*As, so far, **the experimental signatures that identify a topological superconductor (TSC) are elusive** [see, e.g., M. Mandal et al., **arXiv:2303.15581**] and there has been no conclusive experimental observation of Majorana bound states in proximitized topologically trivial semiconductors [see, e.g., R. Hess et al., **Phys. Rev. Lett. 130, 207001 (2023)**], particularly timely is search for intrinsic or proximitized superconductivity in topological materials. In addition to MagTop’s comprehensive theoretical effort, MagTop/IFPAN’s growers and experimentalists have been exploring four paths: (i) Weyl semimetals with superconductors’ overlayers; topological crystalline insulators in the form of (ii) bulk crystals; (iii) superlattices, and (iv) nanowires. Surprising and not yet understood results, calling for further work, have been gathered. *

For studies of interface transmission by differential conductance, the (001) surface of the Weyl NbP crystal was covered by several hundred nm thick metallic layers of either Pb, or Nb, or In [1]. Upon cooling across metals’ *T*_{c},s, all junctions show a conductance increase, pointing out to the Andreev reflection. In the case of Pb-NbP and Nb-NbP junctions, the conductance change indicates that the transmission occurs through a small part of the contact area. However, in the In-NbP junction, the peak magnitude and width show that the whole contact area is transmitting and a superconducting

Theory of symmetry-protected topological states in SnTe nanowires in the presence of various combinations of Zeeman field, *s*-wave superconductivity and inversion-symmetry-breaking field was developed [2]. Encouragingly, Andreev-like spectra have been found is a number of topological materials employing a normal- or ferromagnetic-metal tip, also the case of diamagnetic and ferromagnetic bulk (Pb,Sn)Te and (Pb,Sn,Mn)Te with silver paint contacts [3]. However, no global superconductivity was found, and the effect was discussed in terms of the correlation gap in 1D topological states at surface atomic steps. However, is some PbTe/SnTe strained superlattices, in addition to Andreev-type features, global superconductivity was found (Figure), as observed earlier by other groups. Whether this superconductivity is topological and originates from the dislocation network, as E. Tang and L. Fu [Nat. Phys. 10, 964 (2014)] model predicts or results from superconducting nanoprecipitates, is to be demonstrated.

[1] G. Grabecki, A. Dąbrowski, __P. Iwanowski__, A. Hruban, B. J. Kowalski, N. Olszowska, J. Kołodziej, M. Chojnacki, __K. Dybko__, A. Łusakowski, __T. Wojtowicz, T. Wojciechowski__, R. Jakieła, __A. Wiśniewski__, C*onductance spectra of (Nb,Pb,In)/NbP superconductor/Weyl semimetal junctions**,* *Phys. **Rev. B* **101**, 085113 (2020).

[2] N. M. Nguyen, W. Brzezicki, T. Hyart, *Corner states, hinge states and Majorana modes in SnTe nanowires*, *Phys. Rev. B* **105**, 075310(2022).

[3] __G. P. Mazur, K. Dybko__, A. Szczerbakow, J. Z. Domagala, __A. Kazakov__, M. Zgirski, E. Lusakowska, S. Kret, J. Korczak, T. Story, M. Sawicki, __T. Dietl__, *Experimental search for the origin of low-energy modes in topological materials*, *Phys. Rev. B ***100**, 041408(R) (2019) [Editors’ Suggestions].

[4] __P. Sidorczak__, W. Wołkanowicz, K. Gas, A. Kaleta, S. Gierałtowska, R. Minikayev, S. Kret, M. Sawicki, __T. Wojtowicz__, D. Wasik, M. Gryglas-Borysiewicz, __K. Dybko__ (unpublished).

*One of the most challenging aims in the current condensed matter physics research is the demonstration of non-Abelian Majorana statistics — the underlying fundamental property that would enable the realization of a topological quantum computer. Though not experimentally proven, it is theoretically well established that Majorana zero modes (MZMs) can be realized in semiconducting nanowires with strong Rashba spin-orbit coupling in the presence of induced superconductivity and external magnetic field. MagTop’s team studied theoretically **ferromagnetic-semiconducting-superconducting hybrids with MZMs, and demonstrated that this system; (i) constitutes a novel **topological charge, spin, ** **and heat transistor; (ii) shows quantization of spin under spin pumping conditions.*

By exploring the magnetisation dynamics in ferromagnetic-semiconducting-superconducting hybrids, we have unraveled a novel quantised effect—*the spin pumping*—which characterises the topology of the system similarly to the conductance in static cases. We have demonstrated quantised spin pumping in quantum spin Hall insulting edges hosting Majorana zero modes [1], as well as semiconducting-superconducting nanowires covered with ferromagnets [2], two setups that have been under intense experimental scrutiny in the hunt for Majorana fermions (see Figure). Crucially, we showed that in long nanowires there exists a one-to-one correspondence between the quantized conductance and the quantized spin pumping in the topologically nontrivial nanowires but these observables are uncorrelated in the case of accidental zero-energy Andreev bound states in the trivial phase. The observation of correlated and quantized peaks in the conductance and spin pumping would provide strong evidence of MZMs, and allow to distinguish them from quasi-Majorana modes potentially created by imperfections at the lead-nanowire interface. Furthermore, harnessing the magnetisation dynamics could open the pathway to real technological applications involving MZMs [3].

[1] __V. Fernández Becerra, Mircea Trif, and Timo Hyart__, *Topological charge, spin and heat transistor*,* Phys. Rev. B* 103, 205410 (2021).

[2] __V. Fernández Becerra, Mircea Trif, and Timo Hyart__, *Quantized spin pumping in topological ferromagnetic – superconducting nanowires*, *Phys. Rev. Lett*. 130, 237002 (2023).

[3] __V. Fernández Becerra, Mircea Trif, and Timo Hyart__, European Patent Application:*Topological charge, spin, and heat transistor*(https://patents.google.com/patent/EP3975275A1/en – pending).

*Magnetic impurities in s-wave superconductors provide a viable platform for realizing a topological quantum computer based on Majorana zero modes (MZMs). However, MZMs alone do not provide a universal set of quantum gates and manipulating coherently quantum degrees of freedom in these systems remains an open challenge. MagTop’s team **introduced a new type of quantum bit, a Yu-Shiba-Rusinov qubit, stemming from two nearby magnetic impurities on a superconductor and demonstrated how to determine relevant quantum gate and topological characteristics, including interactions with *MZMs,* by **scanning tunneling microscopy-electron spin resonance techniques, couplings to microcavity modes, and dynamic magnetic susceptibility. *

Figure depicts a new type of quantum bit, a Yu-Shiba-Rusinov qubit (YSRQ), stemming from two nearby magnetic impurities on a superconductor [1]. We demonstrated that the coherent rotation and the readout of the qubit states is possible by exploiting the dynamics of the impurity spins. We have established a protocol for generation of Rabi oscillations induced by the dynamics of the magnetic impurities which is robust for a wide range of experimentally feasible parameters. The precession of magnetic impurity also generates a feedback torque acting on the impurity [2] so that the resonance frequency of the impurity spin depends on the qubit state. We showed that it is possible to utilize this effect to readout the YSRQ via the well-established scanning tunneling microscopy-electron spin resonance (STM-ESR) techniques. We estimated that the difference in the resonance frequencies, corresponding to the two qubit states, is well within the STM-ESR resolution.

YSRQs can be integrated with topological qubits based on MZMs, allowing the possibility to transfer quantum information coherently between them [3,4]. In particular, it is possible to manipulate and readout the Majorana qubits via the YSRQ, facilitating implementation of universal set of quantum gates. In the future, we plan to investigate quantum adatom spins, as well as using machine-learning techniques to extract the topology of the Shiba chain from spin susceptibility data .

[1] __Archana Mishra__, Pascal Simon, __Timo Hyart__, and __Mircea Trif__, *Yu-Shiba-Rusinov qubit*, *Phys. Rev. X Quantum* 2, 040347 (2021).

[2] __Archana Mishra__, So Takei, Pascal Simon, and __Mircea Trif__, *Dynamical torque from Shiba states in s-wave superconductors*, *Phys. Rev. B* 103, L121401 (2021).

[3] Pei-Xin Shen, Silas Hoffman, and __Mircea Trif__, *Theory of topological spin Josephson junctions*, *Phys. Rev. Research* 3, 013003 (2021).

[4] __Peixin Shen__, Vivien Perrin, __Mircea Trif__, and Pascal Simon, *Majorana-m**agnon **interactions in t**opological Shiba **c**hains,* arXiv:2303.13513** **(under review in *Phys. Rev. Lett.*).