Quantum dots and superconductivity in Ge-Si nanowires

**Joost is PhD-Student in the research group of NanoElectronics. His supervisor is Wilfred van der Wiel from the Faculty of Electrical Engineering, Mathematics and Computer Science.**

All information in classical computers is processed with discrete bits which can be either ‘0’ or ‘1’, which are physically represented by macroscopic currents and charges. Quantum computers work in a fundamentally different way and employs quantum mechanical bits, or *qubits*, as their smallest building blocks. A qubit must consist of a quantum mechanical two-level system which can be fully and coherently controlled. For instance, for an electron spin qubit, the spin of a single electron represents the two-level system, and full control over the position and spin state of the electron is required. Qubits are in a superposition of their two eigenstates and which must be mapped to physical properties (for instance spin-up or spin-down). For *n* qubits, a quantum computer can therefore be in 2* ^{n}* states simultaneously. This property can be exploited using specific quantum algorithms for which problems scale differently with increasing complexity and can thus be solved in a completely different timescale than on a classical computer. The quest for a quantum computer is a major research effort, since it requires an unprecedented level of control on a nanoscale and it was only fifteen years ago when the first single qubits appeared. Nowadays, qubits have been realised in a large variety of systems but it is yet unclear which will be used for the first universal quantum computer.

We investigate Ge-Si core-shell nanowires as a possible candidate for spin qubits and Majorana qubits. Ge-Si nanowires are hole conductors and for the spin qubits, we localise these holes in the nanowires to create quantum dots. The 1-dimensional nanowires provide confinement in the radial direction, while gates oriented perpendicular to the nanowire provide confinement in the direction of transport. This allows us to ‘trap’ the holes in specific segments of the nanowire and investigate the effect of the electrostatic potential and magnetic fields. For the Majorana zero modes we use superconducting contacts to induce a Josepshon current in the nanowires and investigate the effects of the charge occupancy, magnetic field, microwave field and temperature.

Ge-Si nanowires exhibit highly promising properties: (1) A free hole gas exists in the Ge core without applying external potentials or doping, (2) they consist of group IV materials with potentially zero hyperfine interaction providing long coherence times, (3) they have a predicted enhanced Rashba type direct spin-orbit coupling, a crucial ingredient for Majorana zero modes and enables spin rotations with AC electrical fields, (4) they have a tunable, electric field dependent, *g*-factor, (5) they can be grown with virtually no defects on lengths scales relevant for qubits, (6) the heavy-hole light-hole mixing in the valence band edge is an interesting unexplored physical system.

To characterise the quality of the nanowires we determine the hole mobility in the linear regime of operation of nanowire field-effect transistors (FETs) with a wide variety of nanowire diameters. By performing statistical averaging on the measurement data, we obtain well defined mobility values, at 300 K and 4 K. A clear trend is observed between crystal direction and wire diameter where we see higher mobilities for smaller wire diameters. We furthermore find that the small-diameter nanowires wires grow predominantly in the [110] crystal direction, which corresponds well to a transmission-electron microscopy (TEM) study showing that [110] wires have extremely low defect densities. It is therefore important to select small diameter nanowires for further experiments.

To fabricate quantum dot devices, we deposit nanowires on pre-fabricated bottom-gates and demonstrate the ability to make highly tunable quantum dots of varying lengths between 60 nm and 460 nm determined by the pitch of our gate design. Next, we show a double quantum dot with tunable interdot coupling strength and show that the dot occupancies can be changed with little effect to the tunnel couplings due to negligible gate cross-coupling. As a result, we obtain a set of highly regular bias triangles which underlines the stability of the device.

Before continuing on double quantum dots, we return to a single dot where we use excited state magneto-spectroscopy to measure the Zeeman splitting and map the *g*-factor on three 360° planes on the three main axis with respect to the nanowire. We find that the *g*-factor is highly anisotropic and depends on the electric field, as predicted by our collaborators. We obtain the highest *g*-factor when the magnetic field is oriented perpendicular to both the nanowire and the electric field, while the *g*-factor is almost completely quenched when the magnetic field is oriented parallel to the nanowire. The predicted high spin-orbit coupling of holes in our nanowires enables the use of AC electric fields to perform spin rotations on the Zeeman-split levels. The ability to change the *g*-factor using local electric fields from gates, can thus be utilised to tune quantum dots in and out of resonance of a constant high frequency electric field. This makes quantum dots separately addressable, which is an important step for quantum computation applications.

We then return to the double quantum dot configuration and we analyse a highly regular set of bias triangles. By comparing the energy difference between bias triangle pairs, we observe orbital shell filling and extract the charging and orbital energy. We observe Pauli spin-blockade (PSB) in charge transitions in the double dot, when transport takes place from partially filled orbitals towards filled orbitals. PSB is therefore only observed in the corresponding bias direction and we observe a clear increase in tunnel current when the bias direction is reversed, corresponding to the non-blocked case. Next, we investigate the finite leakage current in (PSB) and we test against three well-known spin-flip mechanisms: hyperfine interaction, spin-flip cotunnelling and spin-orbit interaction. By performing a magnetospectroscopy versus detuning on the three main axes with respect to the nanowire, we find that the leakage current is highly anisotropic with respect to the magnetic field direction and that spin-flip cotunnelling, as well as spin-orbit interaction give a significant contribution. It is therefore possible to carefully choose the magnitude and direction of the applied magnetic, corresponding to the longest spin-relaxation time.

Surprisingly, we now find the highest *g*-factor when the magnetic field is *parallel* to the electric field, which contrasts our result for the single quantum dot where the *g*-factor was the largest when the magnetic field is oriented perpendicular to both the nanowire and the electric field. This difference is partly explained by considering the higher subband population in the case of our double quantum dot, which significantly changes the light-hole heavy-hole mixing.

By using aluminium as superconducting contacts, a Josephson current can be induced in Ge-Si nanowires. A straightforward annealing process is employed to obtain the required highly transparent superconducting contacts. We observe multiple Andreev reflections (MAR) up to the sixth order and show that they follow a BCS temperature dependence, as they are directly related to the superconducting gap of our Al. Upon irradiating our junction with microwaves, Shapiro steps are observed, which is a manifestation of the AC Josephson effect and the height of the steps is equal to the energy of the applied microwaves. Increasing the microwave amplitude ultimately results in 23 Shapiro steps. This clear demonstration of both the DC and the AC Josephson effect is proof that our nanowire device with superconducting contacts is indeed a Josephson junction.

Next, the backgate dependence of the Josephson junction is investigated. For decreasing backgate voltages, we observe a general trend of increasing switching current, while our *I*_{C}*R*_{N} product remains constant and assumes a near-ideal value that is equal to the superconducting gap of our Al. For positive backgate voltages, near depletion, we find a strongly coupled quantum dot in the few-hole regime, where we observe finite supercurrents on the Coulomb diamond crossings, i.e., through the single-particle levels. This result can be used to construct a Kitaev chain of strongly coupled superconducting quantum dots, a system that supports highly robust Majorana fermions.

A magnetospectroscopy of the Josephson junction reveals a second superconducting phase being present inside, or in close proximity to, the nanowire. This superconducting phase has a critical magnetic field much higher than that of Al, while its critical temperature is lower. Our hypothesis is that during annealing, Al diffuses and forms a superconducting Al/Si_{x}/Ge_{y} alloy inside the wire. This is also suggested by a (TEM) study where Al was found inside the nanowire channel. In another device, we find that Al has diffused into the whole nanowire channel which has become metallic and superconducting, with a critical temperature and critical field a few times higher than that of pure Al. This superconducting alloy is an interesting material for applications requiring the combination of superconductivity with high magnetic fields, such as Majorana fermions. Near depletion, a hard superconducting gap is observed, which indicates highly homogeneous interfaces between nanowire and superconductor and we believe this interface is formed between pure Al and the sudden transition to the superconducting alloy. The hardness of the gap in our device is at least comparable to epitaxially grown Al on group III/IV material wires. The hardness of the gap is a measure for number of quasiparticle states in the gap, a major source of decoherence for Majorana zero modes.

The results for both the normal-state quantum dot devices and the superconducting devices, illustrate the versatility and suitability of Ge-Si nanowires for quantum computation applications.