Volkov-Pankratov states in a driven semimetal for a generic interface

Volkov-Pankratov states are nontopological massive bound states which generally arise across the smooth interface between two adjacent regions of a two-band semimetal, over which a gap parameter changes sign smoothly. In this work, we show that these modes can be engineered even for a generic smooth interface without any sign inversion. We consider threefold and twofold topological semimetals in which two adjacent regions are illuminated by light with different phases. We show that the interface can exhibit an asymmetric Rosen-Morse potential well for a certain parameter regime even without any sign change of the gap term. Such a quantum well can host a number of Volkov-Pankratov states. We also note that even in a two-band two-dimensional semimetal like graphene, the Volkov-Pankratov states can emerge if one induces a momentum shift rather than opening a gap. Finally, we discuss the transport signatures over those interfacial quantum wells. We note that although the Ramsauer-Townsend effect appears over the symmetric-type P & ouml;schl-Teller potential well, this effect is absent over an asymmetric Rosen-Morse potential well. We reveal that a transition from a unit transmission to a unit reflection can be achieved by just controlling light parameters in a periodically driven graphene. We observe that the unit reflection phenomenon is direction sensitive; i.e., only incoming electrons from one particular side (left or right) can be perfectly reflected back without any transmission.