Harnessing the photonic local density of states in graphene moiré superlattices

In this work we investigate the electromagnetic local density of states (LDOS) near a twisted bilayer graphene (TBG) deposited over a general isotropic substrate. The band structure of the TBG is calculated within a tight-binding framework, and then used to determine the TBG's conductivity. The latter presents a nontrivial dependence upon the angle of twist, which shows up in the LDOS, allowing for a moiré pattern-dependent quantum emission. For some specific twist angles we show that it is possible to either enhance or decrease the LDOS by an order of magnitude at selected frequencies when compared to the monolayer. This impressive variation is explained in terms of the presence/absence of well defined surface plasmon polaritons (SPPs). Altogether our findings demonstrate that TBG is an alternative, versatile material platform for controlling spontaneous emission and enhancing light-matter interactions, and pave the way for further studies and applications of quantum emission in the emerging class of two-dimensional moiré materials.

Figure 1

Our setup consists of a twisted bilayer of graphene on top of a substrate. The two layers of graphene are twisted by an angle ${\theta }_m$, and the bilayer as a whole has a conductivity $\sigma \left(\omega \right)$. The substrate is characterized by a permittivity $\epsilon \left(\omega \right)$ that, for suspended TBGs, is equal to ${\epsilon }_0$.

Figure 2

Upper plots: Real and imaginary parts of the optical conductivity of a suspended graphene monolayer (full black line), and suspended TBGs with ${\theta }_m=7.{34}^{\circ },13.2^{\circ }$ (dashed red and dotted purple lines). The conductivities are normalized by ${\sigma }_0=(4/\pi )(e^2/h)$. Temperature is set to zero and the chemical potential to $\mu =0.5$ eV. Lower plots: Same as above, but the suspended TBGs now have ${\theta }_m=7.{34}^{\circ },9.{46}^{\circ },13.2^{\circ },16.9^{\circ }$ (red, blue, purple, orange). Temperature is also zero but the chemical potential is set at $\mu =1$ eV.

Figure 3

Electric contribution to the photonic local density of states at $\mu =0.5$ eV, as a function of frequency, for a graphene monolayer (full black line), and bilayer graphene with ${\theta }_m=7.{34}^{\circ },13.2^{\circ }$ (dashed red and dotted purple lines, respectively). The distance is fixed at $z=30$ nm. The inset shows the distance dependence of the photonic LDOS for the same moiré angles as in the main panel for $\omega =2\times {10}^{14}\mathrm{rad}$/s.

Figure 4

Electric contribution to the photonic local density of states at $\mu =1$ eV, as a function of frequency, for a graphene monolayer (full black line), and bilayer graphene with ${\theta }_m=7.{34}^{\circ },9.{46}^{\circ },13.2^{\circ },16.9^{\circ }$ (dashed red, long-dashed blue, dotted purple, and dot-dashed orange lines, respectively). As in Fig 3, the distance is fixed at $z=30$ nm. The inset shows the distance dependence of the photonic LDOS for the same moiré angles as in the main panel for $\omega =2\times {10}^{14}\mathrm{rad}$/s.

Figure 5

The integrand of the electric LDOS as a function of $k_{\parallel }$, for a monolayer (solid black line) and twisted bilayers of $7.{34}^{\circ }$ (dashed red line) and $13.2^{\circ }$ (dotted purple line). One can immediately see the SPP signatures as sharp peaks for the latter two TBGs and the monolayer, while the $7.{34}^{\circ }$ TBG is dominated by lossy surface waves. See text for further discussion.

Figure 6

Left plot: The LDOS of the $\theta =9.{46}^{\circ }$ TBG at four different frequencies, $\omega =3\times {10}^{14}$ (solid line), $3.7\times {10}^{14}$ (dashed line), $3.85\times {10}^{14}$ (dotted line), and $4\times {10}^{14}$ rad/s (dot-dashed line). Right plot: Real (dashed line) and imaginary (dotted line) parts of the conductivity of $\theta =9.{46}^{\circ }$ TBG. In the two plots we set $\mu =1$ eV.