Rapid Transition of the Hole Rashba Effect from Strong Field Dependence to Saturation in Semiconductor Nanowires

Role of anisotropic confining potential and elliptical driving in dynamics of a Ge hole qubit

The squeezing of a Ge planar quantum dot enhances the Rabi frequency of electric dipole spin resonance by several orders of magnitude due to a strong Direct Rashba spin-orbit interaction in such geometries (Boscoet al2021Phys. Rev.B104115425). We investigate the geometric effect of an elliptical (squeezed) confinement and its interplay with the polarization of driving field in determining the Rabi frequency of a heavy-hole qubit in a planar Ge quantum dot. To calculate the Rabi frequency, we consider only thep-linear SOIs viz. electron-like Rashba, hole-like Rashba and hole-like Dresselhaus which are claimed to be the dominant ones by recent studies on planar Ge heterostructures. We derive approximate analytical expressions of the Rabi frequency using a Schrieffer-Wolff transformation for small SOI and driving strengths. Firstly, for an out-of-plane magnetic field with magnitudeB, we get an operating region with respect toB, squeezing and polarization parameters where the qubit can be operated to obtain 'clean' Rabi flips. On and close to the boundaries of the region, the higher orbital levels strongly interfere with the two-level qubit subspace and destroy the Rabi oscillations, thereby putting a limitation on squeezing of the confinement. The Rabi frequency shows different behaviour for electron-like and hole-like Rashba SOIs. It vanishes for right (left) circular polarization in presence of purely electron-like (hole-like) Rashba SOI in a circular confinement. For both in- and out-of-plane magnetic fields, higher Rabi frequencies are achieved for squeezed configurations when the ellipses of polarization and the confinement equipotential have their major axes aligned but with different eccentricities. We also deduce a simple formula to calculate the effective heavy hole mass by measuring the Rabi frequencies using this setup.

Spin-photon interaction in a nanowire quantum dot with asymmetrical confining potential

The electron (hole) spin-photon interaction is studied in an asymmetrical InSb (Ge) nanowire quantum dot. The spin-orbit coupling in the quantum dot mediates not only a transverse spin-photon interaction, but also a longitudinal spin-photon interaction due to the asymmetry of the confining potential. Both the transverse and the longitudinal spin-photon interactions have non-monotonic dependence on the spin-orbit coupling. For realistic spin-orbit coupling in the quantum dot, the longitudinal spin-photon interaction is much (at least one order) smaller than the transverse spin-photon interaction. The order of the transverse spin-photon interaction is about 1 nm in terms of length|zeg|, or 0.1 MHz in terms of frequencyeE0|zeg|/hfor a moderate cavity electric field strengthE0=0.4V m-1.

Two-band description of the strong 'spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire

The low-energy effective Hamiltonian of the strong 'spin'-orbit coupled one-dimensional hole gas in a cylindrical Ge nanowire in the presence of a strong magnetic field is studied both numerically and analytically. Basing on the Luttinger-Kohn Hamiltonian in the spherical approximation, we show this strong 'spin'-orbit coupled one-dimensional hole gas can be accurately described by an effective two-band HamiltonianHef=ℏ2kz2/(2mh∗)+ασxkz+gh∗μBBσz/2, as long as the magnetic field is purely longitudinal or purely transverse. The explicit magnetic field dependent expressions of the 'spin'-orbit couplingα≡α(B)and the effectiveg-factorgh∗≡gh∗(B)are given. When the magnetic field is applied in an arbitrary direction, the two-band Hamiltonian description is still a good approximation.

Anisotropic g-Factor and Spin-Orbit Field in a Germanium Hut Wire Double Quantum Dot

Holes in nanowires have drawn significant attention in recent years because of the strong spin-orbit interaction, which plays an important role in constructing Majorana zero modes and manipulating spin-orbit qubits. Here, from the strongly anisotropic leakage current in the spin blockade regime for a double dot, we extract the full g-tensor and find that the spin-orbit field is in plane with an azimuthal angle of 59° to the axis of the nanowire. The direction of the spin-orbit field indicates a strong spin-orbit interaction along the nanowire, which may have originated from the interface inversion asymmetry in Ge hut wires. We also demonstrate two different spin relaxation mechanisms for the holes in the Ge hut wire double dot: spin-flip co-tunneling to the leads, and spin-orbit interaction within the double dot. These results help establish feasibility of a Ge-based quantum processor.

Uncovering and tailoring hidden Rashba spin-orbit splitting in centrosymmetric crystals

Hidden Rashba and Dresselhaus spin splittings in centrosymmetric crystals with subunits/sectors having non-centrosymmetric symmetries (the R-2 and D-2 effects) have been predicted theoretically and then observed experimentally, but the microscopic mechanism remains unclear. Here we demonstrate that the spin splitting in the R-2 effect is enforced by specific symmetries, such as non-symmorphic symmetry in the present example, which ensures that the pertinent spin wavefunctions segregate spatially on just one of the two inversion-partner sectors and thus avoid compensation. We further show that the effective Hamiltonian for the conventional Rashba (R-1) effect is also applicable for the R-2 effect, but applying a symmetry-breaking electric field to a R-2 compound produces a different spin-splitting pattern than applying a field to a trivial, non-R-2, centrosymmetric compound. This finding establishes a common fundamental source for the R-1 effect and the R-2 effect, both originating from local sector symmetries rather than from the global crystal symmetry per se.