An international team of scientists including Dr. Rajibul Islam from MagTop has demonstrated experimentally the existence of gapless topological step-edge states on the α-As surface. A theoretical analysis has shown that the appearance of such states relies on the simultaneous presence of both a non-trivial strong Z2 invariant and a non-trivial higher-order topological invariant, which provides evidence for hybrid topology.
Topology and interactions are fundamental concepts in the modern understanding of quantum matter. Their nexus yields several research directions including: the competition between distinct interactions, as in several intertwined phases; the interplay between interactions and topology that drives phenomena in twisted layered materials and topological magnets; and the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies till recently. In the work in question, using tunnelling microscopy, photoemission spectroscopy, and theoretical analysis, the researchers unveiled a ‘hybrid’ topological phase of matter in the simple elemental solid arsenic (see Figure). It was found, through a unique bulk-surface-edge correspondence, that arsenic features a conjoined strong and higher-order topology that stabilizes a hybrid topological phase. Although momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topologically induced step-edge conduction channels revealed on various natural nanostructures on the surface. The employed theoretical models showed that the existence of gapless step-edge states in arsenic relies on the simultaneous presence of both a non-trivial strong Z2 invariant and a non-trivial higher-order topological invariant, which provide experimental evidence for hybrid topology.
Figure: The demonstration of hybridization between the gapped edge state and the gapless surface state. Free-standing monolayer exhibits a gapped edge state (left panel). Clean surface of gray arsenic (As) features a gapless Rashba surface state near the Fermi level (middle panel). With the introduction of monolayer step edges, the edge state undergoes hybridization with the gapless surface states, resulting in the emergence of gapless edge states at the step edges (right panel).
Md Shafayat Hossain, Frank Schindler, Rajibul Islam, Zahir Muhammad, Yu-Xiao Jiang, Zi-Jia Cheng, Qi Zhang, Tao Hou, Hongyu Chen, Maksim Litskevich, Brian Casas, Jia-Xin Yin, Tyler A. Cochran, Mohammad Yahyavi, Xian P. Yang, Luis Balicas, Guoqing Chang, Weisheng Zhao, Titus Neupert and M. Zahid Hasan, A hybrid topological quantum state in an elemental solid, Nature 628, 527–533 (2024).
Progress in growth IV-VI heterostructures resulted in observation quantum Hall effect in PbSnSe quantum wells, which composition corresponds to the bulk inverted bandgap. Combination of the experimental studies with detailed k·p calculations revealed topological phase diagram of the IV-VI quantum wells and highlighted pathways to achieving topological edge transport in the absence of the external magnetic fields.
(a) Processed Hallbar to probe anisotropic bandstructure, which schematics is pictured in the inset. (b) Sharp and narrow weak antilocalization cusp around 0 T evidence for extremely large decoherence length. (c) Comparison of the experimentally obtained curves (black) with the calculations results. (d) Topological phase diagram for the quantum spin Hall phases expected in the oblique valleys as a function of the quantum well thickness and tin content.
Researchers have achieved a significant milestone in topological materials science by successfully growing high-quality quantum wells of Pb₁₋ₓSnₓSe/Pb₁₋ᵧEuᵧSe using molecular beam epitaxy, with the Sn content tuned to realize a bulk topological crystalline insulator phase. Through magnetotransport experiments under extreme conditions—magnetic fields up to 36 T and temperatures down to 300 mK—the team uncovered a rich spectrum of quantum phenomena, including weak antilocalization, universal conductance fluctuations, and the quantum Hall effect.
Combining experimental data with detailed k·p band-structure modeling, the researchers quantitatively mapped how strain, valley alignment, and exchange interaction with Eu spins govern the electronic behavior in these heterostructures. Notably, they constructed a topological phase diagram that reveals the critical role of quantum well thickness and composition, and proposed architectures capable of achieving quantized Hall resistance without the need for external magnetic fields.
The work also addresses a major challenge in topological physics: resistance quantization accuracy in the presence of localized states. Due to their proximity to a ferroelectric instability, IV–VI monochalcogenides exhibit exceptionally high dielectric constants that suppress the formation of detrimental localized spins. This enhances topological protection lengths beyond those of conventional quantum spin Hall systems. Beyond fundamental insight, these findings establish IV–VI quantum wells as promising platforms for the quantum devices, realization of the non-Abelian quasiparticles, and high-performance optoelectronics free of critical elements like gallium or indium.
[1] A. Kazakov, V. V. Volobuev, Ch. W. Cho, B. A. Piot, Z. Adamus, T. Wojciechowski, T. Wojtowicz, G. Springholz, T. Dietl, Topological phase diagram and quantum magnetotransport effects in (Pb,Sn)Se quantum wells with magnetic barriers (Pb,Eu)Se, Phys. Rev. B 111, 245419(2025)
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)]. MagTop’s researchers demonstrated that the effect may come from chemical substitution of heavy cations by lighter ones, rather than from the effect of time-reversal symmetry breaking. At the same time, spin-momentum locking, relevant for spin current generation, remains present on the both sides of the topological phase transition.
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Deposition of a transition metal on the surface of a topological crystalline insulator (TCI) n-type Pb1-xSnxSe opens a gap in the surface Dirac cones (ARPES, right panel), but helical spin texture is preserved (after ([1]).
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 Pb1-xSnxSe 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 Pb1-xSnxSe (111) Epilayers probed by Photoelectron Spectroscopy, Appl. Surf. Sci. 610, 155434 (2023).
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) Pb1-xSnxSe hosting TCI states [P. Sessi et al., Science 354, 1269 (2016)]. New results indicate that these states undergo hybridisation splitting by coupling to neighbouring steps and account for Andreev-like point-contact spectra observed in a number of topological systems, including TCI, the insight corroborated by STS data showing a gap when metal overlayers shift the Fermi energy to those states.
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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 Pb1-xSnxSe (0 ≤ x ≤ 0.4), Pb1-xSnxTe (0≤ x ≤ 1) or a ferromagnetic TCI Pb1-x-ySnxMnyTe (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.
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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 lφ(T) in uncovered epilayers do not saturate down to 1.5 K (black and red), while in Se covered epilayers lφ 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 Pb1-xSnxSe 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 lφ, 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 Pb1-xSnxSe, Phys. Rev. B 103, 245307 (2021).
Scanning tunneling microscopy and spectroscopy (STM/STS) studies of surface electronic states in magnetic field applied normal to (001) surface of topological crystalline insulator Pb1-xSnxSe revealed a shift and a spectral imbalance of the position of centers of Landau orbits while crossing surface atomic step. Step of one monolayer height acts as topological domain wall breaking translational symmetry and evidencing a distinguished behavior of massive and massless Dirac fermions residing at zero index Landau levels, also identifying the relation of the effect to chiral symmetry breaking for massive Dirac fermions.
High quality single-crystals of topological crystalline insulator (TCI) Pb1-xSnxSe (x = 0.33) grown in IF PAN by original self-selecting vapor growth method were used at University of Würzburg for scanning tunneling microscopy and spectroscopy (STM/STS) studies of local electronic structure of topological states at (001) surface with atomic steps, subject to strong magnetic field. The effect of Landau quantization was studied at various surface locations: at atomically flat terraces or at atomic steps of the height equal to one or two monolayers (see Figure). Atomic steps at (001) surface of Pb1-xSnxSe single-crystal constitute topological defect breaking translational symmetry and acting as a domain wall changing by π the phase of wave function of Dirac electrons [see P. Sessi et al., Science 354, 1269 (2016) and Ref. 1].
High quality of (001) crystal facets cleaved under ultra-high vacuum warranted rich experimental spectra of magnetic field dependence of local density of states. They were explained as composed of two contributions: due to two electron valleys in surface Brillouin zone hosting massless Dirac electrons and two other valleys hosting massive Dirac electrons. Finite mass and small gap in the energy spectrum of the latter stem from crystal deformation (shift of cation and anion sublattices along surface [11] direction) known to break one out of two (110) mirror-plane symmetries protecting topological TCI states (Ref. 2).
The key observation concerns energy levels with zero Landau index (exhibiting no dependence on magnetic field). It was observed experimentally that for electrons crossing atomic step the trajectory of the centers of cyclotron orbits qualitatively differs for massless Dirac fermions (atomic steps have no effect) and massive Dirac electrons with effective mass of opposite signs corresponding to upper and lower Dirac cone dispersion. Here one observes a shift and spectral imbalance of the position of centers of Landau orbits upon crossing one monolayer step. The observation is explained by theoretical calculations of energy and cyclotron orbits position spectrum of Landau quantized TCI states at the surface with atomic step and under crystal deformation. The model developed shows how chiral symmetry of topological Dirac electrons can be verified experimentally in solid-state experiment (Ref. 2,3).
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| Fig. A, B Topographic (STM) view of (001) surface of Pb1-xSnxSe (x=0.33) single-crystal cleaved under ultra-high vacuum with atomically flat regions separated by atomic steps of the height equal one (0.3 nm) or two (0.6 nm) monolayers. Tunneling spectroscopy (STS) measurements of local density of electron states in magnetic field of 12 T at various sites at the surface (Fig. C, D). Change of the position of cyclotron orbits while crossing the step of one monolayer height (breaking lattice translational symmetry – topologically nontrivial) and the lack of changes for atomic step of two monolayer height (one lattice parameter). Fig. E, F present results of theoretical analysis of crossing one monolayer step by massive and massless Dirac electrons. |
[1] A. Odobesko, J. Jung, A. Szczerbakow, J. Korczak, T. Story, M. Bode, Reversible doping and fine-tuning of the Dirac point position in the topological crystalline insulator Pb1-xSnxSe via sputtering and annealing process, Nanoscale Advances 7, 1885 (2025).
[2] G. Wagner, T. Neupert, R. Thomale, A. Szczerbakow, J. Korczak, T. Story, M. Bode, A. Odobesko, Probing chiral symmetry with a topological domain wall sensor, Newton 1, 10009 (2025).
[3] B. Weber, Chiral symmetry breaking resolved at the atomic scale, Newton 1, 100027 (2025).