Dynamics of quasiparticles in graphene under intense circularly polarized light

A monolayer of graphene irradiated with circularly polarized light suggests a unique platform for surface electromagnetic wave (plasmon-polariton) manipulation. In fact, the time periodicity of the Hamiltonian leads to a geometric Aharonov-Anandan phase and results in a photovoltaic Hall effect in graphene, creating off-diagonal components of the conductivity tensor. The latter drastically changes the dispersion relation of surface plasmon-polaritons, leading to hybrid wave generation. In this paper we present a systematic and self-contained analysis of the hybrid surface waves obtained from Maxwell equations based on a microscopic formula for the conductivity. We consider a practical example of graphene sandwiched between two dielectric media and show that in the one-photon approximation there is formation of propagating hybrid surface waves. From this analysis emerges the possibility of a reliable experimental realization to study Zitterbewegung of charge carriers of graphene.

Figure 1

Monolayer graphene, placed in the $x\text{−}y$ plane and surrounded by two semi-infinite dielectric media with permittivity ${\varepsilon }_1$ and ${\varepsilon }_2$, is irradiated with circularly polarized light [large (yellow (arrow)].

Figure 2

Longitudinal component [Eq. (10)] of the conductivity tensor [Eq. (9)] in the presence of circularly polarized light (in units $c=1$). The real part is almost independent of $\omega$ and shows a set of plateaus which corresponds to the contribution to the conductivity from different quasienergy levels. The imaginary part is characterized by a number of dips, at $\hslash \omega =|\hslash \Omega -2E_F|,2E_F$, and $2E_F+\hslash \Omega$ (one-photon approximation), associated with logarithmic singularities around the absorption threshold in the quasienergy spectrum.

Figure 3

The off-diagonal (Hall) component [Eq. (11)] of the conductivity tensor [Eq. (9)] appears for topological reasons and can be ascribed to the Aharonov-Anandan phase (in units $c=1$). The real part is characterized by two peaks, at $\hslash \omega =|\hslash \Omega -2E_F|$ and $2E_F+\hslash \Omega$, in the one-photon approximation and is absent when the circularly polarized field is switched off. The behavior of the imaginary part is analogous to that of the real part of ${\sigma }_0\left(\omega \right)$ thanks to discontinuity associated with the step function.

Figure 4

The surface plasmon-polariton dispersion relation obtained from Eq. (16) with ${\varepsilon }_1=1$ and ${\varepsilon }_2=4$. A certain type of nonanalyticity can be distinguished around $\hslash \omega =|2E_F+n\hslash \Omega |$, with $n=0,\pm 1$, which can be attributed to interband transition.