Efficient computation of Wigner–Eisenbud functions

Computation of Nanowire Transport Properties

“…(5) gives the complete set of WEFs representing the wavefunction inside the scattering region. 1, 5,9 Separating variables in Eq. (5), r z → r z , and applying the boundary conditions, leads to a complete basis for constructing the WEFs.…”

“…The 1D WEFs, l z , arise as solutions to the scaled Schrödinger equation, 9 − l z + V z l z = E l l z (1) over −1 1 with Neumann boundary conditions l ±1 = 0. To compute l z we write…”

“…9 The Fourier-Bessel basis (9) Supplementary code has been developed to allow users to input arbitrary axial potentials. 9 Realistic potentials are asymmetrical and irregular. Figures 3 and 4 display the 1D and 2D WEFs for a semiconductor heterostructure potential with several layers.…”

“…8 Evaluating Wigner-Eisenbud Functions (WEFs) and their eigenenergies is the first step of the procedure using the R-matrix formalism, as described in Ref. [9]. The second step is to construct the scattering states which contain all the information necessary to calculate the reflection and transmission coefficients.…”

Ballistic electron transport in wrinkled superlattices

“…For the present study, it was chosen as the simulation environment for quantum transport because of its numerical efficiency, which is also described in [25]. This numerical speed gain is obtained by separating the problem into an energy-independent part that solves the Wigner-Eisenbud eigenvalue problem and a second one, in which the transmission is computed at each energy value.…”