Floquet Chern Insulators and Radiation-Induced Zero Resistance in Irradiated Graphene

Abstract

Recent advances in optics and time-resolved techniques have facilitated the exploration of new states of matter under nonequilibrium conditions. Here, we predict that irradiated graphene can host two novel nonequilibrium steady states of matter with zero resistance when exposed to circularly polarized light: (i) Floquet Chern insulators and (ii) a radiation-induced zero-resistance state with spontaneous formation of an inhomogeneous current distribution. Specifically, we calculate nonequilibrium anomalous Hall and longitudinal conductivities to map the nonequilibrium phase diagram of irradiated graphene as a function of the driving frequency and the electric-field strength of circularly polarized light. As a result, Floquet Chern insulators are found to occur at high driving frequencies above the graphene band width. By contrast, at low driving frequencies below the graphene band width, the nonequilibrium anomalous Hall conductivity deviates from the expected quantized values, and the nonequilibrium longitudinal conductivity exhibits highly irregular behavior, including negative resistance. It is predicted that the thermodynamically unstable negative resistance will trigger a catastrophic breakdown, inducing a zero-resistance state with spontaneous formation of an inhomogeneous current distribution, similar to the radiation-induced zero-resistance state observed in quantum Hall systems.

Figures (6)

• Figure 1: Emergence of a Floquet Chern insulator in irradiated Graphene. The left part of the figure shows the energy band structure of graphene at half-filling before irradiation, where the blue and gray energy bands represent occupied and unoccupied states, respectively. Two Dirac cones are located at the corners of the first Brillouin zone, labeled as ${\bf K}$ and ${\bf K}^\prime$. The middle part of the figure shows that graphene is irradiated with circularly polarized light at the driving frequency $\Omega$. In this figure, $\Omega = 8\tau$, where $\tau$ is the hopping parameter between nearest-neighbor carbon atoms. The right part of the figure shows that, after irradiation, an infinite set of well-separated Floquet copies of two quasienergy sub-bands forms, with the overall Floquet energy gap of $\Omega$. The two quasienergy sub-bands have the same energetic and topological structure as the energy bands in the honeycomb Haldane model, with a small energy gap opening at ${\bf K}$ and ${\bf K}^\prime$. The local distribution function, $f_{\rm loc}(\omega)$, indicates the average population of Floquet eigenstates across momenta as a function of quasienergy.
• Figure 2: Nonequilibrium DC electric conductivities of irradiated graphene. ( a) Anomalous Hall conductivity calculated from the TKNN formula, $\sigma^{\rm TKNN}_{xy}$, as a function of the driving frequency, $\Omega/\tau$, and the normalized electric-field strength, $\tilde{A}=eA l/{\hbar c}=eE_0 l/\hbar \Omega$, where $E_0$ is the electric-field strength, and $l$ is the distance between nearest-neighbor carbon atoms. ( b) Nonequilibrium anomalous Hall conductivity calculated from the full nonequilibrium Kubo formula, $\sigma^{\rm full}_{xy}$. ( c) Nonequilibrium longitudinal conductivity calculated from the full nonequilibrium Kubo formula, $\sigma^{\rm full}_{xx}$. The color bars at the top represent the conductivity values in units of $e^2/h$.
• Figure 3: Nonequilibrium anomalous Hall conductivity of irradiated graphene. The nonequilibrium anomalous Hall conductivity calculated from the fully interacting Green's functions, $\sigma_{xy}^{\rm full}$, is compared with that in the impurity-free limit, $\sigma_{xy}^{\rm free}$, and with that calculated using the TKNN formula, $\sigma_{xy}^{\rm TKNN}$. The comparison is conducted at three driving frequencies of ( a) $\Omega/\tau=8$, ( b) $\Omega/\tau=4$, and ( c) $\Omega/\tau=2$. As shown in the comparison, $\sigma_{xy}^{\rm free}$ closely matches $\sigma_{xy}^{\rm full}$, effectively capturing deviations from the quantized values. To demonstrate how $\sigma_{xy}^{\rm free}$ can take non-quantized values, we plot the Berry curvature of the top ($\mu=+$) and bottom ($\mu=-$) quasienergy sub-band of the $n=0$ Floquet level in the Brillouin zone at two different values of $\tilde{A}=0.58$ (left panels) and $2.10$ (right panels) for each value of $\Omega/\tau$. The shaded and unshaded areas show where states are occupied and unoccupied by electrons, respectively.
• Figure 4: Negative longitudinal conductivity and population inversion. ( a) The nonequilibrium longitudinal conductivity calculated from the fully interacting Green's functions, $\sigma^{\rm full}_{xx}$, is plotted in color as a function of $\Omega/\tau$ and $\tilde{A}$. The dashed lines represent the constant frequency lines at $\Omega/\tau=8$, $4$, $2$, and $1$. ( b) Local distribution function, $f_{\rm loc}(\omega)$, is plotted within the first Floquet Brillouin zone ($-\Omega/2<\omega\leq\Omega/2$) in color as a function of $\omega$ and $\tilde{A}$ at four different values of $\Omega/\tau$ corresponding to the dashed lines in ( a). The red and blue colors indicate the occupied and unoccupied states, respectively.
• Figure 5: Nonequilibrium longitudinal conductivity of irradiated graphene. The nonequilibrium longitudinal conductivity calculated from the fully interacting Green's functions, $\sigma_{xx}^{\rm full}$, is compared with that in the fast-driving limit, $\sigma_{xx}^{\rm fast}$. The comparison is conducted at three driving frequencies of ( a) $\Omega/\tau=8$, ( b) $\Omega/\tau=4$, and ( c) $\Omega/\tau=2$. As shown in the comparison, $\sigma_{xx}^{\rm fast}$ closely matches $\sigma_{xx}^{\rm full}$ regardless of the values of $\tilde{A}$ across all three values of $\Omega/\tau$. Considering that $\sigma_{xx}^{\rm fast}$ is the frequency integral of the product of two factors, $\langle {J\rho J\rho} \rangle$ and $-\frac{\partial f_{\rm loc}}{\partial \omega}$, we plot $\langle {J\rho J\rho} \rangle$ and $-\frac{\partial f_{\rm loc}}{\partial \omega}$ in the left and right panels for $\tilde{A}=0.58$ and $2.92$, respectively. We focus on the frequency range of the first Floquet Brillouin zone, $-\Omega/2 < \omega \leq \Omega/2$, because the main contribution to conductivity comes from this range. Note that $\langle J\rho J\rho \rangle$ and $-\frac{\partial f_{\rm loc}}{\partial \omega}$ are plotted in properly normalized units because we are only interested in their relative strength as a function of $\omega$. The red and blue shaded areas indicate that $-\frac{\partial f_{\rm loc}}{\partial \omega}<0$ and $-\frac{\partial f_{\rm loc}}{\partial \omega}>0$, respectively.