Dynamically generated flat-band phases in optical kagome lattices

Motivated by recent advances in the realization of complex two-dimensional optical lattices, we investigate theoretically the quantum transport of ultracold fermions in an optical kagome lattice. In particular, we focus on its extensively degenerate localized states (flat band). By loading fermions in a partial region of the lattice and depleting the mobile atoms at the far boundary of the initially unoccupied region, we find a dynamically generated flat-band insulator, which is also a population-inverted state. We further show that inclusion of weak repulsion leads to a dynamical stripe phase for two-component fermions in a similar setup. Finally, by preparing a topological insulating state in a partially occupied kagome lattice, we find that the topological chiral current decays but exhibits an interesting oscillating dynamics during the nonequilibrium transport. Given the broad variety of lattice geometries supporting localized or topological states, our work suggests new possibilities for using geometrical effects and their dynamics in atomtronic devices.

Figure 1

The setup (top) and the current (bottom) for (a) square and (b) kagome lattices. Initially, atoms are loaded onto the left half and flow to the right. The lattice size in the longitudinal direction is 200 and the size in the transverse direction is $N_y$ as labeled on the plot. For the square lattice the initial fillings on the left half are $n=1,0.75,0.5,0.25$ for the curves with the highest plateau to the lowest. For the kagome lattice, the initial filling is $n=1$ and we show results with $N_y=6,12,24,30$. Inset: The band structure of the kagome lattice. The solid blue (gray) line corresponds to the flat band.

Figure 2

Distribution of the current flow (shown as the arrows) in the quasi-steady-state regime for (a) square lattice and (b) kagome lattice.

Figure 3

Fluctuations of the current in the kagome lattice. (a) The averaged current and its deviation in a window of $15t_0$ for $N_x=200$ and $N_y=30$. Inset: Two examples of localized states forming the flat band. “$+$” and “$-$” refer to the relative phases of the state. (b) The deviation of the current in a window of $15t_0$, taken at $t=(N_x/3)t_0$ for several values of $N_x$ with $N_y=30$ showing that the fluctuations do not decay as the system size scales. (c) The normalized current $\overline{I}$ vs time with and without the localized modes in the MCF calculation.

Figure 4

Dynamically generated flat-band insulator. (a) The current decays to zero. The inset shows the device, where atoms are initially loaded to the left half and a terminator beam removes particles at the far right end. (b) The density approaches the filling of the flat band, $n=1/3$. The inset shows the transversely averaged density profile at $t=250t_0$. Here $N_x=100$ and $N_y=30$.

Figure 5

Dynamical formation of stripe phases in the kagome lattice. Here we show the density profiles (with larger density shown by larger dots) of the left half for kagome lattices for (a) noninteracting fermions in a uniform kagome lattice and (b) two-component repulsive fermions in an uniform kagome lattice. These snapshots are taken for $N_x=100$ at $t=300t_0$.

Figure 6

Left: A snapshot of the chiral current (the arrows) of one component as atoms flow to the right. Right: The evolution of the total chiral current.