Electronic Strengthening of Graphene by Charge Doping

Graphene is known as the strongest 2D material in nature, yet we show that moderate charge doping of either electrons or holes can further enhance its ideal strength by up to $\sim 17\%$, based on first-principles calculations. This unusual electronic enhancement, versus conventional structural enhancement, of the material’s strength is achieved by an intriguing physical mechanism of charge doping counteracting the strain induced enhancement of the Kohn anomaly, which leads to an overall stiffening of the zone boundary $K_1$ phonon mode whose softening under strain is responsible for graphene failure. Electrons and holes work in the same way due to the high electron-hole symmetry around the Dirac point of graphene, while overdoping may weaken the graphene by softening other phonon modes. Our findings uncover another fascinating property of graphene with broad implications in graphene-based electromechanical devices.

Figure 1

Phonon spectra of intrinsic and doped (of $7.6\times {10}^{13}{\mathrm{cm}}^{-2}$ carrier density) graphene under different strains. (a) and (b), The intrinsic graphene. (c), (d), and (e), $n$-type graphene. (f), (g), (h), and (i), $p$-type graphene. The red arrows indicate the $K_1$ mode softened under strain.

Figure 2

The behavior of the $K_1$ mode under strain and doping. (a) The phonon dispersions around the $K_1$ mode under different strains: 0.0%, 5%, 10%, and 14.5%. The frequencies of the $K_1$ modes under different strain are set as the reference of zero frequency. (b) The adiabatic frequency shifts of the $K_1$ mode (in reference to the intrinsic graphene) as a function of the doping level for the unstrained graphene and strained graphene at the 14.9% strain, respectively.

Figure 3

(a) The stress ($\sigma$) versus biaxial strain ($\epsilon$) for intrinsic, electron- and hole-doped (at a doping level of $7.6\times {10}^{13}{\mathrm{cm}}^{-2}$) graphene. The vertical lines denote the locations of structural instabilities. Inset: The graphene supercell used for calculating the stress-strain curve. (b) Atomic displacements of $A_1$ and $B_1$ phonon modes.

Figure 4

The critical strains (where phonon instability occurs) of graphene as a function of carrier concentration of electrons and holes (plotted on the negative $x$ axis). Inset: The phonon spectra of $1.9\times {10}^{14}{\mathrm{cm}}^{-2}$ electron-doped graphene under 16.2% strain.