Origin of Universal Optical Conductivity and Optical Stacking Sequence Identification in Multilayer Graphene

We show that the origin of the universal optical conductivity in a normal $N$-layer graphene multilayer is an emergent chiral symmetry which guarantees that $\sigma (\omega )=N{\sigma }_{\mathrm{uni}}$ in both low and high-frequency limits. [${\sigma }_{\mathrm{uni}}=(\pi /2)e^2/h$]. We use this physics to relate intermediate frequency conductivity trends to qualitative characteristics of the multilayer stacking sequence.

Figure 1

Conductivity for ideal-model bilayer graphene (${\gamma }_3=0$) and for a more realistic model with distant neighbor interlayer hopping (${\gamma }_3=0.3\mathrm{eV}$). The inset shows ideal-model band structure of bilayer graphene.

Figure 2

Ideal-model band structure and real part of the conductivity for all tetralayer graphene stacks, ABCA (top), ABCB, ABAC (middle), and ABAB (bottom). The insets show stacking diagrams where shaded ovals link sublattices $\alpha$ and $\beta$ to the nearest interlayer neighbors.

Figure 3

Real part of the ideal-model conductivity for Bernal (AB), orthorhombic (ABC), and hexagonal (AA) 10 layer graphene stacks.