Fig. 5: Long-wavelength (k → 0) velocity of the bands across all velocity regimes for half-dephasing (a) ϕ = 0 and (b) ϕ = π/4.

Continuous lines and circles are for α = 0.4, whereas the dashed and dotted lines are for α = 0.1, demonstrating the shrinking of the velocity range over which the interaction with the screw is strongest. Note that for ϕ = 0 the screw interacts significantly only with the forward bands, whereas the opposite occurs for ϕ = π/4. Note that the slopes of RHP and LHP bands are always degenerate in the k → 0 limit, as a consequence of PT symmetry. Shaded regions correspond to velocity regimes comprised between the exceptional points \({{{\Omega }}}_{crit}^{-}\) and \({{{\Omega }}}_{crit}^{+}\) (for the α = 0.4 case), while the critical point \({{{\Omega }}}_{crit}^{0}\) (also for α = 0.4), common to both the ϕ = 0 and ϕ = π/2 cases, is marked as a black, dashed line.