The condensed matter realizations of gaped and gapless materials where the low-energy physics reproduce the Dirac equation show surprising surface states when inverted and normal gaps are in contact. These surface states are spin-momentum locked, are usually more metallic than the bulk states and are topologically protected. Such topological surface states (TSS) have been identified by angle resolved photoemission spectroscopy (ARPES), scanning tunneling spectroscopy (STM) and transport.

Along with these TSS the same experiments indicate the existence of massive surface states (MSS) attached to both the valence and conduction bands and that are influenced by band bending. One explanation for this effect is that one observes the quantum-well states associated to the lower (resp. higher) part of the conduction and valence bands due to downward (resp. upward) band-bending. In this description the gaped surface states are a consequence of band bending.

In this talk we will discuss another origin of these massive surface states, as a consequence of a finite-sized interface between the inverted- and normal-gaped materials. The role of band bending is to delocalize and reduce the energy of these states which allows for their manipulation.