• Josephson junctions
• Majorana fermions
• mesoscopic physics
• superconducting films
• superconducting resonators
• Superconductivity

Quantum computers offer a more efficient alternative to modern day computers. Majorana fermions represent a promising platform for their practical realisation; as their non-local nature provides topological protection of the encoded quantum information. A strong external magnetic field along with high spin-orbit coupling in semiconductor nanowire interfaced with a superconductor, are necessary ingredients, in order to induce the topological phase that hosts Majoranas.
After the first experimental signatures, braiding a pair of Majoranas is required for conclusively proving their existence. This requires a sophisticated mesoscopic circuit, which must be resilient to high magnetic fields. Essential to the proposed circuit are SQUIDs for flux-tuning the long-range Coulomb interaction between Majoranas, and a superconducting microwave resonator to read-out the charge parity of a superconducting island.
NbTiN is the preferred superconductor because of its high critical magnetic field (B_c>9 T). In this thesis, magnetic field resilient circuit elements (Josephson junctions for SQUIDs and superconducting resonators) are realised for their application in Majorana braiding circuit.
In achieving the above, optimisation of deposition conditions for high-quality NbTiN films was performed. Several superconducting films were sputtered by means of DC reactive magnetron sputtering from a NbTi target in an argon/nitrogen plasma. Parameters varied include rate of nitrogen flow, substrate temperature, bias voltage and target purity. Resistivity and superconducting transition temperature (T_c) of the films were investigated. As the temperature of the substrate was increased during the deposition (20°C to 320°C), a linear decrease in the resistivity was observed. Corresponding to each substrate temperature, an optimum rate of nitrogen flow for which a maximum T_c was observed. Maximum T_c of 14.1 K was recorded for a film deposited at T=320°C by using a negative DC bias voltage (V_b=-40 V) between sample and target. High-quality NbTiN films were subsequently used for the realisation of both Josephson junctions and superconductive resonators.
Josephson junctions usually fail at high magnetic fields as superconductivity is weakened. In particular, standard Al/AlO/Al Josephson junctions are not suitable as bulk aluminum transitions to normal state at a magnetic field in the order of 10 mT. However, the behaviour of ultra thin aluminum films (<10 nm) is very different (B_c= 2 T). Therefore, junctions of the type thin-Al/AlN/NbTiN were investigated. The first electrode is a very thin Al layer (t_Al=7-9 nm), while the counter electrode is NbTiN (t_NbTiN=100 nm). Effect of sputtering parameters of AlN was studied for optimising junction properties, and IV traces were measured in applied in-plane magnetic fields up to 2 T. Best junctions showed high critical current density (J_c=10 kA/cm2), which could be modulated by magnetic flux through the junction.

Finally, microwave superconducting resonators resilient to high in-plane magnetic fields were developed. Several chips were fabricated, each with different thickness of NbTiN (8 nm to 300 nm). Quarterwave resonators were patterned in each chip and coupled to a common feedline. Resonances lineshapes were measured by using a heterodyne technique with the samples cooled down to T=20 mK. The key finding was that a combination of thin films (22 nm) and artificial pinning sites is essential in order to maintain internal quality factors of 10^{5} and stable resonances up to 5.5 T.
In conclusion, mesoscopic superconducting circuit elements resilient at high in-plane magnetic field for Majorana braiding, were characterised. This experiment is of fundamental importance for confirming their existence.