Position-dependent mass Dirac equation and local Fermi velocity

Abstract

We present a new approach to study the one-dimensional Dirac equation in the background of a position-dependent mass m. Taking the Fermi velocity vf to be a local variable, we explore the resulting structure of the coupled equations and arrive at an interesting constraint of m turning out to be the inverse square of vf. We address several solvable systems that include the free particle, shifted harmonic oscillator, Coulomb and nonpolynomial potentials. In particular, in the supersymmetric quantum mechanics context, the upper partner of the effective potential yields a new form for an inverse quadratic functional choice of the Fermi velocity.

Non-hermitian Dirac Hamiltonian in the presence of local Fermi velocity

“…We let the Fermi velocity to be space-dependent [28,33] for the (1+1)-dimensional hererostructure. In other words, we treat the Fermi velocity to be a local variable (LFV).…”

“…ξ 1 and ξ 2 also satisfy another pair of coupled equations but can be uncoupled easily following the approach of [28]. For our need, we write down the second-order differential equation for ξ 1 (z)…”

“…Mixing of PT -symmetric vector, scalar and pseudoscalar potentials for time-independent Dirac equation has pointed to the existence of real energies in the system [27]. We investigated a (1+1)-dimensional position-dependent mass (PDM) Dirac equation by considering the effects of a local Fermi velocity (LFV) to generate a large class of associated solvable potentials [28]. The idea of LFV was also explicitly used in [29].…”

So (2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation

“…Tunneling spectroscopy experiments also confirmed this issue [32][33][34]. From a theoretical side, the necessity of a local Fermi velocity (LFV) was subsequently examined in [35][36][37][38], which included a study on the electronic transport in two-dimensional strained Dirac materials [39].…”

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.…”