IST Austria Thesis

Nowadays, quantum computation is receiving more and more attention as an alternative to the classical way of computing. For realizing a quantum computer, different devices are investigated as potential quantum bits. In this thesis, the focus is on Ge hut wires, which turned out to be promising candidates for implementing hole spin quantum bits. The advantages of Ge as a material system are the low hyperfine interaction for holes and the strong spin orbit coupling, as well as the compatibility with the highly developed CMOS processes in industry. In addition, Ge can also be isotopically purified which is expected to boost the spin coherence times. The strong spin orbit interaction for holes in Ge on the one hand enables the full electrical control of the quantum bit and on the other hand should allow short spin manipulation times. Starting with a bare Si wafer, this work covers the entire process reaching from growth over the fabrication and characterization of hut wire devices up to the demonstration of hole spin resonance. From experiments with single quantum dots, a large g-factor anisotropy between the in-plane and the out-of-plane direction was found. A comparison to a theoretical model unveiled the heavy-hole character of the lowest energy states. The second part of the thesis addresses double quantum dot devices, which were realized by adding two gate electrodes to a hut wire. In such devices, Pauli spin blockade was observed, which can serve as a read-out mechanism for spin quantum bits. Applying oscillating electric fields in spin blockade allowed the demonstration of continuous spin rotations and the extraction of a lower bound for the spin dephasing time. Despite the strong spin orbit coupling in Ge, the obtained value for the dephasing time is comparable to what has been recently reported for holes in Si. All in all, the presented results point out the high potential of Ge hut wires as a platform for long-lived, fast and fully electrically tunable hole spin quantum bits

Fast Hole Tunneling Times in Germanium Hut Wires Probed by Single-Shot Reflectometry

Heavy holes confined in quantum dots are predicted to be promising candidates for the realization of spin qubits with long coherence times. Here we focus on such heavy-hole states confined in Germanium hut wires. By tuning the growth density of the latter we can realize a T-like structure between two neighboring wires. Such a structure allows the realization of a charge sensor, which is electrostatically and tunnel coupled to a quantum dot, with charge-transfer signals as high as 0.3e. By integrating the T-like structure into a radio-frequency reflectometry setup, single-shot measurements allowing the extraction of hole tunneling times are performed. The extracted tunneling times of less than 10$\mu$s are attributed to the small effective mass of Ge heavy-hole states and pave the way towards projective spin readout measurements

Single-shot readout of hole spins in Ge

The strong atomistic spin orbit coupling of holes makes single-shot spin readout measurements difficult because it reduces the spin lifetimes. By integrating the charge sensor into a high bandwidth radio-frequency reflectometry setup we were able to demonstrate single-shot readout of a germanium quantum dot hole spin and measure the spin lifetime. Hole spin relaxation times of about 90 $\mu$s at 500\,mT are reported. By analysing separately the spin-to-charge conversion and charge readout fidelities insight into the processes limiting the visibilities of hole spins has been obtained. The analyses suggest that very high hole visibilities are feasible at realistic experimental conditions underlying the potential of hole spins for the realization of viable qubit devices

Ge hole spin qubit

Holes confined in quantum dots have gained considerable interest in the past few years due to their potential as spin qubits. Here we demonstrate double quantum dot devices in Ge hut wires. Low temperature transport measurements reveal Pauli spin blockade. We demonstrate electric-dipole spin resonance by applying a radio frequency electric field to one of the electrodes defining the double quantum dot. Next, we induce coherent hole spin oscillations by varying the duration of the microwave burst. Rabi oscillations with frequencies reaching 140MHz are observed. Finally, Ramsey experiments reveal dephasing times of 130ns. The reported results emphasize the potential of Ge as a platform for fast and scalable hole spin qubit devices

Zero field splitting of heavy-hole states in quantum dots

Using inelastic cotunneling spectroscopy we observe a zero field splitting within the spin triplet manifold of Ge hut wire quantum dots. The states with spin ±1 in the confinement direction are energetically favored by up to 55 μeV compared to the spin 0 triplet state because of the strong spin–orbit coupling. The reported effect should be observable in a broad class of strongly confined hole quantum-dot systems and might need to be considered when operating hole spin qubits

Heavy hole states in Germanium hut wires

Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a so far unexplored type of nanostructure. Low temperature magnetotransport measurements reveal a large anisotropy between the in-plane and out-of-plane g-factors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function which is of heavy hole character. A light hole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the out-of-plane g-factors. However, this tiny light hole contribution does not influence the spin lifetimes, which are expected to be very long, even in non isotopically purified samples

Self-controlled growth of highly uniform Ge/Si hut wires for scalable qubit devices

Semiconductor nanowires have been playing a crucial role in the development of nanoscale devices for the realization of spin qubits, Majorana fermions, single photon emitters, nanoprocessors, etc. The monolithic growth of site-controlled nanowires is a prerequisite towards the next generation of devices that will require addressability and scalability. Here, combining top-down nanofabrication and bottom-up self-assembly, we report on the growth of Ge wires on pre-patterned Si (001) substrates with controllable position, distance, length and structure. This is achieved by a novel growth process which uses a SiGe strain-relaxation template and can be generalized to other material combinations. Transport measurements show an electrically tunable spin-orbit coupling, with a spin-orbit length similar to that of III-V materials. Also, capacitive coupling between closely spaced wires is observed, which underlines their potential as a host for implementing two qubit gates. The reported results open a path towards scalable qubit devices with Si compatibility

Ge/Si quantum wires for quantum computing

We firstly introduce the self-assembled growth of highly uniform Ge quantum wires with controllable position, distance and length on patterned Si (001) substrates. We then present the electrically tunable strong spin-orbit coupling, the first Ge hole spin qubit and ultrafast operation of hole spin qubit in the Ge/Si quantum wires