# Topological Quantum Phases in Layered Systems with Rashba Spin-Orbit Interaction

Volpez, Yanick André. Topological Quantum Phases in Layered Systems with Rashba Spin-Orbit Interaction. 2020, Doctoral Thesis, University of Basel, Faculty of Science.

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Official URL: https://edoc.unibas.ch/78101/

Moreover, it is shown (see Chapter 4) how a Rashba bilayer can be used to generate different 2D topological superconducting phases. The setup consists of a conventional $s$-wave superconductor sandwiched between two Rashba layers. Due to the proximity to the superconductor, the Rashba layers themselves become superconducting by the virtue of two competing pairing mechanisms: $(i)$ direct Andreev pairing -- a process where a Cooper pair as a whole tunnels into one of the layers and $(ii)$ crossed Andreev pairing -- a process where a Cooper pair splits and the electrons tunnel into opposite layers. The competition of these two processes leads to a 2D time-reversal invariant (TRI) topological superconducting phase when crossed Andreev pairing dominates. By applying a Zeeman, field the setup can be brought either into a chiral topological superconducting phase or a 2D gapless superconducting phase with unidirectional edge states. In essence, a Rashba bilayer system is a versatile platform which allows the realization of various 2D topological superconducting phases.
In Chapter 5, a system consisting of two tunnel-coupled Rashba layers which are proximitized by a top and bottom $s$-wave superconductor with a phase difference $\phi$ close to $\pi$ is studied. This system is predicted to be a 2D TRI topological superconductor if the tunnel coupling is stronger than the proximity induced superconducting pairing strength. By breaking time-reversal symmetry with an inplane magnetic field, the system can be brought into the recently discovered second-order topological superconducting phase. In this phase, the bulk as well as the edges of the system are gapped, while in a square geometry two MBSs appear on opposite corners. Numerical results show that this finding even holds true if deviations from the $\phi=\pi$ phase difference between the parent superconductors is as large as $\delta \phi \approx \pi/3$. This implies that in an experiment, the phase difference does not need to be fine tuned.
In Chapter 6, an alternative way to fabricate a 1D TRI topological superconducting phase in a Josephson bijunction is presented. Concretely, the setup consists of a thin superconductor~-~insulator~-~superconductor ($SIS$) $\pi$-Josephson junction sandwiched between Rashba layers with opposite SOI. Due to the proximity effect, the Rashba layers themselves form a superconductor~-~normal conductor~-~superconductor ($SNS$) junction. The $SIS$ junction is assumed to be thin enough such that electron tunneling between the Rashba layers is possible. This leads to a hybridization between the Andreev bound state bands (ABSBs) that emerge in the normal regions in the Rashba layers. Roughly speaking, the 1D channels formed by the ABSBs mimick the physical situation in tunnel coupled nanowires, and it is shown that indeed a topological phase with a Kramers pair of MBSs can emerge at the end of the normal regions.