Chiral topological phases in optical lattices without synthetic fields

Synthetic fields applied to ultracold quantum gases can realize topological phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser beams in particular are under scrutiny as a route to create synthetic fields in neutral gases to mimic ordinary magnetic and electric fields acting on charged matter. Yet external laser beams can impose heating and losses that make cooling into many-body topological phases challenging. We propose that atomic or molecular dipoles placed in optical lattices can realize a topological phase without synthetic fields by placing them in certain frustrated lattices. We use numerical modeling on a specific example to show that the interactions between dipolar fermions placed in a kagome optical lattice spontaneously break time-reversal symmetry to lead to a topological Mott insulator, a chiral topological phase generated entirely by interactions. We estimate realistic entropy and trapping parameters to argue that this intriguing phase of matter can be probed with quantum gases using a combination of recently implemented technologies.

Figure 1

Plot of a kagome optical lattice potential [38] (see Appendix pp1 for the explicit formula) as a function of position in the $x\text{−}y$ plane. The two particles represent schematics of dipoles separated in the plane by $|\mathit{r}-{\mathit{r}}^{\prime }|$ with moments oriented perpendicular to the plane to ensure mutual repulsion.

Figure 2

(a) Single-particle energies as a function of wave vector on a kagome lattice with only nearest-neighbor tunneling. At a density of $2/3$, the bands marked with solid (dashed) lines are filled (empty), and the red arrow shows where the Fermi surface touches the empty band at the quadratic band crossing point. The inset shows the definition of various high-symmetry points in the first Brillouin zone. (b) The charge density wave pattern obtained from Eq. (1) with $V_1=2$. The sizes of the dots are proportional to the average occupation number. (c) The chiral current pattern in a topological Mott insulator phase with a quantum anomalous Hall effect obtained from Eq. (1) with $V_1=1.8$. Exact diagonalization and mean-field theory obtained the same patterns found in both (b) and (c).

Figure 3

(a) Current plotted against the nearest-neighbor interaction strength at zero temperature on a 27-site kagome lattice, obtained from exact diagonalization (dots) and mean-field theory (line) applied to Eq. (1). Nonzero current implies a topological Mott insulator with a quantum anomalous Hall effect. Here finite-size effects (see Appendix pp3) lead to a nonzero current at $V_1=0$. Both methods capture the transition from the topological Mott insulator (small $V_1$) to a charge density wave (large $V_1$). (b) Current plotted against the interaction strength at zero temperature on an infinite system using mean-field theory on Eq. (1), showing the absence of current at $V_1=0$ and the same transition as in (a). (c) The same as (b), but plotting the maximum attainable entropy per particle.

Figure 4

(a) The mean-field phase diagram of Eq. (1) obtained by plotting the magnitude of the current against temperature and interaction strength. The white line uses the density difference between sites, $\delta n$, to plot the boundary between the charge density wave ($\delta n>0$) and the normal phase (an absence of order with $\delta n=0$). (b) Current and entropy per particle plotted against temperature where the quantum anomalous Hall effect is strongest, $V_1=1.33$. The kink in the entropy shows a first-order phase transition from the topological Mott insulator to a charge density wave.