Scattering states of a particle, with position-dependent mass, in a double heterojunction

Abstract

The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain -when the region within the heterojunctions is described by a non Hermitian PT symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian PT symmetric systems -viz., left / right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed.

Scattering states of a particle, with position-dependent mass, in a ${{{\mathcal P}{\mathcal T}}}$-symmetric heterojunction

“…Pdem formalism is extremely important in describing the electronic and transport properties of quantum wells and quantum dots, impurities in crystals, He-clusters, quantum liquids, semiconductor heterostructures, etc. In a recent work, we obtained the exact analytical scattering solutions of a particle (electron or hole) in a semiconductor double heterojunction -potential well / barrier -where the effective mass of the particle varies with position inside the heterojunctions [27]. It was observed that the spatial dependence on mass within the well / barrier introduces a nonlinear component in the plane wave solutions of the continuum states.…”

“…[27], in an attempt to extend the pdem formalism further into the complex domain. Instances of such attempts are found in other works as well -e.g., the problem of relativistic fermions subject to a PT symmetric potential in the presence of position-dependent mass was studied in ref.…”

Analytical Solution of the Position Dependent Mass Schr\"{o}dinger Equation With a Hyperbolic Tangent Potential

“…This method is also extend to mass-variable Schrödinger equation (see [1], [10], [25], [24]) and [19]). This equation is used to describe for example the dynamics of semiconductor systems where the effective mass of the electrons and holes vary with the position (see [15] and [23]).…”

Exact solutions of the position-dependent-effective mass Schrödinger equation

“…The concept of a position-dependent effective mass (PDEM) in the Schrödinger equation has gained much interest [1][2][3][4][5][6][7] in the last two decades, because of its applications in several fields of physics [8][9][10][11][12][13][14] from semiconductors 15,16 to quantum fluids. 17,18 For example, the transport proprieties in semiconductors, 19 the effective interaction in nuclear physics, 20 and the dynamical properties of a neutron superfluid in a neutron star 21 are described by the PDEM Schrödinger equation.…”

“…[42][43][44] We can cite the point-canonical transformation, 24,25,45,46 Nikiforov-Uvarov (NU) method [45][46][47][48][49] Green's function, 50 the Heun equation, 51 the potential algebra 52 and the supersymmetric approach 53,54 as analytical methods to generate solutions for the PDEM Schrödinger equation. However, the exact solutions are limited to a small set of systems.…”