Electronic and spin properties of hole point contacts

We have studied theoretically the effect of a tuneable lateral confinement on two-dimensional hole systems realised in III-V semiconductor heterostructures. Based on the 4 × 4 Luttinger description of the valence band, we have calculated quasi-onedimensional (quasi-1D) hole subband energies and anisotropic Landé g-factors. Confinement-induced band mixing results in the possibility to manipulate electronic and spin properties of quasi-1D hole states over a much wider range than is typically possible for confined conduction-band electrons. Our results are relevant for recent experiments where source-drain-bias spec-troscopy was used to measure Zeeman splitting of holes in p-type quantum point contacts. 1 Introduction Low-dimensional hole systems provide an interesting playground for engineering spin properties of charge carriers. In typical semiconductors, quantum confinement affects the physical properties of holes much more strongly than those of electrons [1]. This is because subband quantisation causes an energy splitting between heavy-hole (HH) and light-hole (LH) bands, and modifies their residual coupling. The Zeeman splitting of 2D hole systems for in-plane magnetic fields is a good example; it is suppressed for HH states [2] but doubled for LH states [3]. On the most basic level, this behaviour can be understood by noting that the heavy and light-hole bands belong to a quadruplet of states having total angular momentum j = 3/2. More detailed theory [4] based on the Luttinger description [5] of the valence band provides realistic values for the Landé g-factors of 2D holes, including the in-plane Zeeman-splitting anisotropy in low-symmetry heterostructures. The competition between confinement-induced band mixing and HH-LH energy splitting also determines the physical properties of hole quantum wires [6], dots [7], and localised acceptor states [8]. Recently, transport measurements in hole wires [9] and point contacts [10] have become possible, opening up new possibilities to investigate electronic and spin properties of quasi-1D hole systems. Here we investigate the confinement dependence of hole g-factors in quasi-1D structures, mapping the crossover between the weakly confined 2D and symmetrically confined 1D limits.