Enhanced Rashba effect for hole states in a quantum dot

The effect of Rashba spin-orbit (SO) interaction on the hole states in a quantum dot is studied in the presence of an external magnetic field. We demonstrate here that the Rashba SO coupling has a profound effect on the energy spectrum of the holes revealing level repulsions between the states with the same total momentum. We also show that the resulting spin-orbit gap is much larger than the corresponding one for the electron energy levels in a quantum dot. Inter-hole interactions only marginally reduce the spin-orbit gap. This enhanced Rashba effect would manifest itself in the tuneling current which depends on the spin-orbit coupling strength. Introduction. – Semiconductor quantum dots are the nanoscale zero-dimensional systems with discrete energy levels, much like in atoms (and hence the popular name, artificial atoms [1]). They have one great advantage that their shape and the number of electrons in those systems can be controlled externally and as a result, they have been the subject of intense research in recent years. They are particularly promising as components of futuristic devices for quantum information processing [2] and for coherent spin transport [3]. The spin states of these systems are ideal for applications because of their relative insensitivity to electrical noise in a device environment [4]. One proposed mechanism for coherent spin manipulation in quantum nanostructures is via the Rashba spin-orbit (SO) coupling [5, 6]. The SO interaction can arise in a quantum dot due to confinement and lack of inversion symmetry of the nanostructure which creates a local electric field perpendicular to the electron plane [7, 8]. The SO coupling strength can be varied by changing the asymmetry of the quantum structure with an external electric field. The magnetic field effects on the properties of lowdimensional systems, such as quantum wells and quantum dots with the Rashba interaction has been reported in experiments [9] and theory [10]. In our work on Rashba effects in electron dots [11], we found multiple level crossings and level repulsions that resulted from the interplay between the Zeeman and the SO couplings. Level anticrossings observed in quantum nanostructures have been attributed to the presence of SO coupling in those systems [12]. However, studies of the Rashba effect on quantum dots as yet, are limited only to the case of electrons as charge carriers. The importance of holes in semiconductor spintronics is well documented [13] in the literature. Some theoretical results about hole states in quantum dots have been reported earlier [14–16]. Experiments on hole levels in quantum dots have also been reported recently [17–19]. Rashba effect is expected to be stronger in p-type quantum wells [20]. Interestingly, for holes the Dresselhaus effect (due to bulk inversion asymmetry) is small compared to the Rashba effect [21]. In this Letter, we report on our studies involving the hole levels in planar quantum dots with Rashba SO interactions. We find that the SO gap at the anticrossings of the energy levels is much larger than those for the case of electrons. Inter-particle interactions (Coulomb type) reduce the gap somewhat, but it is still orders of magnitude larger than the corresponding ones for electrons. The Rashba effect for holes is different from that for the electrons. It is well known that the electron Rashba coefficient increases nearly linearly with an increase of the electric field. But the two-dimensional heavy hole systems in single heterostructures exhibit a decrease of Rashba SO splitting with an increase of the electric field [22]. The effect for a two-dimensional light hole system is however the same as that for the electrons. Determination of the Rashba coefficient for holes was reported for the InP quantum wires [23] where the band mixing was taken into account. The result was that as the electric field increases, the hole Rashba coefficient increases at first, then