Fig. 10: Local density of states and valley Hall marker in a finite flake.
From: Quantized valley Hall response from local bulk density variations
a, b The local density of states discriminated by sublattice ρα(ε, r) [see Eq. (22)] for τ > 0 and τ < 0, respectively. The energy has been taken to be ε = μF = 0.1 t and ∣τ∣ = 0.07. The terminations have been chosen so as to alternate between bearded and zigzag-like edges. We exploit the mirror symmetry of the flake with respect to the y = yc axis to plot separately half of the A-sublattice (the upper part) and half of the B-sublattice (the lower part). A corresponding cut of the panels along \({{{{{{{\bf{r}}}}}}}}={x}_{c}\hat{{{{{{{{\bf{x}}}}}}}}}+y\hat{{{{{{{{\bf{y}}}}}}}}}\) is shown to the left, where we have restored the entire spatial distribution. c, d The corresponding local marker \({{\mathfrak{S}}}_{\alpha }({{{{{{{\bf{r}}}}}}}})\) differentiated by sublattice [see Eq. (23)].
