We study Zeeman splitting of zone-center subband edges in a cylindrical hole wire subject to a magnetic field parallel to its axis. The g-factor turns out to fluctuate strongly as a function of wire-subband index, assuming values that differ substantially from those found in higher-dimensional systems. We analyze the spin properties of hole-wire states using invariants of the spin-3/2 density matrix and find a strong correlation between gfactor value and the profile of hole-spin polarization density. Our results suggest possibilities for confinement engineering of hole spin splittings. PACS numbers: 73.21.Hb, 72.25.Dc, 71.70.Ej Spin splitting of charge carriers in semiconductors has been a focus of recent research interest, partly because it may form the basis for the new paradigms of spin-based electronics and quantum information processing. 1 Besides such possible applications, intriguing fundamental-science questions motivate the study of charge carriers' spin properties. In particular, the quantum-mechanical coupling between spin and orbital degrees of freedom enables a host of, sometimes counterintuitive, mechanisms for manipulating spins in nanostructures. 2 As states in the valence band of a typical semiconductor are subject to a strong spin-orbit coupling, hole spin splittings will be highly tunable by geometrical and quantumconfinement effects. Large anisotropies of hole g-factors in quantum wells, 3 point contacts, 4 quantum dots, 5 and localized acceptor states 6 provide pertinent examples. The origin of such peculiar hole-spin properties can be traced to the fact that quasiparticles from the top-most valence band are characterized by total angular momentum (spin) 3/2. (Conductionband electrons are spin-1/2 particles like electrons in vacuum.) Although spin is an intrinsically quantum degree of freedom, it has been possible to rationalize spin-1/2 physics largely in terms of a magnetic-dipole analogy. This classical-physicsinspired vehicle for our understanding succeeds because any spin-1/2 density matrix is fully characterized 7 by the (trivial) particle density and a dipole moment associated with spinpolarization. In contrast, the spin-3/2 density matrix has two more invariants, a quadrupole and an octupole moment. 8 As a surprising implication, magnetic fields do not always induce a spin polarization in two-dimensional (2D) hole systems. 9 Our theoretical study presented here reveals the drastic influence of a quantum-wire confinement on spin-3/2 physics. Figure 1 shows universal results for the Landé g-factors of low-lying subband edges in cylindrical quantum wires subject to a parallel magnetic field. Two surprising features are apparent. First, g * is seen to assume unusual values. Considering the wire axis to be a natural quantization axis for hole spin and remembering that spin-3/2 projection eigenvalues are ±3/2 and ±1/2, we would expect to find only 6κ and 2κ as possible g-factors. (Here κ is the hole g-factor in the bulk material.) 10 In Fig. 1, quite different numbers are found. Second, ...

We have analyzed theoretically the Zeeman splitting of hole-quantum-wire subband edges. As is typical for any bound state, their g factor depends on both an intrinsic g factor of the material and an additional contribution arising from a finite bound-state orbital angular momentum. We discuss the quantum-confinement-induced interplay between bulk-material and orbital effects, which is nontrivial due to the presence of strong spin-orbit coupling. A compact analytical formula is provided that elucidates this interplay and can be useful for predicting Zeeman splitting in generic hole-wire geometries.

We present a detailed theoretical study of the electronic spectrum and Zeeman splitting in hole quantum wires. The spin-3/2 character of the topmost bulk-valence-band states results in a strong variation of subband-edge g factors between different subbands. We elucidate the interplay between quantum confinement and heavy-holelight-hole mixing and identify a certain robustness displayed by low-lying hole-wire subband edges with respect to changes in the shape or strength of the wire potential. The ability to address individual subband edges in, e.g., transport or optical experiments enables the study of holes states with nonstandard spin polarization, which do not exist in spin-1/2 systems. Changing the aspect ratio of hole wires with rectangular cross-section turns out to strongly affect the g factor of subband edges, providing an opportunity for versatile in-situ tuning of hole-spin properties with possible application in spintronics. The relative importance of cubic crystal symmetry is discussed, as well as the spin splitting away from zone-center subband edges.