Observation of vacancy-induced suppression of electronic cooling in defected graphene

Previous studies of electron-phonon interaction in impure graphene have found that disorder can give rise to an enhancement of electronic cooling at high temperatures. We investigate the effect of lattice vacancy in both mono- and bilayer graphene and observe an order of magnitude suppression of electronic cooling at low temperatures compared with clean graphene. The dependence of the coupling constant on the phonon temperature implies its link to the dynamics of disorder. Our study highlights the effect of disorder on electron-phonon interaction in graphene. In addition, the suppression of electronic cooling holds great promise for improving the performance of graphene-based bolometer and photodetector devices.

Figure 1

Resistance of defected graphene. (a) Temperature dependence of resistance in sample SM1 at different gate voltages, showing divergence at low temperature. Inset: Optical micrograph of a typical device configuration. (b) Resistance of SM1 as a function of Joule heating current at different gate voltages at $T=1.5$ K. The CNP is at 14.5 V. (c) Thermal model for the structure. The pathways of heat dissipation are indicated by red arrows.

Figure 2

Cooling power of monolayer and bilayer defected graphene. (a), (b) Cooling power $P$ against $T_{\mathrm{e}}^3-T_{\mathrm{ph}}^3$ shows a linear dependence for both monolayer and bilayer samples. Inset: $P$ versus $T_{\mathrm{e}}$.

Figure 3

Suppression of electronic cooling in defected graphene. (a) Cooling power of monolayer graphene. The solid line is a plot of Eq. (2) for clean graphene at $n=4\times {10}^{11} {\text{cm}}^{-2}$. The solid symbol represents experiment results of pristine graphene from others' work. The up triangle represents data from [37] at $n=4\times {10}^{11} {\text{cm}}^{-2}$ and $T_{\mathrm{ph}}=1.8$ K, while the down triangles represent data from [35] at $n=2.2\times {10}^{12} {\text{cm}}^{-2}$ and $T_{\mathrm{ph}}=0.8$ K. The open symbol represents our data. $n_0$ is $4\times {10}^{11} {\text{cm}}^2$ to account for charge puddles near CNP. $T_{\mathrm{ph}}$ is 1.5 K in SM1 and 7 K in SM2. (b) Cooling power of bilayer graphene. The solid line is a plot of Eq. (3) for clean graphene at $n=2.8\times {10}^{12} {\text{cm}}^{-2}$ and $T_{\mathrm{ph}}=1.5$ K. The solid symbol represents experiment results of pristine graphene at $n=2.7\times {10}^{12} {\text{cm}}^{-2}$ and $T_{\mathrm{ph}}=1.8$ K, taken from [37]. The open symbol depicts our results for SB2 at $n=2.8\times {10}^{12} {\text{cm}}^{-2}$ and $T_{\mathrm{ph}}=1.5$ K. The data for SB1 (not shown) almost overlap SB2.

Figure 4

Coupling constant $A$. (a) Extracted coupling constant $A$ as a function of carrier density $n$ in monolayer samples. (b) Dependence of $A$ on carrier density $n$ in bilayer graphene samples. The curves for two samples with similar degree of disorder align reasonably well, confirming the consistency of our experiment. (c) Dependence of $A$ on phonon temperature $T_{\mathrm{ph}}$. The data of SM2 are plotted with respect to the right $y$ axis. The error bar reflects the difference of $A$ obtained by the nonlinear $IV$ at the positive bias and negative bias.