Effect of boundary conditions on the behavior of Bloch electrons

Abstract

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Determination of ab initio polarizabilities of polymers: Application to polyethylene and polysilane

“…However, as shown by Churchill and Holmstrom [19,20], serious difficulties arise in imposing realistic periodic boundary conditions to solve the one-electron eigenvalue equation; under the boundary conditions commonly used in treating the zero-field case (e.g., Born-Khan boundary conditions), this equation either leads to physically inconsistent results or, still worse, has no solution at all. This difficulty is a consequence of the pathological nature of the perturbing term, -F * r. On an other hand the periodic character of the perturbation is not guaranteed under the nonperiodic linear external perturbation, which would rule out the use of field-perturbed Bloch orbitals.…”

Quantum Transport in Semiconductor Nanostructures

“…A necessary condition is that the field be sufficiently weak that tunneling across the gap does not occur. 510,511,512,513 The wave number increases in time according to k = eE/h in an electric field E. The time interval between two Bragg reflections is 2π/a k = h/eaE. The oscillatory current thus would have a frequency ∆V e/h, with ∆V = aE the electrostatic potential drop over one unit cell.…”

Intersubband electroabsorption spectra of semiconductor quantum wells

“…It will be canceled by the ͱL factor in the density of states as L→ϱ. The DOS under electric field is given by 13,15 N͑E ͒ϭ…”

“…15 is for a large confining box with an infinite potential barrier that does not include a quantum well near the center. However, with the presence of a quantum well near the center ͑as considered in the present case͒, the DOS will be changed by a finite amount ⌬(E), which is independent of the size of the large confining box.…”