Local heat current flow in ballistic phonon transport of graphene nanoribbons (2024)

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  Figure 1

  A sketch of the two terminal graphene nanoribbons. The reservoirs ($L$ and $R$) are connected to the ribbon through narrower leads, such that heat can be locally injected or extracted from the ribbon. $N^Z,N_{\mathrm{Res}}^Z$, and $N^A$ are geometric parameters.

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  Figure 2

  Spatial pattern of local heat current (a)and local temperature (b)for a temperature bias of $T_L=325$K, $T_R=275$K. The coupling strength of the system and the temperature probe is $\hslash {\gamma }_p=0.065$meV. Geometric parameters: $N^Z=30,N^A=11,$ and $N_{\mathrm{Res}}^Z=6$.

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  Figure 3

  Detailed profile of Fig.2. (a)Local heat flux across the vertical dashed line cut in Fig.2. The cell position is counted from bottom to top along the line cut. (b)Local temperature of the atoms on the left and right vertical border of the ribbon. The selected atoms are marked by the gray dashed boxes in Fig.2. The atom site in the middle is set to be position 0. Dashed line: average temperature in the ribbon. (c)Local temperature of the atoms shown in Fig.2with same color markers as a function of the coupling parameter ${\gamma }_p$.

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  Figure 4

  Local heat flux in the ribbon with mass disorder, where $\mathrm{\Delta }$ is the disorder strength. The disordered current pattern is averaged from 50 ensembles. The rest of the parameters are the same in Fig.2.

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  Figure 5

  Thermal profile in a narrow ribbon. (a)Local heat current. (b)Local temperature. Geometric parameters: $N^Z=16,N_{\mathrm{Res}}^Z=6,$ and $N^A=11$. The rest of the settings are the same as Fig.2.

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  Figure 6

  Zigzag graphene nanoribbon with defects. $N^A=9$ is the only parameter to mark its width. (a)A sketch of the ribbon and defects. The defect is placed at the middle marked by the purple box. (b)Transmission of zigzag graphene nanoribbon with Stone-Wales and ${\mathrm{SiC}}_4$ defects. Insets show phonon modes with zero transmission.

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  Figure 7

  Local heat current and temperature of zigzag graphene nanoribbon with Stone-Wales (SW) (a), (c), (e) and ${\mathrm{SiC}}_4$ (b), (d), (f) defect. Averaged local temperature in (a)and (b)is calculated by the atoms sharing the same horizontal coordinate, from the left reservoir to the right. Temperature distribution near the defect is demonstrated by light blue lines, extracted from the shaded region at the middle of the nanoribbon in Fig.6. (c), (d)Local heat current through the defect atoms are given by ${\vec{J}}_n={\sum }_{m(\ne n)}{\vec{J}}_{nm}$, the color gradient is consistent with ${\vec{J}}_{\mathrm{Cell}}$. (e), (f) Frequency resolved ${\vec{J}}_n$ at $\hslash \omega =157.87$ (e) and 150.02meV (f). These frequencies are found in the insets of Fig.6.

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