Valley and spin splittings in PbSe nanowires

Abstract

We use an empirical tight-binding approach to calculate electron and hole states in [111]-grown PbSe nanowires. We show that the valley-orbit and spin-orbit splittings are very sensitive to the atomic arrangement within the nanowire elementary cell and differ for [111]-nanowires with microscopic $D_{3d}$, $C_{2h}$ and $D_{3}$ symmetries. For the nanowire diameter below 4 nm the valley-orbit splittings become comparable with the confinement energies and the $\boldsymbol{k}\cdot\boldsymbol{p}$ method is inapplicable. Nanowires with the $D_{3}$ point symmetry having no inversion center exhibit giant spin splitting $E = \alpha k_z$, linear in one-dimensional wave vector $k_z$, with the constant $\alpha$ up to 1 eV$\cdot$\AA.Comment: 15 pages, 9 figure

Shape effect on the valley splitting in lead selenide nanowires

“…4 we show the local density of states in reciprocal space (kLDOS, see Refs. [27,42] for details). For quantitative description of the valley coupling we introduce "valley admixture"…”

“…Without the valley coupling all the L valleys are independent and their energy spectra are fully determined by mass anisotropy [21] and quantum confinement [37]. The latter we associate with a set of quantum numbers q, well established for cylindrical PbSe nanowires [27]. It is important, that sets of states with a certain q (valley multiplets) are well distinguishable in the tight binding [27,38,39], where we consider the abrupt NW boundary as a perturbation that mix the valley states.…”

“…The latter we associate with a set of quantum numbers q, well established for cylindrical PbSe nanowires [27]. It is important, that sets of states with a certain q (valley multiplets) are well distinguishable in the tight binding [27,38,39], where we consider the abrupt NW boundary as a perturbation that mix the valley states.…”

“…It was shown [27] for cylindrical PbSe NWs and spherical quantum dots [26], that the valley splitting depends on diameter and the point symmetry of the considered structure. In this work we also take the shape of the NW into account.…”

Interplay of Bright Triplet and Dark Excitons Revealed by Magneto‐Photoluminescence of Individual PbS/CdS Quantum Dots

“…The procedure is outlined in more details in refs. [20,38]. In the present work the external magnetic field was introduced following the method of ref.…”