Bound states of Dirac fermions in the presence of a Fermi velocity modulation

Abstract We investigate the effect of a position-dependent Fermi velocity on the electronic properties of two-dimensional Dirac materials. A physical Fermi velocity distribution, which approaches a finite value at infinity and experiences a modulation near x = 0, is considered. Such a position-dependent Fermi velocity could be realized in the curved graphene or by applying strain. It is shown that the bound states are absent in the presence of a pure Fermi velocity modulation without an electrostatic potential well. However, an extra electrostatic potential modulation could produce the bound states. A set of discrete energy level spectrum and the corresponding wave functions are obtained by solving the Dirac equation exactly. Local probes such as scanning tunnel microscopy should be able to observe the predicted bound states in two-dimensional materials.