Many-Body Dynamics and Gap Opening in Interacting Periodically Driven Systems

We study transient dynamics in a two-dimensional system of interacting Dirac fermions subject to a quenched drive with circularly polarized light. In the absence of interactions, the drive opens a gap at the Dirac point in the quasienergy spectrum, inducing nontrivial band topology. We investigate the dynamics of this gap opening process, taking into account the essential role of electron-electron interactions. Crucially, scattering due to interactions (1) induces dephasing, which erases memory of the system’s prequench state and yields the intrinsic timescale for gap emergence, and (2) provides a mechanism for the system to absorb energy of the drive, leading to heating which must be mitigated to ensure the success of Floquet band engineering. We characterize the gap opening process via the system’s generalized spectral function and correlators probed by photoemission experiments, and we identify a parameter regime at moderate driving frequencies where a hierarchy of timescales allows a well-defined Floquet gap to be produced and studied before the deleterious effects of heating set in.

Figure 1

We study the dynamics of a single species of interacting 2D Dirac fermions subjected to a quenched periodic drive. A normally incident circularly polarized driving field, described by the vector potential $\mathcal{A}(t)$, opens a gap in the single-particle spectrum. Local interactions with strength $U$ lead to dynamical renormalization of the induced gap. We impose a finite bandwidth via a momentum cutoff $|p_x|$, $|p_y|\le W/v$, where $v$ is the Fermi velocity [see Eq. (1)].

Figure 2

Dynamics of Floquet gap opening. For $t<t_0$ the driving is off, and thus the spectrum is gapless. (a) TRARPES signal, Eq. (3), at $p_y=0$, for a probe pulse width $\sigma =16T_{\mathrm{\Omega }}$. Because of the initial band degeneracy, a small density of particles is excited to the upper band after the quench. (b) TRARPES signal at $\mathit{p}=0$. The extracted value of the Floquet gap is $\mathrm{\Delta }=0.134W$, which is enhanced compared to its value in the noninteracting case, ${\mathrm{\Delta }}_0=0.116W$. (c) Generalized spectral function, Eq. (4), at $\mathit{p}=0$. Sinclike peaks from the remnant and emergent quasienergy bands, from before and after the quench, yield the checkerboardlike pattern. Parameter values for all panels are $\mathrm{\Omega }=3W$, $A=0.6$, $U=0.3W$.

Figure 3

(a) Many-body Floquet gap $\mathrm{\Delta }$ and (b) inverse dephasing time $t_{\mathrm{dph}}^{-1}$ vs interaction strength, $U$. Both quantities are obtained through fitting $\nu (t,\omega =0)$ to the model described in the text. We take $A=0.6$ as in Fig. 2. (a) The gap enhancement is approximately linear in $U$. When heating rates are high, $\mathrm{\Delta }$ evolves nonmonotonically in time and cannot be extracted unambiguously (empty circles). The fit lines correspond to $\mathrm{\Delta }={\mathrm{\Delta }}_0(1+CU/W)$, where ${\mathrm{\Delta }}_0$ is the noninteracting gap value for each $\mathrm{\Omega }$. The extracted values of the slope $C$ slightly increase with increasing driving frequency $\mathrm{\Omega }$, i.e., for decreasing ${\mathrm{\Delta }}_0$: $C=[0.34,0.64,0.77,0.85]$ for $\mathrm{\Omega }=[2W,3W,4W,6W]$. (b) The inverse dephasing time increases with $U$ and decreases for increasing $\mathrm{\Omega }$. Lines corresponding to $t_{\mathrm{dph}}^{-1}\sim U^2$ are added as guides for the eye.

Figure 4

Heating in the high frequency regime for $A=0.6$. (a) Period-averaged absorbed energy $\overline{\delta E}(t)$ as a function of time for $\mathrm{\Omega }=4W$. Curves for both the noninteracting ($U=0$, black) and interacting ($U=0.4W$, blue) cases oscillate, but only the latter has an overall slope, which we extract as the effective energy absorption rate, $\overline{\gamma }$. (b) Effective energy absorption rate $\overline{\gamma }$ as a function of interaction (log-log plot) for $\mathrm{\Omega }=[2W,3W,4W]$. At low heating rates we find $\overline{\gamma }\sim U^2$ (fitted lines). Note the quick decay of $\overline{\gamma }$ with increasing $\mathrm{\Omega }$.