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PhD Defence Bob de Ronde

the path of least resistance through topology

Bob de Ronde is a PhD student in the research group Interfaces and correlated electrons. His supervisor is A. Brinkman from the faculty of Science and Technology.

The primary focus of this dissertation is studying the interaction between topological materials and superconducting materials. As described in Chapter 1, sandwiching a topological material between two superconductors, a structure known as a Josephson junction, is predicted to create a Majorana bound state. This state possesses the interesting property of non-Abelian exchange statistics. This allows the use of Majorana bound states for braiding, the process that is the foundation of topological quantum computation.

In Chapter 2, the transport properties of the three-dimensional topological insulator BiSbTeSe2 in a magnetic field are studied by measuring Hall bar structures. These devices are equipped with both top- and back-gates, which allows the charge carrier density of both surfaces of the topological insulator to be controlled individually. This control can be utilized to tune both surfaces through several Landau levels at a magnetic field of 15 T. As expected, integer quantization is observed when both surfaces are tuned to be dominated by charge carriers of the same sign. However, when the surfaces are populated by charge carriers of opposite sign, non-integer quantization is observed. This phenomenon is theoretically supported by adding a coupling term between the surfaces to the Landauer-Büttiker formalism, justified by the quantum mechanical similarity of oppositely charged carriers on opposite surfaces in a three-dimensional topological insulator. These results display control over the Landau levels in BiSbTeSe2.

The remaining chapters of this thesis address junctions between topological materials and superconductors in various forms. The most prevalent type of junction studied in this work is the Josephson junction. Josephson junctions based on topological materials are expected to provide an indication of the presence of Majorana bound states in the form of a doubled periodicity, observed as missing odd Shapiro steps or a missing first Shapiro step in a signal composed of both 2π and 4π periodicity. Chapter 3 describes Josephson junctions based on the nodal line semimetal ZrSiS. Despite exhibiting the linear dispersion often associated with spin-momentum locking, no signs of a disappearing first Shapiro step at low excitation frequency were observed in these junctions. However, a high critical current of 280 μA was measured and the systematic study of the clear radio frequency response of ZrSiS-based Josephson junctions at various frequencies and temperatures provides a benchmark for Shapiro step measurements in other materials.

A similar measurement scheme was employed on Josephson junctions based on BiSbTeSe2 in Chapter 4.  At the base temperature of 20 mK, a missing first Shapiro step was observed at 4.7 GHz. However, multiple steps were missing at a frequency of 1.81 GHz. These additional missing steps can be explained by the retrapping voltage at low temperature. This was confirmed by measurements at 1 K, which show that the steps beyond the first reappear at 1.81 GHz, while the first step is still missing at 4.7 GHz. Moreover, calculations using the resistively shunted junction model with a 4π-periodic contribution of 5% to the supercurrent qualitatively correspond to the measurement data. These observations provide an indication of a 4π-periodic contribution to the supercurrent in Josephson junctions based on BiSbTeSe2. Additionally, gate control over these devices was also shown, an important ingredient for applications that might be concocted of these devices.

Another way of obtaining indications of Majorana zero modes in a topological material is studying the spectroscopy of an interface between a topological material and a superconductor. Since the mode resides at zero energy, a zero-bias conductance peak is expected in these measurements. Spectroscopic measurements were performed on an interface between BiSbTeSe2 and Nb and presented in Chapter 5. A superconducting gap structure was observed in these devices at the base temperature of 20 mK. Applying a magnetic field revealed a zero-bias conductance peak of 1.42 e2/h around 0.45 T. The measurement of a zero-bias conductance peak in a device without a clear interface, other than the superconductor interface, might suggest that hybridization at the crystal flake edge localizes the mode. Combined with the missing Shapiro step in Chapter 4, the zero-bias conductance peak in proximitized BiSbTeSe2 provides a good indication of Majorana bound states in BiSbTeSe2.

The periodicity of Shapiro steps was also studied in Josephson junctions based on the Dirac semimetal Bi0.97Sb0.03, as presented in Chapter 6. Junctions of several lengths and regimes were fabricated. The 500 nm long junctions were found to be in the ballistic regime, while the 800 nm and 1 μm junctions resided in the diffusive limit. Comparing the 500 nm of the shorter junctions to normal state magnetotransport data, the origin of the ballistic modes was traced back to bulk electron bands at the L point. In response to radio frequency irradiation, the first Shapiro step is missing below 2 GHz in these devices, indicating 4π periodicity. Comparison to the resistively shunted junction model yields an estimation of the 4π-periodic contribution to the supercurrent of 20%, indicating the presence of Majorana bound states in Bi0.97Sb0.03 as well. Furthermore, comparison of the parallel magnetic field response of the supercurrent to complex coherence length calculations indicates finite momentum pairing of the Cooper pairs and transitions between the 0- and the π-state of the junctions, owing to the high g-factor of 800-1000 of Bi0.97Sb0.03.

These 0-π transitions were investigated further by making a superconducting quantum interference device (SQUID) based on Bi0.97Sb0.03, described in Chapter 7. These SQUIDs consist of a Bi0.97Sb0.03-based Josephson junction and Nb constriction circuited in parallel. The significantly higher critical current of the Nb constriction permits the scrutiny of the current-phase relation of the Bi0.97Sb0.03 junction. This current-phase relation shows a sawtooth shape, indicating the presence of higher harmonics in the supercurrent, consistent with a ballistic junction. Varying the out-of-plane magnetic field or the magnetic field parallel to the Bi0.97Sb0.03 junction drives the transition between the 0- and the π-state of the Bi0.97Sb0.03 junction. These results show the control over the phase of a Bi0.97Sb0.03-based Josephson junction that can be exerted using magnetic fields.

The results yielded by these junctions between topological materials and superconductors grant us a compelling incentive to definitively prove the presence of Majorana bound states in these systems. The prospect of producing an interesting topological quantum computer would certainly make this endeavor worthwhile.