Universal behavior of electron g -factors in semiconductor nanostructures

Abstract

We combine analytic developments and numerical tight-binding calculations to study the evolution of the electron g-factors in homogeneous nanostructures of III-V and II-VI semiconductors. We demonstrate that the g-factor can be always written as a sum of bulk and surface terms. The bulk term, the dominant one, just depends on the energy gap of the nanostructure but is otherwise isotropic and independent of size, shape, and dimensionality. At the same time, the magnetic moment density at the origin of the bulk term is anisotropic and strongly dependents on the nanostructure shape. The physical origin of these seemingly contradictory findings is explained by the relation between the spin-orbit-induced currents and the spatial derivatives of the electron envelope wave function. The tight-binding calculations show that the g-factor versus energy gap for spherical nanocrystals can be used as a reference curve. In quantum wells, nanoplatelets, nanorods, and nanowires, the g-factor along the rotational symmetry axis can be predicted from the reference curve with a good accuracy. The g-factors along nonsymmetric axes exhibit more important deviations due to surface contributions but the energy gap remains the main quantity determining their evolution. The importance of surface-induced anisotropies of the g-factors is discussed.

Origin of Two Larmor Frequencies in the Coherent Spin Dynamics of Colloidal CdSe Quantum Dots Revealed by Controlled Charging

“…26 The size dependence of the g1 factor agrees well with the model calculations of the electron g factor in CdSe QDs. 4,27,28 These calculations imply that the g1 electron is exposed to the QD confinement potential only and, therefore, the electron wavefunction is centered in the QD. n-type photodoping in the presence of provides resident electrons in the QD core.…”

Mesoscopic g-factor renormalization for electrons in III-V interacting nanolayers

“…Due to the increasing interest in spintronics [6] and in new schemes for quantum computation, including the detection of Majorana fermions [7], much attention has been given lately to the renormalization of the electron g factor in semiconductor nanostructures [8][9][10][11][12][13][14][15][16][17][18]. The mesoscopic confining potential in semiconductor nanostructures further renormalizes the bulk effective g factor (already renormalized from the bare value 2) and introduces extra anisotropies, transforming scalar g factors into tensors.…”

Robustness of states at the interface between topological insulators of opposite spin Chern number

“…In each supercell, we introduce the disorder as a random on-site potential with a Gaussian distribution of a standard deviation σ = 10 meV. The disorder is therefore periodic, the wave vector k is still a good quantum number, the width of the Brillouin zone has just been reduced by a factor 5. σ being smaller than the width of the topological gaps, the disorder is not sufficiently strong to destroy the topological order [43,44]. For the sake of clarity, all figures in this section only show band structures in the energy region corresponding to the second (central) topological gap of the bulk.…”