Quasiparticle renormalization in $ABC$ graphene trilayers

We investigate the effect of electron-electron interactions in $ABC$-stacked graphene trilayers. In the gapless regime, we show that the self-energy corrections lead to the renormalization of the dynamical exponent $z=3+{\alpha }_1/N$, with ${\alpha }_1\approx 0.52$ and $N$ is the number of fermionic species. Although the quasiparticle residue is suppressed near the neutrality point, the lifetime has a sublinear scaling with the energy and the quasiparticles are well defined even at zero energy. We calculate the renormalization of a variety of physical observables, which can be directly measured in experiments.

Figure 1

Left: Polarization bubble in one loop calculated numerically from Eq. (6). The real part (black curve) has a logarithmic singularity at the edge of the particle-hole continuum, at $\omega =\gamma q^3/4,$ shown in detail in the inset. Red curve: Imaginary part. Right panel: Polarization in imaginary frequencies, which is a purely real function. For $\omega /\gamma q^3\gg 1,{\Pi }^{\left(0\right)}(q,i\omega )\to -3N{q}^2/\left(16\omega \right)$ (see text).

Figure 2

One-loop correction to the self-energy with the dressed Coulomb interaction.

Figure 3

(a) On-shell scattering rate $\tau \left(\omega \right)$ vs energy in units of $t_{\perp }\sim 0.4$ eV. (b) Density plot of the spectral function as a function of energy $(\omega /t_{\perp })$ and momentum $\left(q/\Lambda \right)$. Solid black line: Bare energy spectrum. White line: Renormalized one. Light regions indicate a higher intensity.