Position-dependent mass with modulated velocity in 1-D heterostructures

Abstract

We study the ($1+1$)-dimensional Dirac equation for charge carriers in some heterostructures. Both, the mass profile and the modulated Fermi velocity of the quasi-particle, are considered position dependent. We have used mass and Fermi velocity that admit only approximate analytical solutions. However, we also calculate numerically the \textit{exact} energy spectra of each heterostructure through the corresponding reflection coefficient poles.

Dirac equation in curved spacetime: the role of local Fermi velocity

“…Confirmations in this direction also come from spectroscopy experiments [30][31][32][33]. In addition, the need for a local Fermi velocity (LFV) emerges from the electronic transport in two-dimensional strained Dirac materials [34]; the latter feature has triggered a wide range of researches [35][36][37][38][39][40][41].…”

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

“…For the two-dimensional materials, their Fermi velocity is independent of momentum and can be controlled by adjusting the interaction between electrons, the curved graphene, different substrates, or applying external strain [8,[14][15][16][17][18][19][20][21][22][23][24][25][26]. Recently, the position-dependent Fermi velocity structures such as velocity wells or barriers have attracted extensive research interest [27][28][29][30][31][32][33][34][35][36]. In this structure, the transport properties in the Fermi velocity modulated region are very different from the traditional Klein tunneling controlled by electromagnetic fields.…”

“…In refs. [27][28][29][30][31], the Fermi velocities are assumed to approach zero or 50001-p1 infinite for ease of solution. However, the Fermi velocity equal to a non-zero finite value is more valuable to study in Dirac materials.…”

“…It is hard to discriminate the effect of the Fermi velocity modulation from an electrostatic potential on the bound state formation. Furthermore, some unphysical Fermi velocity distribution cases are considered, such as the Fermi velocity approaches zero or is infinitely large at infinity [27][28][29][30][31].…”