# Franziska Maier

## Contact

Department of Physics
University of Basel
Klingelbergstrasse 82
CH-4056 Basel, Switzerland
 office: 4.8 email: view address tel: +41 (0) 61 267 3746

## CV

 since 2015 Postdoctoral associate at the University of Basel in the group of Prof. Dr. Daniel Loss 2010 - 2014 PhD student at the University of Basel, under the supervision of Prof. Dr. Daniel Loss 2009 - 2010 Diploma thesis under the supervision of Prof. Dr. Guido Burkard 2004 - 2010 Undergraduate studies in Physics at the University of Konstanz

## Research Interests

• Spin relaxation and decoherence
• Holes in semiconductor nanostructures

## Publications

Show all abstracts.

 1. Electrically-tunable hole g-factor of an optically-active quantum dot for fast spin rotations Jonathan H. Prechtel, Franziska Maier, Julien Houel (University of Lyon), Anderas V. Kuhlmann, Arne Ludwig (Ruhr-University Bochum), Andreas D. Wieck (Ruhr-University Bochum), Richard J. Warburton, and Daniel Loss. Phys. Rev. B 91, 165304; arXiv:1412.4238. We report a large g factor tunability of a single hole spin in an InGaAs quantum dot via an electric field. The magnetic field lies in the in-plane direction x, the direction required for a coherent hole spin. The electrical field lies along the growth direction z and is changed over a large range, 100 kV/cm. Both electron and hole g factors are determined by high resolution laser spectroscopy with resonance fluorescence detection. This, along with the low electrical-noise environment, gives very high quality experimental results. The hole g factor ghx depends linearly on the electric field Fz,dghx/dFz=(8.3±1.2)×10−4 cm/kV, whereas the electron g factor gex is independent of electric field dgex/dFz=(0.1±0.3)×10−4 cm/kV (results averaged over a number of quantum dots). The dependence of ghx on Fz is well reproduced by a 4×4 k·p model demonstrating that the electric field sensitivity arises from a combination of soft hole confining potential, an In concentration gradient, and a strong dependence of material parameters on In concentration. The electric field sensitivity of the hole spin can be exploited for electrically driven hole spin rotations via the g tensor modulation technique and based on these results, a hole spin coupling as large as ∼1 GHz can be envisaged. 2. Majorana Fermions in Ge/Si Hole Nanowires Franziska Maier, Jelena Klinovaja (Harvard), and Daniel Loss. Phys. Rev. B 90, 195421; arXiv:1409.8645. We consider Ge/Si core/shell nanowires with hole states coupled to an s-wave superconductor in the presence of electric and magnetic fields. We employ a microscopic model that takes into account material-specific details of the band structure such as strong and electrically tunable Rashba-type spin-orbit interaction and g factor anisotropy for the holes. In addition, the proximity-induced superconductivity Hamiltonian is derived starting from a microscopic model. In the topological phase, the nanowires host Majorana fermions with localization lengths that depend strongly on both the magnetic and electric fields. We identify the optimal regime in terms of the directions and magnitudes of the fields in which the Majorana fermions are the most localized at the nanowire ends. In short nanowires, the Majorana fermions hybridize and form a subgap fermion whose energy is split away from zero and oscillates as a function of the applied fields. The period of these oscillations could be used to measure the dependence of the spin-orbit interaction on the applied electric field and the g factor anisotropy. 3. Strongly Interacting Holes in Ge/Si Nanowires Franziska Maier, Tobias Meng, and Daniel Loss. Phys. Rev. B 90, 155437; arXiv:1408.0631. We consider holes confined to Ge/Si core/shell nanowires subject to strong Rashba spin-orbit interaction and screened Coulomb interaction. Such wires can, for instance, serve as host systems for Majorana bound states. Starting from a microscopic model, we find that the Coulomb interaction strongly influences the properties of experimentally realistic wires. To show this, a Luttinger liquid description is derived based on a renormalization group analysis. This description in turn allows to calculate the scaling exponents of various correlation functions as a function of the microscopic system parameters. It furthermore permits to investigate the effect of Coulomb interaction on a small magnetic field, which opens a strongly anisotropic partial gap. 4. Nuclear Spin Diffusion Mediated by Heavy Hole Hyperfine Non-Collinear Interactions Hugo Ribeiro, Franziska Maier, and Daniel Loss. arXiv:1403.0490 We show that the hyperfine mediated dynamics of heavy hole states confined in neutral self- assembled quantum dots leads to a nuclear spin diffusion mechanism. It is found that the oftentimes neglected effective heavy hole hyperfine non-collinear interaction is responsible for the low degree of nuclear spin polarization in neutral quantum dots. Moreover, our results demonstrate that after pumping the nuclear spin state is left in a complex mixed state, from which it is not straightforward to deduce the sign of the Ising-like interactions. 5. Anisotropic g factor in InAs self-assembled quantum dots Robert Zielke, Franziska Maier, and Daniel Loss. Phys. Rev. B 89, 115438; arXiv:1311.0908. We investigate the wavefunctions, spectrum, and g factor anisotropy of low-energy electrons confined to self-assembled, pyramidal InAs quantum dots (QDs) subject to external magnetic and electric fields. We present the construction of trial wavefunctions for a pyramidal geometry with hard-wall confinement. We explicitly find the ground and first excited states and show the associated probability distributions and energies. Subsequently, we use these wavefunctions and 8-band $k\cdot p$ theory to derive a Hamiltonian describing the QD states close to the valence band edge. Using a perturbative approach, we find an effective conduction band Hamiltonian describing low-energy electronic states in the QD. From this, we further extract the magnetic field dependent eigenenergies and associated g factors. We examine the g factors regarding anisotropy and behavior under small electric fields. In particular, we find strong anisotropies, with the specific shape depending strongly on the considered subband. Our results are in good agreement with recent measurements [Takahashi et al., Phys. Rev. B 87, 161302 (2013)] and support the possibility to control a spin qubit by means of g tensor modulation. 6. Tunable g factor and phonon-mediated hole spin relaxation in Ge/Si nanowire quantum dots Franziska Maier, Christoph Kloeffel, and Daniel Loss. Phys. Rev. B 87, 161305(R); arXiv:1302.5027. We theoretically consider g factor and spin lifetimes of holes in a longitudinal Ge/Si core/shell nanowire quantum dot that is exposed to external magnetic and electric fields. For the ground states, we find a large anisotropy of the g factor which is highly tunable by applying electric fields. This tunability depends strongly on the direction of the electric field with respect to the magnetic field. We calculate the single-phonon hole spin relaxation times T1 for zero and small electric fields and propose an optimal setup in which very large T1 of the order of tens of milliseconds can be reached. Increasing the relative shell thickness or the longitudinal confinement length prolongs T1 further. In the absence of electric fields, the dephasing vanishes and the decoherence time T2 is determined by T2 = 2 T1. 7. Effect of strain on hyperfine-induced hole-spin decoherence in quantum dots Franziska Maier and Daniel Loss. Phys. Rev. B 85, 195323; arXiv:1203.3876. We theoretically consider the effect of strain on the spin dynamics of a single heavy-hole (HH) confined to a self-assembled quantum dot and interacting with the surrounding nuclei via hyperfine interaction. Confinement and strain hybridize the HH states, which show an exponential decay for a narrowed nuclear spin bath. For different strain configurations within the dot, the dependence of the spin decoherence time $T_2$ on external parameters is shifted and the non-monotonic dependence of the peak is altered. Application of external strain yields considerable shifts in the dependence of $T_2$ on external parameters. We find that external strain affects mostly the effective hyperfine coupling strength of the conduction band (CB), indicating that the CB admixture of the hybridized HH states plays a crucial role in the sensitivity of $T_2$ on strain.