FIG. 19.

(a) Brillouin zone and Dirac points Q_± for the brick-wall lattice of Fig. 10. (b) When the degeneracy is lifted by introducing an energy offset between the A and B sites, the subbands are topologically trivial. For the lowest band, the Berry curvature has opposite signs in the vicinity of Q_±. The anomalous velocity (white arrows) thus has opposite chirality at these points. (c) Lifting of degeneracy obtained by adding complex next-nearest-neighbor (NNN) couplings (Haldane, 1988). The Berry curvature then keeps a constant sign over the BZ, and the anomalous velocity has the same chirality at both points. Adapted from Jotzu et al., 2014.