transmittance of (a) graphyne and (b) graphene. The red solid line and blue dashed line represent the results obtained by the IFC with and without corrections, respectively. Insets are the enlargements around the Gamma point. (c) Phonon thermal conductance of graphyne (red solid line) compared with that of graphene (black dashed line). Enlargement of the low temperature region is illustrated in the inset. κ 0 is the normalized thermal conductance as 10−10 W/K divided by the cross section length in Å. (d) Comparison of the three acoustic phonon branches of graphyne (red solid line) and graphene (black dashed line). The vibrational modes are marked to the corresponding branch. LA is for longitudinal acoustic mode, TA is for transverse acoustic mode, and ZA is for the flexural mode. 1/2 M is for the middle point of the line of ΓM.
Temperature dependent electron thermal conductance of (a) graphyne and (b) graphene with different chemical potentials. The phonon thermal conductance (black solid line) is also plotted in the figure for comparison.
The thermoelectric power (TEP) of graphyne and graphene. Contour plot of the TEP of (a) graphyne and (b) graphene as a function of chemical potentials and temperatures. The color bar shows the positive and negative values of the TEP. Chemical potential dependent TEP at typical temperatures of graphyne (c) and (d). Temperature dependent TEP at different chemical potentials of graphyne (e) and (f).
The figure of merit ZT as a function of chemical potentials and temperatures of graphyne (a) and graphene (b).
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