Unconventional Quasiparticle Lifetime in Graphene

We address the question of how large can the lifetime of electronic states be at low energies in graphene, below the scale of the optical phonon modes. For this purpose, we study the many-body effects at the $K$ point of the spectrum, which induce a strong coupling between electron-hole pairs and out-of-plane phonons. We show the existence of a soft branch of hybrid states below the electron-hole continuum when graphene is close to the charge neutrality point, leading to an inverse lifetime proportional to the cube of the quasiparticle energy. This implies that a crossover should be observed in transport properties, from such a slow decay rate to the lower bound given at very low energies by the decay into acoustic phonons.

Figure 1

Plot of the region corresponding to the $e\mathrm{\text{−}}h$ continuum (shaded area) and the dispersion of the hybrid states made of an optical phonon and an $e\mathrm{\text{−}}h$ pair, obtained from the poles of $D_{+}$ and $D_{-}$ for $g/v_F=1$.

Figure 2

Plot of the contributions to the decay rate arising from the low-energy branch of hybrid states at the $K$ point (full line) and from acoustic phonons (dashed line). The inset shows the decay rate from the hybrid states over a larger scale, where it is seen the crossover from cubic to linear dependence on QP energy at the scale ${\omega }_0$ ($\approx 70\mathrm{meV}$).