Figure 3: Surface states and quantum oscillations in Dirac SMs.
From: Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals
Viewing the Dirac SM as two superposed copies of a Weyl SM with opposite chiralities suggests two sets of surface arcs, labelled R (blue) and R′ (red), that curve in opposite directions and meet at the bulk Weyl nodes with a discontinuous kink (a,b). Crystal symmetry-breaking perturbations mix R and R′, but the corner/‘kink’ feature in (b) is perturbatively stable against this effect (vertical dashed lines). A sufficiently strong surface potential may reconstruct the surface arcs into a ‘conventional’ surface state (c), but cannot remove it entirely due to bulk topological contraints. Then for sufficient bulk doping, a surface state initially near the Γ point will intersect the bulk Fermi pockets as shown in (d) for two different bulk Fermi wavevectors kF and 
. The surface states exhibit spin–momentum locking as indicated schematically by the small black arrows in (b–d). Strong magnetic fields mix the R and R' chiral LLs in the bulk, and lead to a crossover from magnetic orbits through the bulk at low fields to orbits confined near each surface at high fields with two possible intermediate crossover behaviours (e,f).
