Towards hole spin qubits and Majorana fermions in Germanium

Even though Ge was used in the demonstration of the first transistor in 1947, it was Si which was adopted as the material of choice for electronic devices. A renewed interest on Ge has been recently sparked by the prospects of exploiting its lower effective mass and higher hole mobility to improve the performance of the ever smaller transistors. Ge also emerges as a promising material in the field of spin qubits, as its spin coherence times are expected to be much longer than in III-V systems. Finally, it has been very recently proposed that ultrathin Ge/Si core/shell NWs show an unusually large spin orbit interaction, suggesting thus that such one-dimensional wires also constitute a suitable system for the realization of Majorana fermions. In view of the above facts, one is able to envision a new era of Ge in information technology. The self-assembled growth of crystalline Ge islands on Si was reported for the first time in 1990. This created great expectations that such nanostructures could provide a valid route towards innovative, scalable and CMOS- compatible nanodevices. Two decades later the PI was able to realize the first devices based on such structures, and to investigate for the first time their electronic properties. His results indicate that Ge self-assembled quantum dots display a rather unique combination of properties, i.e. low hyperfine interaction, strong and tunable spin-orbit coupling and spin selective tunneling. In 2012, the PI`s group went a step further and realized for the first time ultra-small self-assembled Ge nanowires monolithically integrated on standard Si substrates, which will allow thus the PI`s group to move towards double quantum dots and Majorana fermions. In view of their exceptionally small and self-defined cross section, these Ge wires hold promise for the realization of hole systems with exotic properties and provide a new development route for silicon-based nanoelectronics. Within this project, the PI aims to explore these newly developed Ge self-assembled nanowires, both for spin based as well as for topological (Majorana fermions) quantum computation. His long term vision is to couple these two types of "quantum hardware" in one "technological platform" enabling thus the coherent transfer of quantum information between them.

There is a worldwide effort to find suitable systems that can be used as building blocks for the realization a quantum processor. Quantum dots formed in semiconductor materials are among the most promising candidates as they are solid state systems with enormous upscaling potential. Quantum dots in silicon and germanium, in particular, have the key advantage that they are compatible with standard silicon technology. So far the focus of research had been mainly on electrons. Holes, i.e. missing electrons, have attracted interest just recently because of their strong spin orbit coupling which could lead to the realization of fully electrically controllable quantum bits based on the spin degree of freedom. In this project we worked with nanowires and realized for the first time a Germanium hole spin qubit. The nanowires were grown under ultra high vacuum conditions and the had a height of about 2nm. In such nanowires, holes were localized in order to investigate the spin properties and realize spin qubits. The confinement of holes was possible in quantum dots which were formed in the nanowires by applying appropriate voltages to metallic electrodes acting as gates. In addition, by sending high frequency microwave signals the spin of a single hole could be manipulated and a qubit was realized. Coherent oscillations of the spin, the so-called Rabi oscillations, could be demonstrated. In addition, the results showed that for holes in Germanium quantum information can "live" for more than 120ns, known as dephasing time. In order to further investigate what is the limitation in the coherence time for the Germanium qubit we demonstrated, we performed measurements to extract the time it takes for a spin to relax from its excited to its ground state. This time, known as the spin relaxation time, is an upper bound for the coherence time. For measuring the spin relaxation time we coupled two vertically grown nanowires. One of them was used as a charge sensor which can transform the information of charge into spin information. Our experiments showed that the spin relaxation time for a magnetic field of 0.5 Tesla is close to 100s emphasizing that hole spins in Ge are very interesting for quantum information. The results of the project underline the potential of Ge as a platform for the realization of fully electrically tunable spin qubits with large upscaling potential. Indeed, in 2020, two years after the realization of the first Ge qubit during the duration of this project, three more groups have published Ge hole spin qubit results, showing the enormous potential of Germanium.