*Whether magnetism really opens a gap in topological surface states has become one of most intriguing question in topological physics [see, e.g., Y. L. Chen et al., **Science 329, 659 (2010)**; E. D. L. Rienks et al., **Nature 576, 423 (2019)*

Pb

MagTop’s MBE group monitored the evolution of angle- and spin-resolved photoelectron spectra (SR-ARPES) with *in-situ* deposition of Mn and Fe atoms onto TCI Pb_{1-x}Sn_{x}Se epilayers grown by molecular beam epitaxy in the (111) orientation. During the experiments, ARPES and spin-resolved energy dispersive profiles in a photon energy range of 50-90 eV were recorded. As a first step, the topological transition as a function of the Sn content and temperature was scrutinized. Interestingly, it was found that helical spin polarization is not limited to samples with topological compositions but also exists in the trivial ones, which possess an open band gap (as depicted in Figure). **The in-plane spin component exhibited a significant spin polarization of approximately 30%, while the out-of-plane component showed minimal polarization.** Importantly, a drastic reduction in spin polarization was observed when the topological surface states overlapped with the bulk states.

**While studying the interactions between TCIs and transition metals, it was observed that the spin polarization remains unaffected. However, the presence of a transition metal on the TCI surface shifts the temperature of topological phase transition to lower values, making it more „trivial”. **This observation is explained by a substitution of the heavier elements (Pb, Sn) by lighter elements (Mn, Fe), and the associated narrowing of the topological phase.

These findings have significant implications for spin-charge conversion devices, as they indicate that not only topological but also trivial IV-VI semiconductors can be used for such applications, as both phases possess helical spin polarization. The knowledge gained about spin textures and their behavior under different conditions opens up new possibilities for exploiting the unique properties of these materials in spintronic and reveal details which should be considered in the design of future spintronic devices.

__[1] B. Turowski__, __A. Kazakov__, __R. Rudniewski__, T. Sobol, E. Partyka-Jankowska, __T. Wojciechowski__, __M. Aleszkiewicz__, __W. Zaleszczyk__, M. Szczepanik, __T. Wojtowicz__, __V. Volobuev__, *Spin-polarization of Topological Crystalline and Normal Insulator Pb _{1-x}Sn_{x}Se (111) Epilayers probed by Photoelectron Spectroscopy*,

*High-quality TCI crystals grown at IFPAN/MagTop allowed to demonstrate by scanning tunneling spectroscopy (STS) the presence 1D higher-order topological states residing at the edges of odd-atom-high steps at (001) **Pb _{1-x}Sn_{x}Se*

Motivated by IFPAN experimental discovery of a new class of topological materials – topological crystalline insulators [TCI, P. Dziawa et al., *Nat. Mater.* 11, 1023 (2012)], MagTop/IFPAN researchers have actively developed growth methods of various topologically nontrivial bulk IV-VI semiconductor crystals, like Pb_{1-x}Sn_{x}Se (0 ≤* x* ≤ 0.4), Pb_{1-x}Sn_{x}Te (0≤ *x* ≤ 1) or a ferromagnetic TCI Pb_{1-x-y}Sn_{x}Mn_{y}Te (0 ≤ y ≤ 0.16). The collaboration with German and Swiss teams on scanning tunneling microscopy and spectroscopy (STM/STS) studies of TCI materials resulted in the discovery of new higher-order 1D topological states residing at the edges of atomic steps at the (001) crystal plane hosting TCI states [P. Sessi et al., *Science* 354, 1269 (2016)] and in the demonstration of hybridization between states originating from the neighboring steps [1]. Furthermore, MagTop researchers found Andreev-like spectra in differential conductance employing a soft Ag mm-size contacts to topological surfaces [2] (see, Figure), the phenomenon observed in parallel by other groups for a variety of topological materials, and assigned to interfacial superconductivity. According to MagTop’s theory, the effect results from the gap opening by magnetic order in the 1D step bands [3]. The predicted gap has indeed been observed in STM/STS experiments, when the Fermi level was shifted to the step states by metal deposition [4].

[1] J. Jung, A. Odobesko, R. Boshuis, A. Szczerbakow, __T. Story__, M. Bode,* Systematic Investigation of the Coupling between One-Dimensional Edge States of a Topological Crystalline Insulator*, *Phys. Rev. Lett.* **126**, 236402 (2021).

[2] __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].

[3] __W. Brzezicki, M. M. Wysokiński, T. Hyart__, *Topological properties of multilayers and surface steps in the SnTe material class*, *Phys. Rev. B* **100**, 121107(R) (2019).

[4] G. Wagner, S. Das, J. Jung, A. Odobesko,** **F. Küster, F. Keller, __J. Korczak__, A. Szczerbakow, __T. Story__, S. S. P. Parkin, R. Thomale, T. Neupert, M. Bode, P. Sessi, *Interaction Effects in a 1D Flat Band at a Topological Crystalline Step Edge, **Nano Lett.* **23**, 2476 (2023).

**invited talks:** T. Dietl, Materials Research Meeting 2019, Yokohama, Japan; Quantum Complex Matter 2018, Frascati, Italy.

W. Brzezicki, Superstripes 2019, Ischia, Italy

W. Brzezicki, 45 Zjazd Fizyków Polskich, Kraków, Polska

W. Brzezicki, Topological Quantum Science 2021, Erice, Italy

*Topological crystalline insulators (TCIs) have revealed that topologically protected gapless surface states can be brought about by crystal symmetries. MagTop’s researchers demonstrated experimentally and theoretically that breaking of reflection symmetry by an overlayer of an amorphous semiconductor leads to a temperature independent phase coherence length controlling quantum localization magnetoresistance. Furthermore, in agreement with MagTop’s ARPES data, spin-momentum locking, and thus quantization of the Berry phase, exists on the both sides of the topological phase transitions.*

*Evolution of the WAL magnetoresistance with increasing temperature in uncovered (left, upper panel) and Se covered (left, lower panel) epilayers. Experimental points (empty squares) are fitted using one-channel Hikami-Larkin-Nagaoka expression for a strong spin-orbit interaction (solid lines). Right figure shows, that l _{φ}(T) in uncovered epilayers do not saturate down to 1.5 K (black and red), while in Se covered epilayers l_{φ} saturates below 5-7 K (blue and magenta).*

The magnetotransport studies focused on weak localization (WL) and weak antilocalization (WAL) effects, which arise from interference of electron wave functions. For the Dirac surface fermions encircling the Fermi surface, an additional π Berry phase is acquired, resulting in a positive magnetoresistance known as WAL. Consequently, WAL is commonly regarded as an indicator of surface state transport in three-dimensional topological matter.

MagTop’s theoretical analysis revealed that the quantization of the Berry phase ϕ for electrons encircling the Fermi surface relies on both the crystalline mirror and time-reversal symmetries, irrespective of whether the system is in a topologically trivial or non-trivial phase. Moreover, it was also demonstrated that intentionally breaking the mirror symmetry, for example by introducing an additional amorphous insulator layer, introduces a new length scale that affects the magnitude of the WAL magnetoresistance (MR)

Those theoretical predictions are corroborated by experimental observations, as WAL MR was indeed observed in both topologically trivial and non-trivial range of Sn content *x* of Pb_{1-x}Sn_{x}Se thin films. In addition, the effect of the amorphous Se layer on WAL MR was studied in details. It becomes evident that the suppression of WAL MR occurs at low temperatures in these Se covered layers. This phenomenon was attributed to the saturation of the phase coherence length l_{φ}, which is governed by the aforementioned new length scale resulting from the destruction of the quantized value of ϕ.

__A. Kazakov__, __W. Brzezicki__, __T. Hyart__, __B. Turowski__, __J. Polaczyński__, Z. Adamus, M. Aleszkiewicz, __T. Wojciechowski__, J.Z. Domagala, O. Caha, A. Varykhalov, G. Springholz, __T. Wojtowicz__, __V.V. Volobuev__, __T. Dietl__,* Signatures of dephasing by mirror-symmetry breaking in weak-antilocalization magnetoresistance across the topological transition in Pb _{1-x}Sn_{x}Se*, Phys. Rev. B