## 27 Novembre – Thesis defense - Bogusz Bujnowski

09 h San Sebastian, University of the Basque country UPV/EHU, Berio Pasealekua - Donostia (Espagne)

Equilibrium and transport properties of hybrid junctions between superconductors and spin active materials.

We investigate the interplay of the pairing state in conventional superconductors (S) and spin-active fields. In conventional S electrons with opposite momenta and spins bind into so-called Cooper pairs. The pair correlations penetrate normal conducting materials (N) on the length scale of the superconducting coherence length, what is known as the proximity effect. The proximity effect gives rise to interesting phase coherent phenomena that are strongly modified in the presence of spin active fields. For example it is strongly suppressed in a ferromagnet (F), which prefers a parallel spins of the electrons and counters the conventional pairing mechanism. A prominent manifestation of the proximity effect is the Josephson effect, where the phase difference between the macroscopic wavefunctions of two spatially separated S leads to a non dissipative current at zero voltage.

We consider the Josephson effect in a junctions involving spin splitted S, where the orientation of the exchange field can be controlled individually in both S. In such junctions, when the fields are oriented antiparallely, it is possible to increase the critical current by increasing the magnitude of the exchange fields. This is a counter intuitive result considering the pair breaking nature of the fields. The formation of the Andreev bound states (ABS) has not been investigated so far. We analyze the spectral properties of this junction and show that for collinear orientations of the fields, any deviation from the case of equal fields leads to finite intervals of phases without ABS. In general the spectral composition of the current is found to be a superposition of the contributions from the ABS and the continuous spectrum and strongly depends on the transmissivity of the junction.

The suppression of the proximity effect in magnetic heterostructures can be avoided by generating triplet components of the pair correlations with spin projections perpendicular to the field, so-called long range triplet correlations (LRTC). LRTCs can be generated due to the presence of spin-orbit coupling (SOC) and a homogeneous exchange field, what has not been confirmed experimentally yet. We propose favorable junction setups to observe the LRTCs and calculate the Josephson current considering two common types of SOC, that result in spin precession and anisotropic spin relaxation effects. The contributions to the current from the effects depend on the orientation of the exchange field and their competition leads to current reversal scenarios which represent a signature of the LRTCs.

We then turn to another equilibrium phenomenon, namely equilibrium spin currents (ESC). We show that in a nanowire with SOC, breaking the time-reversal symmetry by a Zeeman field leads to a bulk equilibrium spin current which manifests itself in a sizable edge spin polarization, transverse to the Zeeman field. This property occurs in both, the normal and superconducting state, independently of the degree of disorder. The transverse edge spin polarization is strongly enhanced in the superconducting state when the Zeeman energy is of the order of the induced superconducting gap. This leads to a unknown transverse magnetic susceptibility that can be much larger than the known longitudinal one.

At the end of the thesis, we investigate electronic transport in heterostructures of the recently discovered Weyl semimetals (WSM). This material class exhibits a pseudo-relativistic dispersion around so-called Weyl points in the Brillouin zone, that are characterized by their chirality in the low-energy limit. We discovered a interesting chiral filtering effect when interfacing two distinct WSMs, if the Weyl nodes on each side of the interface are separated in energy and momentum space. We calculate the differential conductance across the interface and identify the regimes where it is possible to achieve transport of one, none, or both chiralities.