Two-dimensional second-order topological superconductors (SOTSCs) have gapped bulk and edge states, with zero-energy Majorana bound states localized at corners. Motivated by recent advances in Majorana nanowire experiments, we propose to realize a tunable SOTSC as a two-dimensional nanowire array. We show that the coupling between the Majorana modes of adjacent wires can be controlled by phase-biasing the device, allowing to access a variety of topological phases. We characterize the system using scattering theory, which provides access to its transport properties and its topological invariants. The setup is robust against disorder, both in the nanowires themselves and in the Josephson junctions formed between adjacent wires. Further, we identify a parameter regime in which an initially trivial system is rendered topological upon adding disorder, providing an example of a second-order topological Anderson phase.

We study numerically the formation of Majorana bound states in a finite-size quasi-one-dimensional square-lattice strip with Rashba spin-orbit coupling, in the presence of a proximity-induced superconducting pairing and a magnetic field perpendicular to the strip. We take into account both the Zeeman and orbital effects of the field. First, using the Majorana polarization, we demonstrate that such a system can host more than one pair of Majorana quasiparticles. We construct the corresponding topological phase diagram and we conclude that the topological regions are extended in the presence of orbital effects, however the gap protecting the topological states is reduced.

Topological phases of matter that have an insulating bulk and robust gapless boundary states can exist both in static materials and when system parameters are changed periodically in time. In the latter case, the periodic driving can lead to so called ``anomalous'' topological phases. Here, the authors show that, in the newly introduced higher-order topological insulators, anomalous phases can exist even if the system is static, and provide an example of such behavior using a two-dimensional model with topological corner charges. This work opens up the possibility of studying anomalous phases without the inherent difficulties associated with time-periodic changes of a material, such as the risk that it will ``heat up'' due to the driving field and lose its topological features.