We develop a theory for the spin-echo dynamics of a heavy hole in a quantum dot, accounting for both hyperfine- and electric-field-induced fluctuations. We show that a moderate applied magnetic field can drive this system to a motional-averaging regime, making the hyperfine interaction ineffective as a decoherence source. Furthermore, we show that decay of the spin-echo envelope is highly sensitive to the geometry. In particular, we find a specific choice of initialization and π-pulse axes which can be used to study intrinsic hyperfine-induced hole-spin dynamics, even in systems with substantial electric-field-induced dephasing. These results point the way to designed hole-spin qubits as a robust and long-lived alternative to electron spins.

Summary. -We review recent theoretical results for hole spins influenced by spin-orbit coupling and Coulomb interaction in two-dimensional quantum wells as well as the decoherence of single hole spins in quantum dots due to hyperfine interaction with surrounding nuclear spins. After reviewing the different forms of spin-orbit coupling that are relevant for electrons and heavy holes in III-V semiconductor quantum wells, we illustrate the combined effect of spin-orbit coupling and Coulomb interactions for hole systems on spin-dependent quasiparticle group velocities. We further analyze spin-echo decay for a single hole spin in a nuclear-spin bath, demonstrating that this decoherence source can be controlled in these systems by entering a motional-averaging regime. Throughout this review, we emphasize physical effects that are unique to hole spins (rather than electrons) in nanoscale systems.

We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlettriplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical results for spin-echo envelope modulations of arbitrary spin components of a hole spin in a quantum dot, going beyond a standard secular approximation. We account for general dynamics in the presence of a pure-dephasing process and identify a crossover timescale at which it is again advantageous to initialize the qubit in the non-interacting ground state. Finally, we consider a general two-axis dynamical decoupling sequence and determine initial conditions that maximize purity, minimizing leakage to the environment.

We calculate differential and integrated cross sections for the Compton interaction as well as mass attenuation (), mass energy-transfer (), and mass energy-absorption () coefficients, within the relativistic impulse approximation (RIA) using Compton profiles (CPs) obtained from unrestricted Hartree–Fock electron densities. We investigate the impact of using molecular as opposed to atomic CPs on dosimetric photon interaction coefficients for air, water and graphite, and compare our cross sections to the simpler Waller–Hartree (WH) and Klein–Nishina (KN) formalisms. We find that differences in and resulting from the choice of CPs within the RIA are small relative to the differences between the RIA, WH, and KN calculations. Surprisingly, although the WH binding corrections seem accurate when considering , there are significant discrepancies between the WH and RIA results when we look at . The WH theory can differ substantially from the predictions of KN and the RIA in the tens of keV range (e.g. 6%–10% at 20 keV), when Compton scattering becomes the dominant interaction mechanism. For lower energies, the disagreement further grows to about one order of magnitude at 1 keV. However, since the photoelectric effect transfers more energy than the Compton interaction in the tens of keV range and below, the differences in the total values resulting from the choice of Compton models (KN, WH, or RIA) are not larger than 0.4%, and the differences between WH and the other two theories are no longer prominent.

The relativistic binary-encounter-dipole (RBED) model for electron-impact ionization of atoms combines classical binary-encounter theory and the asymptotic dipole interaction, which is based on the plane-wave Born approximation, with the only non-trivial ingredient being the optical oscillator strength (OOS). Due to the difficulty of obtaining accurate OOSs, the performance of the RBED model has so far not been fully assessed. In the present work we compare RBED inner-shell ionization cross sections (total and differential) of neutral atoms evaluated using three types of OOSs, namely an empirical power-law OOS, analytical hydrogenic OOSs and ab initio OOSs calculated numerically from self-consistent atomic potentials. We find that, compared to the distorted-wave Born approximation (DWBA), the RBED with either hydrogenic or numerical OOSs generally yields more accurate total cross sections (TCSs) than the RBED with the power-law OOS, especially for the most tightly bound shells. In the highly relativistic limit the RBED model does not recover the Bethe asymptotic behavior because of its different energy-dependent prefactor, hence we investigate an alternative prefactor which restores the correct Bethe asymptote. Finally, we suggest multiplying the RBED differential cross sections (DCSs) by the ratio of DWBA to RBED TCSs and verify that this renormalization improves the agreement with the DWBA DCSs.