Enhanced thermoelectric figure of merit in edge-disordered zigzag graphene nanoribbons

We investigate electron and phonon transport through edge-disordered zigzag graphene nanoribbons based on the same methodological tool of nonequilibrium Green functions. We show that edge disorder dramatically reduces phonon thermal transport while being only weakly detrimental to electronic conduction. The behavior of the electronic and phononic elastic mean-free paths points to the possibility of realizing an electron-crystal coexisting with a phonon-glass. The calculated thermoelectric figure of merit $\left(ZT\right)$ values qualify zigzag graphene nanoribbons as a very promising material for thermoelectric applications.

Figure 1

(Color online) Schematics of the system (a). The central region with edge disorder has length $L$ and is connected to semi-infinite ZGNRs free of disorder. Transmission spectra of phonons, ${\overline{\mathcal{T}}}_{\text{ph}}$, for pristine and disordered ZGNR are plotted for $N_z=10$ and 20 in (b) and (c), respectively. The dark (red) regions represent the difference in transmission between pristine ZGNR(10) and ZGNR(8) (b) and the same for ZGNR(20) and ZGNR(18) (c). ${\overline{\mathcal{T}}}_{\text{ph}}$ is suppressed with increasing $L=15.7$, 63, 252, and 504 nm. Elastic mean free paths are given in the insets.

Figure 2

(Color online) The ratio of phonon thermal conductance ${\kappa }_{\text{ph}}\left(T,L\right)$ to its pristine value ${\kappa }_{\text{ph}}^o\left(T\right)$ is plotted for ZGNR(20) at different temperatures. The ratio is fitted to a curve using Eq. (1). Inset shows ${\kappa }_{\text{ph}}$ of ZGNR(20) as a function of $T$.

Figure 3

(Color online) Electron transport through edge-disordered ZGNRs. Ensemble averaged transmission spectra ${\overline{\mathcal{T}}}_{\text{el}}$ are plotted for pristine ZGNRs and with varying sample lengths for $N_z=10$ (upper) and $N_z=20$ in (lower). Sample lengths are $L=7.9$, 31.5, 126, and 252 nm [and additionally 1 and $2\mu \text{m}$ for ZGNR(20)]. Elastic mean-free paths ${\ell }_{\text{el}}$ vs energy are extracted from the transmission data. Zero of the energy is set to the CNP.

Figure 4

(Color online) Thermoelectric figure of merit, $ZT$, versus chemical potential $\mu$ at different temperatures $T$ for ZGNR(10) (left) and ZGNR(20) (right) having lengths $L=0.25\text{nm}$ and $4\mu \text{m}$, respectively. Zero of $\mu$ is the CNP and the dotted lines represent the FCP edges.